# Probabilistic Load Forecasting for Building Energy Models

^{*}

^{†}

## 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 |

## References

- Marinakis, V.; Doukas, H. An advanced IoT-based system for intelligent energy management in buildings. Sensors
**2018**, 18, 610. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jia, M.; Komeily, A.; Wang, Y.; Srinivasan, R.S. Adopting Internet of Things for the development of smart buildings: A review of enabling technologies and applications. Autom. Constr.
**2019**, 101, 111–126. [Google Scholar] [CrossRef] - Lu, X.; O’Neill, Z.; Li, Y.; Niu, F. A novel simulation-based framework for sensor error impact analysis in smart building systems: A case study for a demand-controlled ventilation system. Appl. Energy
**2020**, 263, 114638. [Google Scholar] [CrossRef] - 2019 Global Status Report for Buildings and Construction: Towards a Zero Emissions, Efficient and Resilient Buildings and Construction Sector. Available online: https://wedocs.unep.org/bitstream/handle/20.500.11822/30950/2019GSR.pdf?sequence=1&isAllowed=y (accessed on 15 November 2020).
- Khan, Z.A.; Hussain, T.; Ullah, A.; Rho, S.; Lee, M.; Baik, S.W. Towards Efficient Electricity Forecasting in Residential and Commercial Buildings: A Novel Hybrid CNN with a LSTM-AE based Framework. Sensors
**2020**, 20, 1399. [Google Scholar] [CrossRef] [PubMed][Green Version] - El Jaouhari, S.; Jose Palacios-Garcia, E.; Anvari-Moghaddam, A.; Bouabdallah, A. Integrated Management of Energy, Wellbeing and Health in the Next Generation of Smart Homes. Sensors
**2019**, 19, 481. [Google Scholar] [CrossRef][Green Version] - Lee, S.; Choi, D.H. Energy Management of Smart Home with Home Appliances, Energy Storage System and Electric Vehicle: A Hierarchical Deep Reinforcement Learning Approach. Sensors
**2020**, 20, 2157. [Google Scholar] [CrossRef][Green Version] - Kerk, S.G.; Hassan, N.U.; Yuen, C. Smart Distribution Boards (Smart DB), Non-Intrusive Load Monitoring (NILM) for Load Device Appliance Signature Identification and Smart Sockets for Grid Demand Management. Sensors
**2020**, 20, 2900. [Google Scholar] [CrossRef] - Lee, S.; Choi, D.H. Reinforcement learning-based energy management of smart home with rooftop solar photovoltaic system, energy storage system, and home appliances. Sensors
**2019**, 19, 3937. [Google Scholar] [CrossRef][Green Version] - Foucquier, A.; Robert, S.; Suard, F.; Stéphan, L.; Jay, A. State of the art in building modelling and energy performances prediction: A review. Renew. Sustain. Energy Rev.
**2013**, 23, 272–288. [Google Scholar] [CrossRef][Green Version] - Amasyali, K.; El-Gohary, N.M. A review of data-driven building energy consumption prediction studies. Renew. Sustain. Energy Rev.
**2018**, 81, 1192–1205. [Google Scholar] [CrossRef] - Bourdeau, M.; Zhai, X.; Nefzaoui, E.; Guo, X.; Chatellier, P. Modeling and forecasting building energy consumption: A review of data-driven techniques. Sustain. Cities Soc.
**2019**, 48, 101533. [Google Scholar] [CrossRef] - Sun, Y.; Haghighat, F.; Fung, B.C. A Review of the-State-of-the-Art in Data-driven Approaches for Building Energy Prediction. Energy Build.
**2020**, 221, 110022. [Google Scholar] [CrossRef] - Chou, J.S.; Ngo, N.T. Time series analytics using sliding window metaheuristic optimization-based machine learning system for identifying building energy consumption patterns. Appl. Energy
**2016**, 177, 751–770. [Google Scholar] [CrossRef] - Nepal, B.; Yamaha, M.; Yokoe, A.; Yamaji, T. Electricity load forecasting using clustering and ARIMA model for energy management in buildings. Jpn. Archit. Rev.
**2020**, 3, 62–76. [Google Scholar] [CrossRef][Green Version] - Moradzadeh, A.; Mansour-Saatloo, A.; Mohammadi-Ivatloo, B.; Anvari-Moghaddam, A. Performance Evaluation of Two Machine Learning Techniques in Heating and Cooling Loads Forecasting of Residential Buildings. Appl. Sci.
**2020**, 10, 3829. [Google Scholar] [CrossRef] - Khoshrou, A.; Pauwels, E.J. Short-term scenario-based probabilistic load forecasting: A data-driven approach. Appl. Energy
**2019**, 238, 1258–1268. [Google Scholar] [CrossRef][Green Version] - Runge, J.; Zmeureanu, R. Forecasting energy use in buildings using artificial neural networks: A review. Energies
**2019**, 12, 3254. [Google Scholar] [CrossRef][Green Version] - Cox, S.J.; Kim, D.; Cho, H.; Mago, P. Real time optimal control of district cooling system with thermal energy storage using neural networks. Appl. Energy
**2019**, 238, 466–480. [Google Scholar] [CrossRef] - Kim, J.H.; Seong, N.C.; Choi, W. Forecasting the Energy Consumption of an Actual Air Handling Unit and Absorption Chiller Using ANN Models. Energies
**2020**, 13, 4361. [Google Scholar] [CrossRef] - Sadeghian Broujeny, R.; Madani, K.; Chebira, A.; Amarger, V.; Hurtard, L. Data-driven living spaces’ heating dynamics modeling in smart buildings using machine learning-based identification. Sensors
**2020**, 20, 1071. [Google Scholar] [CrossRef][Green Version] - Kwak, Y.; Huh, J.H. Development of a method of real-time building energy simulation for efficient predictive control. Energy Convers. Manag.
**2016**, 113, 220–229. [Google Scholar] [CrossRef] - Kwak, Y.; Huh, J.H.; Jang, C. Development of a model predictive control framework through real-time building energy management system data. Appl. Energy
**2015**, 155, 1–13. [Google Scholar] [CrossRef] - Kampelis, N.; Papayiannis, G.I.; Kolokotsa, D.; Galanis, G.N.; Isidori, D.; Cristalli, C.; Yannacopoulos, A.N. An Integrated Energy Simulation Model for Buildings. Energies
**2020**, 13, 1170. [Google Scholar] [CrossRef][Green Version] - Ghosh, S.; Reece, S.; Rogers, A.; Roberts, S.; Malibari, A.; Jennings, N.R. Modeling the thermal dynamics of buildings: A latent-force-model-based approach. ACM Trans. Intell. Syst. Technol.
**2015**, 6, 1–27. [Google Scholar] [CrossRef] - Gray, F.M.; Schmidt, M. A hybrid approach to thermal building modelling using a combination of Gaussian processes and grey-box models. Energy Build.
**2018**, 165, 56–63. [Google Scholar] [CrossRef] - Huang, H.; Chen, L.; Hu, E. A neural network-based multi-zone modelling approach for predictive control system design in commercial buildings. Energy Build.
**2015**, 97, 86–97. [Google Scholar] [CrossRef] - Luo, J.; Hong, T.; Fang, S.C. Benchmarking robustness of load forecasting models under data integrity attacks. Int. J. Forecast.
**2018**, 34, 89–104. [Google Scholar] [CrossRef] - Zhang, Y.; Lin, F.; Wang, K. Robustness of Short-Term Wind Power Forecasting Against False Data Injection Attacks. Energies
**2020**, 13, 3780. [Google Scholar] [CrossRef] - Henze, G. Model predictive control for buildings: A quantum leap? J. Build. Perform. Simul.
**2013**. [Google Scholar] [CrossRef][Green Version] - Petersen, S.; Bundgaard, K.W. The effect of weather forecast uncertainty on a predictive control concept for building systems operation. Appl. Energy
**2014**, 116, 311–321. [Google Scholar] [CrossRef] - Sandels, C.; Widén, J.; Nordström, L.; Andersson, E. Day-ahead predictions of electricity consumption in a Swedish office building from weather, occupancy, and temporal data. Energy Build.
**2015**, 108, 279–290. [Google Scholar] [CrossRef] - Thieblemont, H.; Haghighat, F.; Ooka, R.; Moreau, A. Predictive control strategies based on weather forecast in buildings with energy storage system: A review of the state-of-the art. Energy Build.
**2017**, 153, 485–500. [Google Scholar] [CrossRef][Green Version] - Zhao, J.; Duan, Y.; Liu, X. Uncertainty analysis of weather forecast data for cooling load forecasting based on the Monte Carlo method. Energies
**2018**, 11, 1900. [Google Scholar] [CrossRef][Green Version] - Agüera-Pérez, A.; Palomares-Salas, J.C.; González de la Rosa, J.J.; Florencias-Oliveros, O. Weather forecasts for microgrid energy management: Review, discussion and recommendations. Appl. Energy
**2018**, 228, 265–278. [Google Scholar] [CrossRef] - Wang, Z.; Hong, T.; Piette, M.A. Building thermal load prediction through shallow machine learning and deep learning. Appl. Energy
**2020**, 263, 114683. [Google Scholar] [CrossRef][Green Version] - Henze, G.P.; Kalz, D.E.; Felsmann, C.; Knabe, G. Impact of forecasting accuracy on predictive optimal control of active and passive building thermal storage inventory. HVAC R Res.
**2004**, 10, 153–178. [Google Scholar] [CrossRef] - Oldewurtel, F.; Parisio, A.; Jones, C.N.; Gyalistras, D.; Gwerder, M.; Stauch, V.; Lehmann, B.; Morari, M. Use of model predictive control and weather forecasts for energy efficient building climate control. Energy Build.
**2012**, 45, 15–27. [Google Scholar] [CrossRef][Green Version] - Hong, T.; Fan, S. Probabilistic electric load forecasting: A tutorial review. Int. J. Forecast.
**2016**, 32, 914–938. [Google Scholar] [CrossRef] - Hong, T.; Pinson, P.; Fan, S.; Zareipour, H.; Troccoli, A.; Hyndman, R.J. Probabilistic energy forecasting: Global energy forecasting competition 2014 and beyond. Int. J. Forecast.
**2016**, 32, 896–913. [Google Scholar] [CrossRef][Green Version] - Gerossier, A.; Girard, R.; Kariniotakis, G.; Michiorri, A. Probabilistic day-ahead forecasting of household electricity demand. CIRED-Open Access Proc. J.
**2017**, 2017, 2500–2504. [Google Scholar] [CrossRef][Green Version] - Van der Meer, D.W.; Shepero, M.; Svensson, A.; Widén, J.; Munkhammar, J. Probabilistic forecasting of electricity consumption, photovoltaic power generation and net demand of an individual building using Gaussian Processes. Appl. Energy
**2018**, 213, 195–207. [Google Scholar] [CrossRef] - Rouleau, J.; Ramallo-González, A.P.; Gosselin, L.; Blanchet, P.; Natarajan, S. A unified probabilistic model for predicting occupancy, domestic hot water use and electricity use in residential buildings. Energy Build.
**2019**, 202, 109375. [Google Scholar] [CrossRef] - El-Baz, W.; Tzscheutschler, P.; Wagner, U. Day-ahead probabilistic PV generation forecast for buildings energy management systems. Sol. Energy
**2018**, 171, 478–490. [Google Scholar] [CrossRef] - Zhao, X.; Liu, J.; Yu, D.; Chang, J. One-day-ahead probabilistic wind speed forecast based on optimized numerical weather prediction data. Energy Convers. Manag.
**2018**, 164, 560–569. [Google Scholar] [CrossRef] - Huber, J.; Dann, D.; Weinhardt, C. Probabilistic forecasts of time and energy flexibility in battery electric vehicle charging. Appl. Energy
**2020**, 262, 114525. [Google Scholar] [CrossRef] - Yan, X.; Abbes, D.; Francois, B. Uncertainty analysis for day ahead power reserve quantification in an urban microgrid including PV generators. Renew. Energy
**2017**, 106, 288–297. [Google Scholar] [CrossRef] - Xu, L.; Wang, S.; Tang, R. Probabilistic load forecasting for buildings considering weather forecasting uncertainty and uncertain peak load. Appl. Energy
**2019**, 237, 180–195. [Google Scholar] [CrossRef] - Dahl, M.; Brun, A.; Andresen, G.B. Using ensemble weather predictions in district heating operation and load forecasting. Appl. Energy
**2017**, 193, 455–465. [Google Scholar] [CrossRef] - Fan, C.; Liao, Y.; Zhou, G.; Zhou, X.; Ding, Y. Improving cooling load prediction reliability for HVAC system using Monte-Carlo simulation to deal with uncertainties in input variables. Energy Build.
**2020**, 226, 110372. [Google Scholar] [CrossRef] - Luna, A.C.; Meng, L.; Diaz, N.L.; Graells, M.; Vasquez, J.C.; Guerrero, J.M. Online energy management systems for microgrids: Experimental validation and assessment framework. IEEE Trans. Power Electron.
**2017**, 33, 2201–2215. [Google Scholar] [CrossRef] - Lamoudi, M.Y.; Béguery, P.; Alamir, M. Use of simulation for the validation of a model predictive control strategy for energy management in buildings. In Proceedings of the Building Simulation 2011, 11th international IBPSA conference, Sydney, Australia, 14–16 November 2011; pp. 2703–2710. [Google Scholar]
- Lazos, D.; Sproul, A.B.; Kay, M. Optimisation of energy management in commercial buildings with weather forecasting inputs: A review. Renew. Sustain. Energy Rev.
**2014**, 39, 587–603. [Google Scholar] [CrossRef] - Crawley, D.B.; Lawrie, L.K.; Winkelmann, F.C.; Buhl, W.F.; Huang, Y.J.; Pedersen, C.O.; Strand, R.K.; Liesen, R.J.; Fisher, D.E.; Witte, M.J.; et al. EnergyPlus: Creating a new-generation building energy simulation program. Energy Build.
**2001**, 33, 319–331. [Google Scholar] [CrossRef] - Crawley, D.B.; Lawrie, L.K.; Pedersen, C.O.; Winkelmann, F.C.; Witte, M.J.; Strand, R.K.; Liesen, R.J.; Buhl, W.F.; Huang, Y.J.; Henninger, R.H.; et al. EnergyPlus: An update. Proc. Simbuild
**2004**, 1, 1. [Google Scholar] - DOE, E. Auxiliary Programs: EnergyPlus
^{TM}Version 8.9.0 Documentation; US Department of Energy: Washington, DC, USA, 2018. [Google Scholar] - Romero-Quete, D.; Cañizares, C.A. An affine arithmetic-based energy management system for isolated microgrids. IEEE Trans. Smart Grid
**2018**, 10, 2989–2998. [Google Scholar] [CrossRef] - González, V.G.; Colmenares, L.Á.; Fidalgo, J.F.L.; Ruiz, G.R.; Bandera, C.F. Uncertainy’s Indices Assessment for Calibrated Energy Models. Energies
**2019**, 12, 2096. [Google Scholar] [CrossRef][Green Version] - Rao, B.P. Nonparametric Function Estimation; Academic Press: London, UK, 1983. [Google Scholar]
- Bashtannyk, D.M.; Hyndman, R.J. Bandwidth selection for kernel conditional density estimation. Comput. Stat. Data Anal.
**2001**, 36, 279–298. [Google Scholar] [CrossRef][Green Version] - Scott, D.W. Multivariate Density Estimation: Theory, Practice, and Visualization; John Wiley & Sons: New York, NY, USA, 2015. [Google Scholar]
- Shrivastava, N.A.; Panigrahi, B.K. Point and prediction interval estimation for electricity markets with machine learning techniques and wavelet transforms. Neurocomputing
**2013**, 118, 301–310. [Google Scholar] [CrossRef] - SABINA SmArt BI-directional multi eNergy gAteway. Available online: https://sabina-project.eu/ (accessed on 20 April 2020).
- Guglielmetti, R.; Macumber, D.; Long, N. OpenStudio: An Open Source Integrated Analysis Platform; Technical Report; National Renewable Energy Laboratory (NREL): Golden, CO, USA, 2011. [Google Scholar]
- Ruiz, G.R.; Bandera, C.F.; Temes, T.G.A.; Gutierrez, A.S.O. Genetic algorithm for building envelope calibration. Appl. Energy
**2016**, 168, 691–705. [Google Scholar] [CrossRef] - Ruiz, G.R.; Bandera, C.F. Analysis of uncertainty indices used for building envelope calibration. Appl. Energy
**2017**, 185, 82–94. [Google Scholar] [CrossRef] - Fernández Bandera, C.; Ramos Ruiz, G. Towards a new generation of building envelope calibration. Energies
**2017**, 10, 2102. [Google Scholar] [CrossRef][Green Version] - Gutiérrez González, V.; Ramos Ruiz, G.; Fernández Bandera, C. Empirical and Comparative Validation for a Building Energy Model Calibration Methodologya. Sensors
**2020**, 20, 5003. [Google Scholar] [CrossRef] [PubMed] - Meteoblue. Available online: https://meteoblue.com/ (accessed on 20 April 2020).
- Segarra, E.L.; Ruiz, G.R.; González, V.G.; Peppas, A.; Bandera, C.F. Impact Assessment for Building Energy Models Using Observed vs. Third-Party Weather Data Sets. Sustainability
**2020**, 12, 6788. [Google Scholar] [CrossRef]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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