# Short-Term Electric Load Forecasting Based on Signal Decomposition and Improved TCN Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. CEEMDAN

- Add white noise to the original signal $x(t)$ to obtain ${x}_{i}(t)$:$${x}_{i}(t)=x(t)+{\beta}_{0}{\omega}_{i}(t)$$
- Use EMD to decompose the first set of ${x}_{i}(t)$ and obtain the residual ${r}_{1}(t)$:$$IM{F}_{1}(t)=\frac{1}{I}{\displaystyle \sum _{i=1}IM{F}_{1}^{i}}(t)$$$${r}_{1}(t)=x(t)-IM{F}_{1}(t)$$
- Use EMD on ${r}_{1}(t)$ after adding adaptive noise to obtain the second-order modal component $IM{F}_{2}(t)$ and the residual ${r}_{2}(t)$:$${r}_{1}(t)+{\beta}_{1}{M}_{1}({\omega}_{i}(t))=IM{F}_{2}(t)+{r}_{2}(t)$$
- Repeat step (3), calculating the (k + 1)th order modal component and residual, until the residual becomes a monotonic function and can no longer be further decomposed into IMFs.

#### 2.2. Principles of TCN and the Improved SF-TCN

#### 2.3. Principles of SMA

- Approaching food$$\overrightarrow{X(t+1)}=\left(\right)open="\{">\begin{array}{c}\overrightarrow{{X}_{b}(t)}+\overrightarrow{vb}\cdot (\overrightarrow{W}\cdot \overrightarrow{{X}_{A}(t)}-\overrightarrow{{X}_{B}(t)}),rp\\ \overrightarrow{vc}\cdot \overrightarrow{X(t)},r\ge p\end{array}$$The updated formula for $p$ is as follows:$$p=\mathrm{tanh}|S(i)-DF|$$The formula of $\overrightarrow{vb}$ is $\overrightarrow{vb}=[-a,a]$, and its updated formula is as follows:$$a=\mathrm{arctan}\mathrm{h}(-(\frac{t}{{\mathrm{max}}_{\_t}})+1)$$The updated formula for $\overrightarrow{W}$ is as follows:$$\overrightarrow{W(SmellIndex(i))}=\left(\right)open="\{">\begin{array}{l}1+r\xb7\mathrm{log}(\frac{bF-S(i)}{bF-wF}+1),\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\\ 1-r\xb7\mathrm{log}(\frac{bF-S(i)}{bF-wF}+1),\mathrm{others}\end{array}$$$$SmellIndex=sort(S)$$
- Encircling FoodDepending on the quality of the food, slime mold can adjust its search patterns. When the food concentration is high, it places more emphasis on that area; conversely, when the food concentration is low, it reduces the weight of that area and turns to explore other regions. The mathematical formula for updating the position of the slime mold is as follows:$$\overrightarrow{{X}^{*}}=\left(\right)open="\{">\begin{array}{l}rand\xb7(UB-LB)+LB,randz\\ \overrightarrow{{X}_{b}(t)}+\overrightarrow{vb}\xb7(W\xb7\overrightarrow{{X}_{A}(t)}-\overrightarrow{{X}_{B}(t)}),rp\\ \overrightarrow{vc}\xb7\overrightarrow{X(t)},r\ge p\end{array}$$
- Capturing FoodSlime mold employs biological oscillators to generate propagation waves that alter the flow of its cytoplasm, enabling it to search for and select food resources within its environment. By adjusting its oscillation frequency and engaging in random exploratory behavior, the slime mold adapts to varying concentrations of food, allowing the cells to more swiftly converge upon sources of high-quality food, while allocating a portion of its resources to the exploration of additional areas. The oscillation of parameters and their synergistic effect simulate the selective behavior of slime mold, empowering it to discover superior food sources and circumvent local optima. Despite facing numerous constraints during propagation, these very limitations afford the slime mold opportunities, enhancing its likelihood of locating high-quality food sources.

#### 2.4. CEEMDAN-SF-TCN-SMA

## 3. Data Sources and Preprocessing

#### 3.1. Data Sources

#### 3.2. Data Preprocessing

## 4. Experiment and Results Analysis

#### 4.1. Model Configuration and Evaluation Metrics

#### 4.2. CEEMDAN-SF-TCN-SMA Forecasting Analysis

^{2}) greater than 0.999 across all seasons, as shown in Figure 7, indicating an excellent load curve fitting accuracy and reflecting its good prediction accuracy and robustness.

#### 4.3. Comparative Analysis

## 5. Conclusions

- By utilizing the CEEMDAN, our study effectively decomposes electric power load data into high-frequency and low-frequency components. This enables a more detailed analysis, capturing subtle fluctuations in the load curve that traditional methods may overlook.
- The introduction of an improved SF-TCN addresses the challenges in predicting high-frequency components. This model enhancement not only reduces the impact of noise but also improves the accuracy of short-term forecasts.
- The application of the shuffled memetic algorithm (SMA) for adjusting the neural network’s hyperparameters and soft thresholding enhances the neural network’s adaptability and forecasting ability.
- Our experimental results demonstrate that, compared to un-decomposed SVR, RNN, GRU, LSTM, CNN-LSTM, and TCN models as well as decomposed CEEMDAN-TCN and CEEMDAN-SF-TCN models, our method possesses superior forecasting capabilities.

^{2}value exceeding 0.999, indicating that the model can highly accurately fit the existing data. Theoretically, introducing more relevant variables, such as weather conditions or socio-economic indicators, could potentially improve the model’s forecasting accuracy since these factors might have a significant impact on the electricity load. However, incorporating more variables would also increase the model’s complexity, which could lead to more challenging data processing, a more cumbersome model structure, and possibly overfitting, in which the model becomes overly sensitive to the training data, reducing its generalization ability for unknown data. Therefore, while adding additional variables might help enhance its forecasting accuracy, this also brings a series of challenges that need further exploration and investigation in future research.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Network Layer | Network Parameters | Low Frequency | High Frequency |
---|---|---|---|

First Layer TCN | nb_filters | 16 | Refer to Table 2 |

kernel_size | 3 | Refer to Table 2 | |

dilations | [1,2,4,8] | [1,2,4,8] | |

activation | ReLU | ReLU | |

threshold | No Parameter | Refer to Table 2 | |

Second Layer TCN | nb_filters | 16 | Refer to Table 2 |

kernel_size | 3 | Refer to Table 2 | |

dilations | [1,2,4,8] | [1,2,4,8] | |

activation | ReLU | ReLU | |

threshold | No Parameter | Refer to Table 2 | |

First Layer Dense | dense_units | 16 | Refer to Table 2 |

activation | ReLU | ReLU | |

Second Layer Dense | dense_units | 1 | 1 |

activation | Linear | Linear | |

Training Parameters | batch_size | 16 | Refer to Table 2 |

epochs | 100 | 100 |

Hyperparameters | Spring | Summer | Autumn | Winter |
---|---|---|---|---|

nb_filters_1 | 220 | 223 | 218 | 27 |

kernel_size_1 | 4 | 7 | 8 | 6 |

threshold_1 | 0.043 | 0.969 | 0.221 | 0.008 |

nb_filters_2 | 81 | 250 | 150 | 187 |

kernel_size_2 | 5 | 6 | 9 | 6 |

threshold_2 | 0.224 | 0.964 | 0.189 | 0.556 |

dense_units_1 | 44 | 21 | 40 | 33 |

batch_size | 39 | 104 | 111 | 52 |

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

SVR | kernel=‘rbf’, C=1, gamma=0.5, epsilon=0.01 |

RNN | hidden_units_1=16, hidden_activation_1=‘relu’ hidden_units_2=16, hidden_activation_2=‘relu’ dense_units_1=16, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=16, epochs=100 |

GRU | hidden_units_1=16, hidden_activation_1=‘relu’ hidden_units_2=16, hidden_activation_2=‘relu’ dense_units_1=16, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=16, epochs=100 |

LSTM | hidden_units_1=140, hidden_activation_1=‘relu’ hidden_units_2=60, hidden_activation_2=‘relu’ dense_units_1=16, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=64, epochs=100 |

CNN-LSTM | filters=64, kernel_size=3, strides=1, pool_size=2, dropout=0.3, hidden_units_1=140, hidden_activation_1=‘relu’, hidden_units_2=60, hidden_activation_2=‘relu’, dense_units_1=16, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=64, epochs=100 |

Informer | seq_len=12, label_len=6, pred_len=1, enc_in=1, dec_in=1, c_out=1, d_model=512, n_heads=8, e_layers=2, d_layers=2, s_layers=‘3, 2, 1’, d_ff=2048, fator=5, padding=0, distill=‘store_false’, dropout=0.05, attn=‘prob’, embed=‘timeF’, activation=‘gelu’, output_attention=‘store_true’, do_predict=‘store_true’, mix=‘store_false’, cols=‘+’, num_workers=0, itr=‘2’, train_epochs=6, batch_size=32, patience=3, learning_rate=0.001, des=‘test’, loss=‘mse’, lradj=‘type1’, use_amp=‘store_true’, inverse=True |

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

CEEMDAN-TCN High-frequency Component | nb_filters_1=32, kernel_size_1=3, hidden_activation_1=‘relu’, dilations_1=[1,2,4,8], nb_filters_2=32, kernel_size2=3, hidden_activation2=‘relu’, dilations2=[1,2,4,8], dense_units1=16, dense_activation1=‘relu’, dense_units2=1, dense_activation2=‘linear’, batch_size=16, epochs=100 |

CEEMDAN-TCN-SMA High-frequency Component | nb_filters_1=Optimization, kernel_size_1=Optimization, hidden_activation_1=‘relu’, dilations_1=[1,2,4,8], nb_filters_2=Optimization, kernel_size_2=Optimization, hidden_activation_2=‘relu’, dilations_2=[1,2,4,8], dense_units_1=Optimization, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=Optimization, epochs=100 |

TCN | nb_filters_1=64, kernel_size_1=3, hidden_activation_1=‘relu’, dilations_1=[1,2,4,8], nb_filters_2=64, kernel_size_2=3, hidden_activation_2=‘relu’, dilations_2=[1,2,4,8], dense_units_1=16, dense_activation_1=‘relu’, dense_units_2=1, dense_activation_2=‘linear’, batch_size=16, epochs=100 |

Season | Metric | SVR | RNN | GRU | LSTM | CNN-LSTM | Informer | TCN |
---|---|---|---|---|---|---|---|---|

Spring | MSE | 1088.32 | 1770.20 | 3959.82 | 2138.16 | 1807.81 | 6264.42 | 1690.01 |

MAPE (%) | 0.23 | 0.30 | 0.43 | 0.32 | 0.33 | 0.57 | 0.30 | |

AbsDEV | 25.59 | 33.51 | 48.67 | 35.82 | 34.97 | 62.91 | 32.53 | |

Summer | MSE | 8212.09 | 8194.42 | 8385.86 | 8278.83 | 7661.2 | 16,603.23 | 5412.53 |

MAPE (%) | 0.45 | 0.38 | 0.39 | 0.41 | 0.49 | 0.65 | 0.32 | |

AbsDEV | 73.62 | 65.11 | 65.14 | 68.15 | 77.45 | 108.38 | 54.63 | |

Autumn | MSE | 1198.91 | 1336.82 | 1351.08 | 1659.37 | 1408.35 | 6762.06 | 1142.42 |

MAPE (%) | 0.22 | 0.24 | 0.24 | 0.27 | 0.25 | 0.52 | 0.22 | |

AbsDEV | 26.17 | 28.33 | 28.24 | 32.16 | 29.51 | 62.20 | 25.97 | |

Winter | MSE | 2295.14 | 4623.00 | 3023.68 | 2910.03 | 2449.34 | 7700.20 | 2109.48 |

MAPE (%) | 0.22 | 0.39 | 0.26 | 0.25 | 0.27 | 0.45 | 0.23 | |

AbsDEV | 31.87 | 55.90 | 37.25 | 34.84 | 37.59 | 63.60 | 33.88 |

Season | Metric | CEEMDAN-TCN | CEEMDAN-TCN-SMA | CEEMDAN-SF-TCN-SMA |
---|---|---|---|---|

Spring | MSE | 971.27 | 862.96 | 628.42 |

MAPE (%) | 0.23 | 0.21 | 0.18 | |

AbsDEV | 25.51 | 23.81 | 19.67 | |

Summer | MSE | 3698.86 | 3609.73 | 3442.13 |

MAPE (%) | 0.28 | 0.27 | 0.27 | |

AbsDEV | 46.03 | 45.36 | 44.39 | |

Autumn | MSE | 1003.2 | 745.43 | 555.45 |

MAPE (%) | 0.20 | 0.17 | 0.15 | |

AbsDEV | 24.23 | 20.99 | 18.17 | |

Winter | MSE | 1167.29 | 1081.12 | 1014.45 |

MAPE (%) | 0.18 | 0.17 | 0.16 | |

AbsDEV | 24.84 | 23.41 | 22.05 |

Hyperparameters | Metric | Value |
---|---|---|

Spring | MSE | 421.00 |

MAPE (%) | 0.15 | |

AbsDEV | 16.47 | |

Summer | MSE | 371.47 |

MAPE (%) | 0.26 | |

AbsDEV | 43.77 | |

Autumn | MSE | 343.39 |

MAPE (%) | 0.11 | |

AbsDEV | 13.60 | |

Winter | MSE | 202.10 |

MAPE (%) | 0.09 | |

AbsDEV | 11.43 |

Season | Metric | CEEMDAN-TCN | CEEMDAN-TCN-SMA | CEEMDAN-SF-TCN-SMA |
---|---|---|---|---|

Spring | MSE | 374.18 | 357.31 | 342.88 |

MAPE (%) | 470.49 | 394.08 | 256.40 | |

AbsDEV | 15.06 | 14.73 | 14.49 | |

Summer | MSE | 477.5 | 454.64 | 331.19 |

MAPE (%) | 337.54 | 282.115 | 250.49 | |

AbsDEV | 16.46 | 16.0916 | 13.87 | |

Autumn | MSE | 428.82 | 330.91 | 269.38 |

MAPE (%) | 297.26 | 272.27 | 205.91 | |

AbsDEV | 16.16 | 14.29 | 12.89 | |

Winter | MSE | 1012.09 | 923.01 | 788.92 |

MAPE (%) | 753.28 | 483.9 | 311.43 | |

AbsDEV | 22.84 | 20.15 | 18.30 |

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## Share and Cite

**MDPI and ACS Style**

Xiang, X.; Yuan, T.; Cao, G.; Zheng, Y.
Short-Term Electric Load Forecasting Based on Signal Decomposition and Improved TCN Algorithm. *Energies* **2024**, *17*, 1815.
https://doi.org/10.3390/en17081815

**AMA Style**

Xiang X, Yuan T, Cao G, Zheng Y.
Short-Term Electric Load Forecasting Based on Signal Decomposition and Improved TCN Algorithm. *Energies*. 2024; 17(8):1815.
https://doi.org/10.3390/en17081815

**Chicago/Turabian Style**

Xiang, Xinjian, Tianshun Yuan, Guangke Cao, and Yongping Zheng.
2024. "Short-Term Electric Load Forecasting Based on Signal Decomposition and Improved TCN Algorithm" *Energies* 17, no. 8: 1815.
https://doi.org/10.3390/en17081815