# An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid

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## Abstract

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## 1. Introduction

- A FPP-MLP-GWDO has been developed, where the preprocessing FPP and postprocessing GWDO have been cascaded with the MLP for accuracy improvement.
- Based on existing feature selection techniques [37], FPP has been developed where the feature interaction concept has been introduced, in addition to filters (irrelevancy, redundancy) for the selection of key features.
- The GWDO has been applied to the returned predictions from the MLP to further improve the accuracy by optimizing the filter threshold (irrelevancy and redundancy) weights and biases.
- The developed hybrid model, FPP-MLP-GWDO, is evaluated using Dayton Ohio grid load data regarding aspects of accuracy (the mean absolute percentage error (MAPE), Theil’s inequality coefficient (TIC), and the correlation coefficient (CC)) and convergence speed (the CT and CR). The findings endorsed the validity and superiority of the developed model compared to the literature models such as the feature selection–support vector machine–modified enhanced differential evolution (FS-SVM-mEDE) [38], the feature selection–artificial neural network (FS-ANN) [26], the support vector machine–differential evolution algorithm (SVM-DEA) [39], and the autoregressive (AR) model regarding aspects of accuracy and convergence speed.

Refs. | Methods | Objectives | Performance Metrics | Advantages/Disadvantages |
---|---|---|---|---|

Time series methods [6,7,8,9,10,11,12,13,14] | Exponential smoothing, Kalman filters, regression methods, grey model, ARIMA, and ARMAX | Forecast accuracy improvement | MAE, MAPE, RMSE | These prediction methods are capable of forecasting electric load. However, the accuracy improvement is not up to the mark due to the method’s inherent shortcomings. For instance, linear regressors are suitable for solving linear problems, but they perform worst while addressing nonlinear problems. Methods such as the ARIMA take historical/current records for prediction while ignoring other influencing parameters. GM methods can only cater to exponential growth trend problems. |

Artificial intelligence methods [16,17,18,19,20] | Expert systems, radial basis fuzzy logic models, machine learning models, and neural networks | Accuracy enhancement and compilation time improvement | MAPE, correlation coefficient | AI models outperform traditional methods when it comes to accuracy. Nevertheless, these advanced techniques have their limitations. For example, expert systems necessitate extensive knowledge acquisition and can need help with handling uncertainty. Radial basis logic models, on the other hand, are computationally expensive and exhibit limited generalization capabilities. Neural network models are powerful. However, they easily get stuck in local optima. |

Deep neural networks and hybrid models [24,25,26,27,28] | MLP, LSTM, RBM, etc. | Accuracy improvement | RMSE, MSE, R, etc. | Deep learning models have been introduced to address the limitations of existing forecasting methods and to enhance prediction accuracy. Nevertheless, these models come with a notable drawback: their high computational complexity. While deep-layer models excel in terms of accuracy compared to intrinsic methods, they often overlook the significance of data preprocessing techniques, which are crucial for achieving improved accuracy. |

Integrated FS-FCRBM-GWDO model [36] | AFC-STLF, MI-mEDE-ANN, FS-ANN, Bi-level. | Accuracy improvement | MAPD, variance, correlation, etc. | A hybrid model is introduced to tackle the constraints associated with current forecasting techniques. The aim is to enhance the prediction accuracy and convergence speed. However, the developed model has comparatively high complexity and a slow convergence. |

This work | FPP-MLP-GWDO | Accuracy, convergence rate, and computational time improvement | TIC, CC, CR, CT, and MAPE | The FPP-MLP-GWDO hybrid model offers several significant advantages over existing models in load forecasting. Its notably improved forecast accuracy stands out, thereby making it a valuable model for precise predictions. Moreover, its ability to converge quickly is ideal for real-time applications, while its adaptability allows it to handle various scenarios and datasets effectively. The model’s prowess in capturing nonlinear load patterns ensures accuracy even in complex situations, and its robustness in the face of data variability instills confidence in its reliability. Furthermore, it enhances resource allocation, thus leading to cost savings, and it is designed for scalability to meet the evolving demands of expanding smart city infrastructures. Lastly, the integration of feature preprocessing simplifies data preparation, thereby streamlining the forecasting process. Overall, the FPP-MLP-GWDO model significantly advances load forecasting, thus offering improved accuracy, efficiency, and fast convergence speed. |

## 2. Developed Hybrid FPP-MLP-GWDO Model

#### 2.1. Feature Preprocessing

#### 2.1.1. Relevant Feature Selection: Relevancy Filter

#### 2.1.2. Redundant Feature Elimination: Redundancy Filter

#### 2.1.3. Feature Interaction

#### 2.1.4. FPP Stepwise Procedure

- The enclosed blocks within the dashed box represent the prefiltering part, during which the relevancy/interaction are computed. The potential inputs are then ranked according to these computed estimates/measures.
- We assess the individual and the gained information to measure the information content. This is done using an adapted form of Equation (4), which is illustrated in the flowchart presented in Figure 2. The function $f(,)$ used in the equation monotonically increases, while the weight factor $\alpha $ balances the relevancy and interaction measures. Depending on the specific forecasting problem, this factor can be adjusted and finely tuned.
- The potential inputs identified in the prefiltering step (${S}^{p}$) are organized in a descending sequence as per their information value.

- The prefiltering stage output serves as the input for the filtering stage, where the preselected features are divided into selected (${S}^{s}$) and nonselected (${S}^{n}$) features, as illustrated in Figure 2. Redundancy measure is computed using Equation (9), which is modeled below:$$R\left(\stackrel{p}{{a}_{i}}\right)=\underset{\stackrel{p}{{a}_{i}}\in \stackrel{p}{S}}{Minimize}\left\{RM(\stackrel{p}{{a}_{i}},\phantom{\rule{0.277778em}{0ex}}\stackrel{p}{{a}_{j}})\right\},$$Here, $R\left(\stackrel{p}{{a}_{i}}\right)$ represents the measure of redundancy for every potential input $\stackrel{p}{{a}_{i}}$ belonging to the set $\stackrel{p}{S}$.
- The assessment of the informational significance of the potential features comprises three metrics: redundancy, relevancy, and interaction. In mathematical terms, this evaluation can be expressed as follows:$$\begin{array}{c}V\left(\stackrel{p}{{a}_{i}}\right)=g\left\{D\left(\stackrel{p}{{a}_{i}}\right),\phantom{\rule{0.277778em}{0ex}}IM\left(\stackrel{p}{{a}_{i}}\right),\phantom{\rule{0.277778em}{0ex}}R\left(\stackrel{p}{{a}_{i}}\right)\right\}\hfill \\ \phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}=D\left(\stackrel{p}{{a}_{i}}\right)+\alpha \times IM\left(\stackrel{p}{{a}_{i}}\right)+\beta \times R\left(\stackrel{p}{{a}_{i}}\right),\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\hfill \end{array}$$Here, $\alpha ,\beta >0$, $V\left(\stackrel{p}{{a}_{i}}\right)$ represents the information content, $g\left(,;\right)$ denotes a monotonically increasing linear function, and $\beta $ corresponds to a tuneable parameter.
- The determination of the information content is made using the following decision process:$$\begin{array}{c}\mathrm{If}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}V\left(\stackrel{p}{{a}_{i}}\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\ge \phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{R}_{th}\to \phantom{\rule{0.277778em}{0ex}}\stackrel{S}{S}=\stackrel{S}{S}+\left\{\stackrel{p}{{a}_{i}}\right\}\hfill \\ \mathrm{If}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}V\left(\stackrel{p}{{a}_{i}}\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\le \phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{R}_{th}\to \phantom{\rule{0.277778em}{0ex}}\stackrel{n}{S}=\stackrel{n}{S}+\left\{\stackrel{p}{{a}_{i}}\right\},\hfill \end{array}$$In this process, information content is compared to the redundancy threshold, which is denoted as ${R}_{th}$. If the information value is equal to or greater than the relevancy threshold, it is added to the list of selected features ($\stackrel{s}{S}$). Otherwise, it is included in the list of ($\stackrel{n}{S}$), which includes nonselected features.

#### 2.2. MLP Forecaster

#### 2.3. GWDO Optimizer

## 3. Results and Discussions

- The convergence speed encompasses two aspects: the CT and CR. The CT refers to the time it takes for the forecaster to return the predicted load pattern. On the other hand, the CR represents the rate at which the model converges to an iteration returning an optimal result, where the error no longer decreases significantly with increasing iterations. Forecasts with lower CT and CR values (requiring fewer epochs to converge) are considered faster, while higher CT and CR values indicate slower convergence. In this study, the CT is expressed in seconds, while the CR is in aspects of iterations.

#### 3.1. Accuracy Evaluation

#### 3.1.1. Day-Ahead Load Prediction

#### 3.1.2. Week-Ahead Load Prediction

#### 3.2. Convergence Speed Evaluation

#### 3.2.1. Convergence Speed in terms of the CT

#### 3.2.2. Convergence Speed in Terms of the CR

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 12.**Developed model evaluation in comparison with existing models in terms of computational time using Dayton Ohio grid data.

**Figure 13.**Proposed model evaluation in comparison with existing models’ convergence speed values in terns of the CR.

Forecaster Parameters | Values |
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Number of epochs | 110 |

Output layer | 1 |

Number of output neurons | 1 |

Hidden layer | 2 |

Neurons in hidden layer | 10 |

Learning rate | $0.0019$ |

Momentum | 0.6 |

Initial weight | 0.1 |

Initial bias | 0 |

Max | 0.9 |

Min | 0.1 |

Feature selection threshold | 0.5 |

Decision variables | 2 |

Number of objectives | 0 |

Population size | 24 |

Delay of weight | 0.002 |

**Table 3.**Evaluating the complexity, CT, CR, and accuracy of the suggested model and existing models such as AR, FS-ANN, SVM-DEA, and FS-SVM-mEDE.

Metrics | Load Forecasters | ||||
---|---|---|---|---|---|

AR | FS-ANN | SVM-DEA | FS-SVM-mEDE | FPP-MLP-GWDO | |

Complexity (level) | Low | Low | Moderate | High | Moderate |

CR (epochs) | 55th | 39th | 35th | 31th | 18th |

CT (s) | 132 | 159 | 240 | 350 | 299 |

Accuracy (%) | 95.7 | 96.5 | 97.5 | 97.9 | 98.999 |

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## Share and Cite

**MDPI and ACS Style**

Alghamdi, H.; Hafeez, G.; Ali, S.; Ullah, S.; Khan, M.I.; Murawwat, S.; Hua, L.-G.
An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid. *Mathematics* **2023**, *11*, 4561.
https://doi.org/10.3390/math11214561

**AMA Style**

Alghamdi H, Hafeez G, Ali S, Ullah S, Khan MI, Murawwat S, Hua L-G.
An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid. *Mathematics*. 2023; 11(21):4561.
https://doi.org/10.3390/math11214561

**Chicago/Turabian Style**

Alghamdi, Hisham, Ghulam Hafeez, Sajjad Ali, Safeer Ullah, Muhammad Iftikhar Khan, Sadia Murawwat, and Lyu-Guang Hua.
2023. "An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid" *Mathematics* 11, no. 21: 4561.
https://doi.org/10.3390/math11214561