# Day Ahead Electric Load Forecast: A Comprehensive LSTM-EMD Methodology and Several Diverse Case Studies

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## Abstract

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## 1. Introduction

- Methodology: Data pre-processing, model training and evaluation, and operational forecasting
- Case Studies: Several datasets are studied via the methodology including buildings, an electric vehicle charging station, and transmission networks
- Results: The intermediate and final results are evaluated and contextualized
- Conclusions: A final summary and evaluation of the methodology are discussed

## 2. Methodology

#### 2.1. Error Metrics

#### 2.2. Data Pre-Processing

#### 2.3. Feature Engineering

#### Empirical Mode Decomposition

#### 2.4. Long Short-Term Memory Model

#### 2.5. Hyperparameter Tuning

#### 2.6. Computational Burden Estimation

## 3. Case Studies

## 4. Results

#### 4.1. Data Pre-Processing

#### 4.2. Forecast

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A simplified process diagram of the long short-term memory (LSTM) methodology begins with the input cumulative raw data and ends at the output of predicted load values and error metrics. For a new dataset, all blocks are included and dashed lines are prioritized over solid ones, such that naive persistence (NP) lag and the autocorrelation function (ACF) are only established once. The dashed lines and blocks are omitted after data have been pre-processed and the model has been hyperparameter optimized, such as during an operational forecast.

**Figure 2.**Example [52] of EMD on a synthetic signal (

**a**), which was constructed by summing a sinusoid and triangle signal. Quartic splines are calculated to form the dotted-line envelope in (

**b**). Then first recursive EMD sifting process produces the first IMF in (

**c**), and then afterwards a second in (

**d**). Remaining is the residual in (

**e**). In this example the residual is exactly zero so the decomposition is perfect.

**Figure 3.**The feature sequence (length S) is input to the LSTM cell chronologically, up to the most recent value at $t=0$, and can be depicted “unrolled” (left) with the same cell multiple times, or “rolled up” showing one cell and the recurrent loop. In either case there is only one set of $\mathbf{W}$-weights (${\mathbf{W}}_{\mathbf{xi}}$, ${\mathbf{W}}_{\mathbf{hi}}$, etc) and $\mathbf{b}$-biases (${\mathbf{b}}_{\mathbf{i}}$, ${\mathbf{b}}_{\mathbf{f}}$, etc). Between time steps, the LSTM cell passes $\mathbf{c}$ and $\mathbf{h}$ to itself in the next time step.

**Figure 4.**The LSTM cell improves upon the basic recurrent neural network with a series of gates to selectively remember and forget information passing through. FC stands for fully connected layer, which is internal to the cell, not the layers in Figure 3.

**Figure 5.**In models with multiple hidden LSTM layers, the LSTM cell is connected to a second LSTM cell, and finally a ANN output layer resulting in a single predicted target at $t+24$ h and features as shown. Multiple features are input to the same first hidden layer. The first LSTM layer has a set of weights ${\mathbf{W}}_{\mathbf{1}}$ and ${\mathbf{b}}_{\mathbf{1}}$, whereas the second LSTM layer has different weights, ${\mathbf{W}}_{\mathbf{2}}$ and ${\mathbf{b}}_{\mathbf{2}}$. The LSTM cell output, $\mathbf{y}$ = $\mathbf{h}$ has the length U. The feature vectors and LSTM cells are tilted 90${}^{\circ}$ clockwise for compactness.

**Figure 6.**Hotel 1 load cleaned of outliers and resampled (for viewing) with a daily average, a strong seasonality and slight decreasing trend can be seen.

**Figure 7.**Hotel 1 data are almost normally distributed but with some leftward skew. The Quantile-Quantile or Q-Q plot (right) shows which measurement quantile matches or deviates from the theoretical quantile. In this case, the Q-Q plot shows deviation from normality in the left and right tails, and also in the second-from-left quartile.

**Figure 8.**Z-score labels statistical outliers, for instance (1) is more than three standard deviations from the mean of all measurements from 1:00–1:45 on Sundays. Then k-means clustering labels geometrically close points, such as (2). The two outlier measurements are replaced with the corresponding values in Replacement Data, which come from 7-day naive persistence according to Table 2. Only the two data points are replaced (the Replacement Data curve is shown for reference).

**Figure 9.**EMD performed on the Hotel 1 load which produced 11 IMFs. This image should be viewed in color for convenience.

**Figure 10.**LSTM-EMD forecast model is qualitatively shown to capture some of the non-linearity and high variance, in this case during midday for the Hotel 1 data. The high midday variance in midday measurements and therefore forecast errors is likely due to the hotel operations which are disaggregated (large cooling compressors and fans) and time-ambivalent occupant behavior (compared to morning and evening which are likely more fixed by staff schedules).

Sector | Papers (Single Site) | Papers (Multiple Sites) |
---|---|---|

Residential | [10,11,12,13,14,15] | [16,17,18,19,20] |

Commercial | [10,21,22] | [9,16] |

Industrial | [10,23,24,25] | [16] |

All Three | [10] | [16] |

Site | Load | Koppen | Length | Interval | Peak | Autocorr. | ADF |
---|---|---|---|---|---|---|---|

Sector ^{1} | Climate | [y] | [min] | [MW] | 1/7 day | Statistic | |

Residence ^{2} | Res. | BSk | 16.4 | 60 | 0.007 | 0.70/0.63 | −17.1 |

Hotel 1 | Com. | Af | 3.2 | 15 | 1.76 | 0.95/0.92 | −4.9 |

Hotel 2 | Com. | BSk | 2.0 | 15 | 0.45 | 0.87/0.80 | −5.5 |

Manufacturing Plant | Ind. | Dfa | 2.9 | 15 | 13.0 | 0.45/0.93 | −20.1 |

EV Charging Station ^{3} | Tra. | Cfa | 2.7 | 10 | 0.16 | 0.70/0.84 | −17.4 |

Distribution Network | Sys. | BSk | 13.8 | 60 | 1.9 | 0.94/0.86 | −10.5 |

Transmission Network ^{4} | Sys. | Many | 10.0 | 60 | 59,700 | 0.78/0.89 | −17.7 |

^{1}Residential, Commercial, Industrial, Transport, System.

^{2}NREL Habitat for Humanity Zero Energy Home, USA.

^{3}Caltech Adaptive Charging Network, USA.

^{4}TERNA, Italy.

Case | Site | LSTM | NP | SARIMA | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Hyperparameters | Weights | Test Error | Test Error | Test Error | |||||||

IMFs | Units | Dropout | Layers | [$\times {10}^{6}$] | [RMSE] | [RMSE] | [SS] | [RMSE] | [SS] | ||

1a | Residence | – | 1024 | 0.1 | 3 | 4.215 | 0.71 kW | 0.73 kW | 2.7% | 0.70 kW | −1.4% |

1b | 1,2,3 | 256 | 0 | 3 | 0.280 | 0.63 kW | 14% | 10% | |||

2a | Hotel 1 | – | 256 | 0 | 4 | 0.793 | 62.41 kW | 73.05 kW | 15% | 56.5 kW | −11% |

2b | 3,4,5 | 256 | 0 | 3 | 0.271 | 60.05 kW | 18% | −6.3% | |||

3a | Hotel 2 | – | 128 | 0 | 3 | 0.068 | 25.27 kW | 33.90 kW | 25% | 24.4 kW | −3.6% |

3b | 3,4,5 | 512 | 0 | 4 | 3.165 | 24.34 kW | 28% | 0.2% | |||

4a | Manufacturing | – | 96 | 0 | 4 | 0.113 | 598.7 kW | 595.1 kW | −0.6% | 1697 kW | 65% |

4b | Plant | 3,4,5 | 96 | 0 | 4 | 0.114 | 451.1 kW | 24% | 73% | ||

5a | Distribution | – | 128 | 0.1 | 4 | 0.200 | 51.01 MW | 58.18 MW | 12% | 58.1 MW | 12% |

5b | Network | 3,4,5 | 96 | 0.1 | 3 | 0.040 | 39.40 MW | 32% | 32% | ||

6a | Transmission | – | 512 | 0.1 | 4 | 3.159 | 1952 MW | 3594 MW | 46% | 4236 MW | 54% |

6b | Network | 3,4,5 | 512 | 0.1 | 4 | 3.165 | 1580 MW | 56% | 63% | ||

7a | EV Charging | – | 96 | 0 | 4 | 0.0039 | 11.23 kW | 24.27 kW | 54% | 19.6 kW | 43% |

7b | Station | 3,4,5,6 | 512 | 0.1 | 3 | 1.067 | 8.93 kW | 63% | 54% |

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**MDPI and ACS Style**

Wood, M.; Ogliari, E.; Nespoli, A.; Simpkins, T.; Leva, S.
Day Ahead Electric Load Forecast: A Comprehensive LSTM-EMD Methodology and Several Diverse Case Studies. *Forecasting* **2023**, *5*, 297-314.
https://doi.org/10.3390/forecast5010016

**AMA Style**

Wood M, Ogliari E, Nespoli A, Simpkins T, Leva S.
Day Ahead Electric Load Forecast: A Comprehensive LSTM-EMD Methodology and Several Diverse Case Studies. *Forecasting*. 2023; 5(1):297-314.
https://doi.org/10.3390/forecast5010016

**Chicago/Turabian Style**

Wood, Michael, Emanuele Ogliari, Alfredo Nespoli, Travis Simpkins, and Sonia Leva.
2023. "Day Ahead Electric Load Forecast: A Comprehensive LSTM-EMD Methodology and Several Diverse Case Studies" *Forecasting* 5, no. 1: 297-314.
https://doi.org/10.3390/forecast5010016