# Electricity Consumption Prediction in an Electronic System Using Artificial Neural Networks

^{1}

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## Abstract

**:**

## 1. Introduction

- Seasonal models are developed to predict amount of consumed energy based on measured hourly-based consumption data provided for this purpose from a cold storage facility in Serbia;
- Data analysis is performed in order to select the inputs to different network structures;
- Several performance indicators are used to estimate performances of the proposed models. Based on these criteria, the best models are chosen.

## 2. Data and Methods

#### 2.1. Consumption Dataset

#### 2.2. Anomalies in Dataset

#### 2.3. Preparation of Data for Training and Testing

## 3. Choosing an Optimal ANN Structure

#### 3.1. LSTM Structure

_{i}in Figure 5. The cell state serves as long-term shared memory for multiple concurrent LSTM units and is used to store and update general information relevant to multiple units in the chain. Different units can add new or delete old information from the cell state, regardless of their distance from each other. The cell state is modified by applying several different activation functions to the inputs of the unit and the activation from the previous unit, and also according to the previous values that the cell state had. Neuron layers are arranged in a specific structure, which modifies the cell state so that the LSTM is resistant to the problem of vanishing gradients, which makes it very useful for applications where longer sequences need to be analyzed.

- (1)
- The forget gate is formed from a layer of neurons with a sigmoid activation function, so the activations of these neurons can have values between 0 and 1. The activations of the neurons are multiplied by the corresponding data in the array of cell states. If the activation is approximately 0, then the corresponding data from the cell state will be deleted, and if it is approximately 1, then the data will be kept.
- (2)
- The input gate examines whether some new information can be obtained from the current input and then whether this information is important for the state of the cells, i.e., if it should be added or ignored. The input gate consists of one sigmoid layer and one layer, activation function of which is the hyperbolic tangent. The hyperbolic tangent layer generates the information, and the σ layer decides which parts of the information should be passed to the cell state.
- (3)
- The output gate generates the output of the unit as well as the new internal state using the modified cell state. It consists of a σ layer that is applied to the input and the previous internal state and a layer, the activation of which is chosen as needed, generating the output data.

#### 3.2. GRU Structure

#### 3.3. Bidirectional Recurrent Networks

#### 3.4. Network Hyperparameters

- (1)
- Prediction horizon affects the structure of the network by determining the number of inputs. Different values of the horizon can affect the prediction results in several ways, e.g., it is intuitively felt that the prediction results could be better if the length of the input is 168 h (7 days) than e.g., a horizon of 48 h, since in that case the input data are more varied and there is more information in the memory (e.g., how consumption behaves on weekends);
- (2)
- Number of neurons in all hidden layers;
- (3)
- Number of network training iterations;
- (4)
- Batch size—the number of input vectors that are entered into the network at each iteration;
- (5)
- Method of initialization of the weight coefficients—it is also known that the initial values of the coefficients have a great influence on the optimization of the network, and that in most cases it is not convenient to simply set them to zero. Often, these initial values are randomly determined, for which different probability distribution functions can be used. Different functions can give different results, so several of them can be taken as hyperparameters;
- (6)
- Dropout factor—dropout is a technique that is often used in FF structures, but it can also be successfully applied in recurrent ones. During each training phase of the network, the influence of some neurons is completely ignored—a number of randomly selected neurons are excluded from the network during a training phase, so their weights are not updated. This technique is applied to prevent the problem of overfitting [52].

## 4. Results

#### 4.1. Hyperparameter Optimization and Cross-Validation

- (1)
- Prediction horizon can be 24 h, 48 h, 96 h, 168 h and 336 h, i.e., one day, two days, four days, one week and two weeks (five values in total);
- (2)
- The number of neurons in the hidden layers is from the set: 80, 120, 160 or 200 (four in total);
- (3)
- Number of training iterations: 100, 150, 200, 250 and 300 (5 in total);
- (4)
- Batch size: 20 (fixed value);
- (5)
- Probability distribution for initialization: uniform, normal, glorot_uniform, lecun_uniform (four in total);
- (6)
- Dropout factor: 0.2 (fixed value).

- (1)
- Full grid search—examines all possible combinations of parameter values. This type of cross-validation is usually performed when there are fewer hyperparameters or simpler networks. However, as the total number of possible combinations for a given case is 400, this technique is not suitable.
- (2)
- Randomized grid search—a fixed number of random combinations are selected, and the best result among them is then selected and good results are given when a large set of hyperparameters is included. For the given case, a randomized grid search was carried out with 8-fold cross-validation for each network type.

#### 4.2. Performance Indices

_{i}is predicted value, x

_{i}is measured value and n is the number of records in the dataset:

^{2}, while MAPE is related to percentage error (%).

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ANN | Artificial Neural Network |

FF | Feed-forward network |

RNN | Recurrent Neural Network |

LSTM | Long Short-Term Memory |

GRU | Gated Recurrent Unit |

LSTMB | Long Short-Term Memory, Bidirectional |

GRUB | Gated Recurrent Unit, Bidirectional |

MAE | Mean Absolute Error |

MSE | Mean Square Error |

RMSE | Root Mean Square Error |

MAPE | Mean Absolute Percentage Error |

STLF | Short-Term Electrical Load Forecasting |

TSO | Transmission System Operator |

ENTSO-E | European Network of Transmission System Operators for Electricity |

ARMA | Autoregressive Moving Average Model |

ARIMA | Autoregressive Integrated Moving Average Model |

k-NN | K-Nearest Neighbor Algorithm |

SVM | Support Vector Machine |

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**Figure 1.**(

**a**) A part of the electricity consumption raw dataset, (

**b**) consumption heatmap for one month.

**Figure 8.**Predictions for one week in April 2019 by GRU with a horizon of 168 h (red line is for predicted values, blue line is for measured values).

**Figure 9.**Predictions for one day in: (

**a**) winter by LSTMB-336 h; (

**b**) spring by GRU-168 h (red line is for predicted values, blue line is for measured values).

No. | i | X | Y | ||||||
---|---|---|---|---|---|---|---|---|---|

x_{i−h+1} | x_{i−h+2} | x_{i−h+3} | x_{i−h+4} | x_{i−h+5} | … | x_{i} | x_{i+1} | ||

1 | h | 36.992 | 52.096 | 48 | 23.936 | 49.024 | … | 64 | 17.024 |

2 | h + 1 | 52.096 | 48 | 23.936 | 49.024 | 64 | … | 20.992 | 23.936 |

3 | h + 2 | 48 | 23.936 | 49.024 | 64 | 20.992 | … | 29.952 | 32 |

4 | h + 3 | 23.936 | 49.024 | 64 | 20.992 | 29.952 | … | 24.064 | 25.984 |

5 | h + 4 | 49.024 | 64 | 20.992 | 29.952 | 24.064 | … | 29.952 | 12.032 |

… | … | … | … | … | … | … | … | … | … |

n − h + 1 | n | 38.912 | 26.112 | 38.912 | 35.072 | 51.968 | … | 36.096 | 43.008 |

Network Configuration | Number of Neurons |
---|---|

RNN | n^{2} + 2n |

LSTM | 4·(n^{2} + 2n) |

GRU | 3·(n^{2} + 2n) |

Type of Network | Type of Error | 24 | 48 | 96 | 168 | 336 |
---|---|---|---|---|---|---|

GRU | MAE | 6.844952 | 6.841905 | 3.703619 | 1.929905 | 0.540190 |

MAPE | 21.119003 | 20.980362 | 11.788948 | 6.265632 | 1.642816 | |

MSE | 85.212794 | 99.907096 | 42.190848 | 5.377365 | 0.523995 | |

RMSE | 9.231078 | 9.995354 | 6.495448 | 2.318915 | 0.723875 | |

GRUB | MAE | 7.053714 | 6.287238 | 3.299810 | 1.033905 | 0.710095 |

MAPE | 20.879806 | 19.450597 | 10.642182 | 3.435867 | 2.305570 | |

MSE | 91.479869 | 93.981355 | 36.013885 | 1.587785 | 0.817835 | |

RMSE | 9.564511 | 9.694398 | 6.001157 | 1.260073 | 0.904342 | |

LSTM | MAE | 7.051429 | 6.472381 | 3.657905 | 0.849524 | 1.075810 |

MAPE | 21.668491 | 19.099335 | 11.680444 | 2.920464 | 2.797340 | |

MSE | 95.445480 | 105.017637 | 41.434453 | 1.098606 | 1.968030 | |

RMSE | 9.769620 | 10.247811 | 6.436960 | 1.048144 | 1.402865 | |

LSTMB | MAE | 6.878476 | 6.359619 | 3.995429 | 0.486095 | 0.561524 |

MAPE | 20.545295 | 19.292223 | 13.531717 | 1.632134 | 1.615307 | |

MSE | 89.904469 | 106.552856 | 41.896424 | 0.410185 | 0.485766 | |

RMSE | 9.481797 | 10.322444 | 6.472745 | 0.640457 | 0.696969 | |

RNN | MAE | 7.216000 | 7.094857 | 7.650286 | 4.026667 | 3.045333 |

MAPE | 24.814516 | 22.877283 | 27.742101 | 13.739010 | 9.262036 | |

MSE | 86.306914 | 84.897012 | 89.222290 | 27.050082 | 13.187267 | |

RMSE | 9.290151 | 9.213957 | 9.445755 | 5.200969 | 3.631428 |

Type of Network | Type of Error | 24 | 48 | 96 | 168 | 336 |
---|---|---|---|---|---|---|

GRU | MAE | 4.395429 | 2.355048 | 0.968381 | 0.787810 | 0.880000 |

MAPE | 14.086003 | 7.365128 | 3.077262 | 2.542950 | 2.868073 | |

MSE | 33.303893 | 10.051096 | 1.451252 | 1.064960 | 1.181111 | |

RMSE | 5.770953 | 3.170346 | 1.204679 | 1.031969 | 1.086789 | |

GRUB | MAE | 4.217905 | 1.866667 | 0.972190 | 0.954667 | 1.010286 |

MAPE | 12.935179 | 6.540375 | 3.187603 | 3.453561 | 3.176468 | |

MSE | 29.726818 | 7.193746 | 1.555895 | 1.379669 | 1.822525 | |

RMSE | 5.452231 | 2.682116 | 1.247355 | 1.174593 | 1.350009 | |

LSTM | MAE | 3.961905 | 1.907810 | 0.937905 | 1.087238 | 0.973714 |

MAPE | 12.855625 | 6.345050 | 2.983061 | 3.489797 | 3.326173 | |

MSE | 26.979962 | 6.901955 | 1.440719 | 1.917806 | 1.518641 | |

RMSE | 5.194224 | 2.627157 | 1.200300 | 1.384849 | 1.232331 | |

LSTMB | MAE | 3.278476 | 1.664000 | 0.826667 | 0.962286 | 1.334095 |

MAPE | 10.639239 | 5.633171 | 2.750414 | 3.478291 | 3.561142 | |

MSE | 17.068520 | 5.215963 | 1.098801 | 1.451057 | 2.993688 | |

RMSE | 4.131406 | 2.283848 | 1.048237 | 1.204598 | 1.730228 | |

RNN | MAE | 6.297143 | 5.829333 | 5.846857 | 5.356952 | 3.129905 |

MAPE | 21.225944 | 20.429040 | 18.677578 | 18.459808 | 10.688008 | |

MSE | 74.995127 | 57.958302 | 58.096299 | 47.486391 | 16.588800 | |

RMSE | 8.659973 | 7.613035 | 7.622093 | 6.891037 | 4.072935 |

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**MDPI and ACS Style**

Stošović, M.A.; Radivojević, N.; Ivanova, M.
Electricity Consumption Prediction in an Electronic System Using Artificial Neural Networks. *Electronics* **2022**, *11*, 3506.
https://doi.org/10.3390/electronics11213506

**AMA Style**

Stošović MA, Radivojević N, Ivanova M.
Electricity Consumption Prediction in an Electronic System Using Artificial Neural Networks. *Electronics*. 2022; 11(21):3506.
https://doi.org/10.3390/electronics11213506

**Chicago/Turabian Style**

Stošović, Miona Andrejević, Novak Radivojević, and Malinka Ivanova.
2022. "Electricity Consumption Prediction in an Electronic System Using Artificial Neural Networks" *Electronics* 11, no. 21: 3506.
https://doi.org/10.3390/electronics11213506