# Short- and Very Short-Term Firm-Level Load Forecasting for Warehouses: A Comparison of Machine Learning and Deep Learning Models

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Data Preprocessing

#### 2.3. Evaluation Metric

## 3. Model Identification

#### 3.1. Machine Learning Models

#### 3.2. Deep Learning Models

#### 3.3. Benchmarks

## 4. Discussion

#### 4.1. Short-Term Load Forecasting

#### 4.2. Very Short-Term Load Forecasting

## 5. Related Work

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Networks |

AMI | Advanced Metering Infrastructure |

ANN | Artificial Neural Network |

ARIMA | Autoregressive Integrated Moving Average |

CV | Co-efficient of Variance |

EPC | Energy Performance Contract |

ESCO | Energy Service Company |

EU | European Union |

GB | Gradient Boosting |

GHG | Greenhouse Gas |

GRU | Gated Recurrent Unit |

HVAC | Heating, Ventilation and Air Conditioning |

LED | Light Emitting Diode |

LSTM | Long Short-Term Memory |

MAE | Mean Absolute Error |

MLR | Multiple Linear Regression |

MAPE | Mean Absolute Percent Error |

MSE | Mean Squared Error |

PV | Solar Photovoltaic |

RF | Random Forest |

RMSE | Root Mean Squared Error |

RNN | Recurrent Neural Networks |

STLF | Short-Term Load Forecasting |

SVM | Support Vector Machines |

SVR | Support Vector Machine Regression |

UN | United Nations |

VSTLF | Very Short-Term Load Forecasting |

XGBoost | Extreme Gradient Boosting |

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**Figure 5.**LSTM architecture (adapted from [73]).

**Figure 6.**GRU architecture (adapted from [73]).

**Figure 7.**Convergence results for the (

**a**) Recurrent Neural Network (RNN)-3-400; (

**b**) RNN-4-200; (

**c**) Long Short-Term Memory (LSTM)-3-200; (

**d**) LSTM-3-300; (

**e**) LSTM-4-400; (

**f**) Gated Recurrent Unit (GRU)-3-100; and (

**g**) GRU-4-300.

**Figure 13.**Hourly load forecasting using (

**a**) the SVR-10-rbf model; (

**b**) the SVR-10-linear model; (

**c**) the Random Forest-9-200 model; (

**d**) the XGBoost-5-100 model; and (

**e**) the XGBoost-7-100 model.

**Figure 14.**Hourly load forecasting using (

**a**) the RNN-3-400 model; (

**b**) the RNN-4-200 model; (

**c**) the LSTM-3-200 model; (

**d**) the LSTM-3-300 model; (

**e**) the LSTM-4-400 model; (

**f**) the GRU-3-100 model; and (

**g**) the GRU-4-300 model.

Quantile Statistics | Descriptive Statistics | ||
---|---|---|---|

Description | Values | Description | Values |

Minimum | 0.00 | Standard deviation | 4.18 |

Maximum | 13.67 | Coefficient of variation | 0.63 |

Median | 7.69 | Mean | 6.68 |

Range | 13.67 | Median Absoluta Deviation | 3.26 |

Interquartile range | 9.02 | Variance | 17.44 |

Technique | Parameter | Levels |
---|---|---|

SVR | Number of C | 0.1, 1, and 10 |

SVR | Type of kernel | Polinomial, RBF, sigmoid, and linear |

Random Forest | Number of max. depth | From 3 to 9, step 2 |

Random Forest | Number of trees | From 50 to 200, step 50 |

XGBoost | Number of max. depth | From 3 to 9, step 2 |

XGBoost | Number of trees | From 50 to 200, step 50 |

Parameter | Levels |
---|---|

Number of nodes | From 100 to 400, step 100 |

Number of layers | From 1 to 4, step 1 |

Model Parameters | |||
---|---|---|---|

Layer Number | Layers | Repetitions of Layer | NUM_UNITS |

1 | LSTM, GRU or RNN | 1, 2, 3 or 4 | 100, 200, 300 or 400 |

2 | Dense (1, activation = adam) | - | - |

Compile Parameters | |||

Loss function | MSE | ||

Optimiser | ADAM | ||

Early stoppin | EarlyStopping (monitor = ’val_loss’, mode = ’auto’, verbose = 1, min_delta = 0.001, patience = 10) | ||

Batch size | 256 | ||

Epochs | 1000 |

Models | RMSE | MAPE (%) | MAE |
---|---|---|---|

ARIMA | 0.1114 | 28.8016 | 0.0615 |

SVR-10-rbf | 0.1001 | 42.8923 | 0.0705 |

SVR-10-linear | 0.1028 | 42.9745 | 0.0610 |

Random Forest-9-200 | 0.0863 | 22.771 | 0.0469 |

XGBoost-5-100 | 0.0844 | 21.659 | 0.0461 |

XGBoost-7-100 | 0.0847 | 21.573 | 0.0453 |

RNN-3-400 | 0.0947 | 28.325 | 0.0592 |

RNN-4-200 | 0.0909 | 29.122 | 0.0552 |

LSTM-3-200 | 0.0912 | 28.805 | 0.0553 |

LSTM-3-300 | 0.0911 | 29.03 | 0.0560 |

LSTM-4-400 | 0.0919 | 28.117 | 0.0564 |

GRU-3-100 | 0.0918 | 28.94 | 0.0558 |

GRU-4-300 | 0.0933 | 28.297 | 0.0585 |

Models | Prediction (h) | RMSE | MAPE (%) | MAE |
---|---|---|---|---|

XGBoost-5-100 | 1 | 0.0844 | 21.659 | 0.0461 |

XGBoost-7-100 | 1 | 0.0847 | 21.573 | 0.0453 |

XGBoost-5-100 | 12 | 0.1835 | 21.580 | 0.1009 |

XGBoost-7-100 | 12 | 0.1717 | 21.749 | 0.0926 |

XGBoost-5-100 | 24 | 0.2342 | 21.603 | 0.1370 |

XGBoost-7-100 | 24 | 0.2149 | 21.639 | 0.1232 |

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**MDPI and ACS Style**

Ribeiro, A.M.N.C.; do Carmo, P.R.X.; Endo, P.T.; Rosati, P.; Lynn, T.
Short- and Very Short-Term Firm-Level Load Forecasting for Warehouses: A Comparison of Machine Learning and Deep Learning Models. *Energies* **2022**, *15*, 750.
https://doi.org/10.3390/en15030750

**AMA Style**

Ribeiro AMNC, do Carmo PRX, Endo PT, Rosati P, Lynn T.
Short- and Very Short-Term Firm-Level Load Forecasting for Warehouses: A Comparison of Machine Learning and Deep Learning Models. *Energies*. 2022; 15(3):750.
https://doi.org/10.3390/en15030750

**Chicago/Turabian Style**

Ribeiro, Andrea Maria N. C., Pedro Rafael X. do Carmo, Patricia Takako Endo, Pierangelo Rosati, and Theo Lynn.
2022. "Short- and Very Short-Term Firm-Level Load Forecasting for Warehouses: A Comparison of Machine Learning and Deep Learning Models" *Energies* 15, no. 3: 750.
https://doi.org/10.3390/en15030750