# A Hybrid Approach to Short-Term Load Forecasting Aimed at Bad Data Detection in Secondary Substation Monitoring Equipment

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## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. Short Term Load Forecasting Framework

#### 3.1. Introduction to Singular Spectrum Analysis

#### 3.2. SSA-ANN-Based Load Forecasting Strategy

#### 3.3. Bad Data Processing. Error Correction/Elimination

#### 3.4. Load Forecasting Accuracy Assessment: Weight Calculation

## 4. Experimental Results: Error Detection.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Forecasted data for two different consecutive days. First 24 h when Model 1 offers a bad prediction and last 24 h when the opposite occurs.

**Figure 7.**Model 1 and Model 2 comparison. (

**a**) MAPE weekly prediction for both models and weighted average. (

**b**) Weekly Wilcoxon signed-rank test under $\mathsf{\alpha}=0.05$.

**Figure 8.**Normalized detected error (${\u03f5}_{\mathrm{norm}}$) as a function of the injected error for the weeks under study.

Model | MAPE (%) | MAE (kW) | NRMSE (%) | RMSE (kW) |
---|---|---|---|---|

Weighted average | $2.3341$ | $34.5086$ | $3.0682$ | $46.2174$ |

Model 1 (SSA-ANN) | $3.1879$ | $46.5177$ | $4.0850$ | $60.3397$ |

Model 2 (ANN) | $3.0596$ | $46.1990$ | $4.0892$ | $63.5167$ |

SARIMA prediction | $3.3283$. | $48.1560$ | $4.1985$ | $60.6915$ |

SSA prediction | $5.9462$ | $83.9145$ | $7.7610$ | $107.4200$ |

$\mathit{\delta}4\mathit{\%}$ | $\mathit{\delta}\le 4\mathit{\%}$ | |
---|---|---|

$\sqrt{{\u03f5}_{\mathsf{\alpha}}{}^{2}+{\u03f5}_{\mathsf{\beta}}{}^{2}}4\%$ | TP | FN |

$\sqrt{{\u03f5}_{\mathsf{\alpha}}{}^{2}+{\u03f5}_{\mathsf{\beta}}{}^{2}}\le 4\%$ | FP | TN |

**Table 3.**Normalized error $\left({\u03f5}_{\mathrm{norm}}\right)$ as a function of the injected error for a random week.

${\mathit{\u03f5}}_{\mathbf{n}\mathbf{o}\mathbf{r}\mathbf{m}}$ | ${\mathit{\u03f5}}_{\mathbf{\beta}}$ | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

$-5\mathbf{\%}$ | $-4\mathbf{\%}$ | $-3\mathbf{\%}$ | $-2\mathbf{\%}$ | $-1\mathbf{\%}$ | $0\mathbf{\%}$ | $1\mathbf{\%}$ | $2\mathbf{\%}$ | $3\mathbf{\%}$ | $4\mathbf{\%}$ | $5\mathbf{\%}$ | ||

${\mathit{\u03f5}}_{\mathit{\alpha}}$ | $\mathbf{-}\mathbf{5}\%$ | $0.071$ | $0.078$ | $0.086$ | $0.111$ | $0.112$ | $0.120$ | $0.138$ | $0.152$ | $0.178$ | $0.162$ | $0.147$ |

$\mathbf{-}\mathbf{4}\%$ | $0.094$ | $0.106$ | $0.120$ | $0.134$ | $0.146$ | $0.150$ | $0.171$ | $0.205$ | $0.207$ | $0.186$ | $0.164$ | |

$\mathbf{-}\mathbf{3}\%$ | $0.103$ | $0.120$ | $0.141$ | $0.167$ | $0.190$ | $0.201$ | $0.223$ | $0.258$ | $0.247$ | $0.210$ | $0.180$ | |

$\mathbf{-}\mathbf{2}\%$ | $0.112$ | $0.135$ | $0.167$ | $0.212$ | $0.269$ | $0.301$ | $0.316$ | $0.328$ | $0.291$ | $0.256$ | $0.213$ | |

$\mathbf{-}\mathbf{1}\%$ | $0.118$ | $0.146$ | $0.190$ | $0.269$ | $0.423$ | $0.602$ | $0.499$ | $0.415$ | $0.362$ | $0.278$ | $0.225$ | |

$\mathbf{0}\%$ | $0.120$ | $0.150$ | $0.201$ | $0.301$ | $0.602$ | $\infty $ | $0.713$ | $0.464$ | $0.382$ | $0.286$ | $0.229$ | |

$\mathbf{1}\%$ | $0.118$ | $0.146$ | $0.190$ | $0.269$ | $0.423$ | $0.702$ | $0.574$ | $0.415$ | $0.362$ | $0.281$ | $0.227$ | |

$\mathbf{2}\%$ | $0.130$ | $0.157$ | $0.195$ | $0.248$ | $0.314$ | $0.353$ | $0.363$ | $0.363$ | $0.318$ | $0.280$ | $0.233$ | |

$\mathbf{3}\%$ | $0.120$ | $0.140$ | $0.165$ | $0.195$ | $0.222$ | $0.235$ | $0.257$ | $0.284$ | $0.273$ | $0.251$ | $0.215$ | |

$\mathbf{4}\%$ | $0.110$ | $0.125$ | $0.141$. | $0.158$. | $0.171$. | $0.177$ | $0.197$. | $0.232$ | $0.251$ | $0.222$ | $0.196$ | |

$\mathbf{5}\%$ | $0.100$ | $0.110$ | $0.121$ | $0.131$ | $0.138$ | $0.141$ | $0.159$ | $0.193$ | $0.215$ | $0.198$ | $0.179$ |

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**MDPI and ACS Style**

Martín, P.; Moreno, G.; Rodríguez, F.J.; Jiménez, J.A.; Fernández, I. A Hybrid Approach to Short-Term Load Forecasting Aimed at Bad Data Detection in Secondary Substation Monitoring Equipment. *Sensors* **2018**, *18*, 3947.
https://doi.org/10.3390/s18113947

**AMA Style**

Martín P, Moreno G, Rodríguez FJ, Jiménez JA, Fernández I. A Hybrid Approach to Short-Term Load Forecasting Aimed at Bad Data Detection in Secondary Substation Monitoring Equipment. *Sensors*. 2018; 18(11):3947.
https://doi.org/10.3390/s18113947

**Chicago/Turabian Style**

Martín, Pedro, Guillermo Moreno, Francisco Javier Rodríguez, José Antonio Jiménez, and Ignacio Fernández. 2018. "A Hybrid Approach to Short-Term Load Forecasting Aimed at Bad Data Detection in Secondary Substation Monitoring Equipment" *Sensors* 18, no. 11: 3947.
https://doi.org/10.3390/s18113947