# Day-Ahead Electric Load Forecast for a Ghanaian Health Facility Using Different Algorithms

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## Abstract

**:**

## 1. Introduction

- SARIMA algorithm
- ILR method
- Neural networks with LSTM neurons
- Custom statistical approach formulated throughout this research

## 2. Data sets

#### 2.1. Load Data

#### 2.2. Temperature Data

## 3. Forecasting Algorithms

#### 3.1. Incremental Learning Method

#### 3.2. Statistical Forecasting

#### 3.3. Seasonal Autoregressive Integrated Moving Average (SARIMA) Algorithm

#### 3.4. Long Short-Term Memory (LSTM) Model

#### 3.5. Forecasting via Incremental Linear Regression (ILR)

## 4. Results

#### 4.1. Statistical Forecasting

#### 4.2. Seasonal Autoregressive Integrated Moving Average (SARIMA) Algorithm

#### 4.3. Long Short-Term Memory (LSTM) Model

#### 4.4. Forecasting via Incremental Linear Regression (ILR)

#### 4.5. Summary

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MPC | Model predictive control |

SARIMA | Seasonal autoregressive integrated moving average |

LSTM | Long short-term memory |

nRMSE | Normalized root mean square error |

PV | Photovoltaic |

LCOE | Levelized cost of electricity |

ILR | Incremental linear regression |

ARIMA | Autoregressive integrated moving average |

LOESS | Locally estimated scatterplot smoothing |

LED | Light-emitting diode |

SD | Standard deviation |

PVGIS | Photovoltaic geographical information system |

ERA5 | European center for medium-range weather forecasts reanalysis 5th generation |

CDD | Cooling degree day |

ARMA | Autoregressive moving average |

RNN | Recurrent neural network |

BPTT | Backpropagation through time |

ADAM | Adaptive moment estimation |

MSE | Mean squared error |

MAPE | Mean absolute percentage error |

ReLU | Rectified linear unit |

EnerSHelF | Energy-self-sufficiency for health facilities in Ghana |

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**Figure 6.**Error distribution of the forecasts generated with the SARIMA algorithm| SARIMA(1,1,1)(1,1,2)96 model.

**Figure 7.**Error distribution of the forecasts generated with the SARIMA algorithm| SARIMA(3,1,1)(0,1,2)96 model.

**Figure 10.**Moving average of the nRMSE generated by the LSTM model and the statistical algorithm (weekdays).

**Figure 11.**Moving average of the nRMSE generated by the LSTM model and the statistical algorithm (Saturdays).

**Figure 12.**Moving average of the nRMSE generated by the LSTM model and the statistical algorithm (Sundays).

**Table 1.**Quantitative statistical evaluation, divided by years and seasons (wet: April–October|dry: November–March). “SD” stands for standard deviation. Values in kW, except variance.

Year | Period | Min. | Max. | Median | Mean | Q0.05 | Q1 | Q3 | Q0.95 | SD | Var. |
---|---|---|---|---|---|---|---|---|---|---|---|

2014 | Mar.–Dec. | 4.2 | 177.36 | 61.28 | 69.52 | 42.88 | 51.08 | 81.48 | 121.96 | 24.99 | 624.51 |

wet season | 5.68 | 177.36 | 60.68 | 68.90 | 42.40 | 50.32 | 80.88 | 121.71 | 24.09 | 629.60 | |

dry season | 4.2 | 175 | 63.04 | 71.62 | 45.51 | 53.52 | 83.17 | 123.4 | 24.52 | 601.33 | |

2015 | Jan.–Dec. | 4.4 | 173 | 59.75 | 66.57 | 42.44 | 50.25 | 77.77 | 111.63 | 22.10 | 488.58 |

wet season | 4.44 | 154.5 | 58.86 | 65.78 | 42.38 | 50.09 | 76.19 | 109.5 | 21.29 | 453.13 | |

dry season | 4.4 | 173 | 61.06 | 67.69 | 42.59 | 50.47 | 79.63 | 115.06 | 23.17 | 536.70 | |

2016 | Jan.–Dec. | 5.68 | 177.75 | 53.49 | 58.87 | 33.41 | 43.72 | 70.25 | 100.81 | 20.78 | 431.75 |

wet season | 5.68 | 155.5 | 53.4 | 59.01 | 35.84 | 43.75 | 70.19 | 99.81 | 20.17 | 406.87 | |

dry season | 6.16 | 177.75 | 53.69 | 58.66 | 30.84 | 43.59 | 70.44 | 101.88 | 21.60 | 466.74 | |

2017 | Jan.–Dec. | 4.0 | 154.88 | 41.19 | 44.31 | 23.56 | 33.15 | 52.38 | 77.63 | 16.67 | 278.00 |

wet season | 4.04 | 121.81 | 40.69 | 43.36 | 22.48 | 32.44 | 51.53 | 75.01 | 16.10 | 259.23 | |

dry season | 4.0 | 154.88 | 41.88 | 45.65 | 25.08 | 34.03 | 53.56 | 81.18 | 17.37 | 301.55 | |

2018 | Jan.–Feb. | 4.32 | 121.16 | 40.92 | 43.49 | 23.78 | 33.76 | 49.69 | 75.76 | 15.78 | 249.04 |

Year | Period | p-Value | z-Value |
---|---|---|---|

2014 | Mar.–Dec. | 0.089 | 1.7 |

2015 | Jan.–Dec. | <<0.05 | −14.13 |

2016 | Jan.–Dec. | <<0.05 | −52.84 |

2017 | Jan.–Dec. | <<0.05 | −17.26 |

2018 | Jan.–Feb. | <<0.05 | 8.35 |

**Table 3.**Statistical results with different time frames, divided into the photovoltaic geographical information system (PVGIS) data set and the European center for medium-range weather forecasts 5th generation (ERA5) data set.

Data Set | Timeframe | Pearson’s r-Value | p-Value |
---|---|---|---|

PVGIS | whole day | 0.54 | <<0.05 |

PVGIS | day-time | 0.2 | <<0.05 |

PVGIS | night-time | 0.49 | <<0.05 |

ERA5 | whole day | 0.5 | <<0.05 |

ERA5 | day-time | 0.27 | <<0.05 |

ERA5 | night-time | 0.28 | <<0.05 |

Data Set | Timeframe | Pearson’s r-Value | p-Value |
---|---|---|---|

PVGIS | whole day | −0.14 | <<0.05 |

ERA5 | whole day | 0.01 | 0.61 |

**Table 5.**Comparison of the normalized root-mean-square error (nRMSE), with different horizon configurations.

Horizon Configuration | Min. nRMSE | Med. nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

4 weeks | 0.023 | 0.065 | 0.068 | 0.2 |

8 weeks | 0.018 | 0.065 | 0.061 | 0.22 |

12 weeks | 0.016 | 0.065 | 0.061 | 0.232 |

16 weeks | 0.018 | 0.065 | 0.062 | 0.234 |

Layer-Type | Amount of Cells | Parameters | Activation Function |
---|---|---|---|

LSTM | 96 | 37,632 | rectified linear unit |

LSTM | 192 | 221,962 | rectified linear unit |

fully connected neural network | 192 | 37,056 | rectified linear unit |

fully connected neural network | 96 | 18,528 | rectified linear unit |

Type | Epochs | Batch Size | Loss Function | Optimizer |
---|---|---|---|---|

initial weekday | 5 | 12 | mean squared error | adaptive moment estimation |

initial saturday | 5 | 12 | mean squared error | adaptive moment estimation |

initial sunday | 5 | 6 | mean squared error | adaptive moment estimation |

continous weekday | 2 | 12 | mean squared error | adaptive moment estimation |

continous saturday | 2 | 12 | mean squared error | adaptive moment estimation |

continous sunday | 2 | 6 | mean squared error | adaptive moment estimation |

Prediction Horizon | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

3 h | 0.003 | 0.047 | 0.056 | 0.41 |

6 h | 0.004 | 0.051 | 0.058 | 0.385 |

9 h | 0.005 | 0.054 | 0.060 | 0.338 |

12 h | 0.009 | 0.056 | 0.062 | 0.302 |

15 h | 0.011 | 0.058 | 0.063 | 0.272 |

18 h | 0.015 | 0.060 | 0.064 | 0.25 |

21 h | 0.018 | 0.061 | 0.064 | 0.234 |

24 h | 0.018 | 0.061 | 0.065 | 0.220 |

**Table 9.**Computational effort for the statistical forecasting method, divided in weekday, Saturday, and Sunday batching, clustered in training and prediction efforts.

Type | Data Batching | Median Computation Time | Overall Computation Time |
---|---|---|---|

training | weekday | 0.067 ms | 131.428 ms |

Saturday | 0.064 ms | 12.229 ms | |

Sunday | 0.014 ms | 2.763 ms | |

prediction | weekday | 0.032 ms | 2.905 s |

Saturday | 0.029 ms | 0.446 s | |

Sunday | 0.029 ms | 0.452 s |

Prediction Horizon | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

3 h | 0 | 0.070 | 0.086 | >1 |

6 h | 0 | 0.075 | 0.09 | >1 |

9 h | 0.002 | 0.081 | 0.094 | >1 |

12 h | 0.005 | 0.087 | 0.098 | >1 |

15 h | 0.021 | 0.091 | 0.102 | >1 |

18 h | 0.028 | 0.095 | 0.105 | >1 |

21 h | 0.029 | 0.097 | 0.107 | >1 |

24 h | 0.032 | 0.099 | 0.109 | >1 |

Prediction Horizon | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

3 h | 0 | 0.066 | 0.081 | >1 |

6 h | 0.002 | 0.071 | 0.085 | >1 |

9 h | 0.002 | 0.076 | 0.088 | >1 |

12 h | 0.003 | 0.080 | 0.091 | >1 |

15 h | 0.018 | 0.084 | 0.094 | >1 |

18 h | 0.026 | 0.086 | 0.096 | >1 |

21 h | 0.029 | 0.088 | 0.098 | >1 |

24 h | 0.032 | 0.09 | 0.099 | >1 |

**Table 12.**Computational effort for both SARIMA configurations, divided in weekday, Saturday, and Sunday batching, clustered in training and prediction efforts.

Configuration | Type | Data Batching | Median Computation Time | Overall Computation Time |
---|---|---|---|---|

SARIMA 1,1,1, 1,1,2 | training | weekday | 17.580 s | 4.787 h |

Saturday | 22.403 s | 1.221 h | ||

Sunday | 17.075 s | 0.931 h | ||

prediction | weekday | 0.488 ms | 46.440 s | |

Saturday | 0.510 ms | 8.546 s | ||

Sunday | 0.490 ms | 10.505 s | ||

SARIMA 3,1,1, 0,1,2 | training | weekday | 20.141 s | 5.484 h |

Saturday | 22.323 s | 1.216 h | ||

Sunday | 17.041 s | 0.928 h | ||

prediction | weekday | 0.460 ms | 45.660 s | |

Saturday | 0.499 ms | 8.678 s | ||

Sunday | 0.481 ms | 8.348 s |

Prediction Horizon | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

3 h | 0.002 | 0.048 | 0.058 | 0.376 |

6 h | 0.006 | 0.053 | 0.06 | 0.287 |

9 h | 0.007 | 0.056 | 0.062 | 0.26 |

12 h | 0.011 | 0.058 | 0.063 | 0.279 |

15 h | 0.018 | 0.059 | 0.064 | 0.281 |

18 h | 0.019 | 0.06 | 0.064 | 0.276 |

21 h | 0.02 | 0.061 | 0.064 | 0.266 |

24 h | 0.02 | 0.061 | 0.064 | 0.254 |

**Table 14.**Computational effort for the LSTM model, divided in weekday, Saturday, and Sunday batching, clustered in training and prediction efforts.

Type | Data Batching | Median Computation Time | Overall Computation Time |
---|---|---|---|

training | weekday | 6.941 s | 22.115 min |

Saturday | 4.783 s | 26.326 min | |

Sunday | 4.784 s | 26.272 min | |

prediction | weekday | 39.987 ms | 61.786 min |

Saturday | 40.106 ms | 25.761 min | |

Sunday | 40.108 ms | 25.696 min |

Prediction Horizon | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

3 h | 0.003 | 0.063 | 0.086 | >1 |

6 h | 0.007 | 0.075 | 0.096 | >1 |

9 h | 0.012 | 0.082 | 0.102 | >1 |

12 h | 0.017 | 0.087 | 0.105 | >1 |

15 h | 0.018 | 0.090 | 0.108 | >1 |

18 h | 0.021 | 0.092 | 0.11 | >1 |

21 h | 0.025 | 0.093 | 0.111 | >1 |

24 h | 0.026 | 0.093 | 0.112 | >1 |

**Table 16.**Computational effort for the ILR method, clustered in initial training, training, and prediction efforts.

Type | Median Computation Time | Overall Computation Time |
---|---|---|

initial training | - | 0.125 ms |

training | 0.126 ms | 12.630 s |

prediction | 21.406 ms | 31.584 min |

Algorithm | Min. nRMSE | Median nRMSE | Mean nRMSE | Max. nRMSE |
---|---|---|---|---|

LSTM model | 0.02 | 0.061 | 0.064 | 0.376 |

statistical algorithm | 0.018 | 0.061 | 0.065 | 0.22 |

SARIMA 1,1,1 1,1,2 | 0.032 | 0.099 | 0.109 | >1 |

SARIMA 3,1,1 0,1,2 | 0.032 | 0.09 | 0.099 | >1 |

ILR algorithm | 0.018 | 0.090 | 0.108 | >1 |

**Table 18.**Descriptive statistics of the moving average nRMSE, generated by the LSTM model and the statistical algorithm (weekdays).

Model | Min. | Max. | Mean | Median |
---|---|---|---|---|

LSTM model | 0.051 | 0.087 | 0.065 | 0.063 |

statistical algorithm | 0.049 | 0.088 | 0.067 | 0.066 |

**Table 19.**Descriptive statistics of the moving average nRMSE, generated by the LSTM model and the statistical algorithm (Saturdays).

Model | Min. | Max. | Mean | Median |
---|---|---|---|---|

LSTM model | 0.060 | 0.078 | 0.067 | 0.066 |

statistical algorithm | 0.052 | 0.079 | 0.061 | 0.059 |

**Table 20.**Descriptive statistics of the moving average nRMSE, generated by the LSTM model and the statistical algorithm (Sundays).

Model | Min. | Max. | Mean | Median |
---|---|---|---|---|

LSTM model | 0.038 | 0.062 | 0.047 | 0.046 |

statistical algorithm | 0.039 | 0.061 | 0.048 | 0.048 |

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**MDPI and ACS Style**

Chaaraoui, S.; Bebber, M.; Meilinger, S.; Rummeny, S.; Schneiders, T.; Sawadogo, W.; Kunstmann, H.
Day-Ahead Electric Load Forecast for a Ghanaian Health Facility Using Different Algorithms. *Energies* **2021**, *14*, 409.
https://doi.org/10.3390/en14020409

**AMA Style**

Chaaraoui S, Bebber M, Meilinger S, Rummeny S, Schneiders T, Sawadogo W, Kunstmann H.
Day-Ahead Electric Load Forecast for a Ghanaian Health Facility Using Different Algorithms. *Energies*. 2021; 14(2):409.
https://doi.org/10.3390/en14020409

**Chicago/Turabian Style**

Chaaraoui, Samer, Matthias Bebber, Stefanie Meilinger, Silvan Rummeny, Thorsten Schneiders, Windmanagda Sawadogo, and Harald Kunstmann.
2021. "Day-Ahead Electric Load Forecast for a Ghanaian Health Facility Using Different Algorithms" *Energies* 14, no. 2: 409.
https://doi.org/10.3390/en14020409