# Short Term Active Power Load Prediction on A 33/11 kV Substation Using Regression Models

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## Abstract

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## 1. Introduction

- SLR and PR models were used to predict the active power load.
- A new approach, i.e., predict the active power load based on load at last three hours and load at one day before was used with various regression models and dimensionality reduction technique was used to reduce the complexity of the model so that overfitting problem was removed.
- Data analytic tools were used to process the data before feeding it to the model

## 2. Methodology

#### 2.1. Simple Linear Regression Model (SLR)

#### 2.2. Multiple Linear Regression Model (MLR)

#### 2.3. Polynomial Regression Model (PR)

#### 2.4. Dimensionality Reduction

#### 2.5. Model Performance Metrics

## 3. Results

#### 3.1. Simple Linear Regression

#### 3.1.1. Data Analysis

#### 3.1.2. Simple Regression Model Performance Analysis

#### 3.2. Multiple Linear Regression

#### 3.2.1. Data Analysis

#### 3.2.2. Multiple Regression Model Performance Analysis

#### 3.2.3. MLR with Dimensionality Reduction (DR)

#### 3.3. Polynomial Regression Model

#### PR Model Performance Analysis

#### 3.4. Comparative Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${d}_{a}$ | Distance between actual and predicted outputs |

$DS$ | Dimensionality reduction |

$L(D,t)$ | Load at Day ‘D’ and at hour ‘t’ |

$L(D,t-1)$ | Load at Day ‘D’ and at hour ‘t – 1’ |

$L(D,t-2)$ | Load at Day ‘D’ and at hour ‘t – 2’ |

$L(D,t-3)$ | Load at Day ‘D’ and at hour ‘t – 3’ |

$L(D-1,t)$ | Load at Day ‘D – 1’ and at hour ‘t’ |

$MAE$ | Mean Absolute Error |

$MLR$ | Multiple Linear Regression Model |

$MSE$ | Mean Square Error |

${N}_{a}$ | Total number of samples |

${n}_{a}$ | Batch size |

p | Degree of polynomial |

$PR$ | Polynomial Regression Model |

$RMSE$ | Root Mean Square Error |

$SLR$ | Simple Linear Regression Model |

${X}_{a}$ | ${a}^{\mathrm{th}}$ sample from input dataset |

${X}_{i}^{a}$ | ${i}^{\mathrm{th}}$ input parameter in ${a}^{\mathrm{th}}$ sample from input dataset |

Y | Predicted output using regression model |

${Y}_{a}$ | ${a}^{\mathrm{th}}$ sample from output dataset |

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**Figure 12.**SLR: Distribution of actual load ${Y}_{a}$ and predicted load with training dataset and with m = 0.7472 and c = 0.1173.

**Figure 13.**SLR: Distribution of actual load ${Y}_{a}$ and predicted load with testing dataset and with m = 0.7472 and c = 0.1173.

**Figure 18.**MLR With Dimensionality Reduction: comparison of actual load and predicted load with trained MLR model.

Load Prediction Type | Time | Usage |
---|---|---|

Short term | Few hours to days | Electric power generation and transmission scheduling |

Medium term | Few weeks to months | Fuel purchase scheduling |

Long term | 1–10 years | Establishment of power sector entities |

Parameter | Input | Output |
---|---|---|

count | 2160 | 2160 |

mean | 6037 | 6028 |

std | 1066 | 1068 |

min | 3378 | 3378 |

25% | 5263 | 5260 |

50% | 5950 | 5935 |

75% | 6747 | 6739 |

max | 8842 | 8842 |

Parameter | L(D,t−1) | L(D,t−2) | L(D,t−3) | L(D−1,t) | L(D,t) |
---|---|---|---|---|---|

count | 2160 | 2160 | 2160 | 2160 | 2160 |

mean | 6028 | 6028 | 6029 | 6037 | 6028 |

std | 1068 | 1068 | 1068 | 1066 | 1068 |

min | 3378 | 3378 | 3378 | 3378 | 3378 |

25% | 5260 | 5260 | 5260 | 5263 | 5260 |

50% | 5933 | 5935 | 5936 | 5950 | 5935 |

75% | 6739 | 6739 | 6739 | 6747 | 6739 |

max | 8842 | 8842 | 8842 | 8842 | 8842 |

${\mathit{m}}_{1}$ | ${\mathit{m}}_{2}$ | ${\mathit{m}}_{3}$ | ${\mathit{m}}_{4}$ | c |
---|---|---|---|---|

0.618733 | −0.00289 | −0.148361 | 0.374255 | 0.07541947 |

Features | L(D,t−1) | L(D,t−2) | L(D,t−3) | L(D−1,t) |
---|---|---|---|---|

L(D,t−1) | 1 | 0.783398 | 0.547211 | 0.660699 |

L(D,t−2) | 0.783398 | 1 | 0.783336 | 0.472053 |

L(D,t−3) | 0.547211 | 0.783336 | 1 | 0.256744 |

L(D−1,t) | 0.660699 | 0.472053 | 0.256744 | 1 |

${\mathit{m}}_{1}$ | ${\mathit{m}}_{2}$ | ${\mathit{m}}_{3}$ | c |
---|---|---|---|

0.596832 | −0.137541 | 0.392209 | 0.07235393 |

MAE | MSE | RMSE | |
---|---|---|---|

With DR | 0.0748 | 0.0113 | 0.107 |

Without DR | 0.0723 | 0.0105 | 0.103 |

MAE | MSE | RMSE | |
---|---|---|---|

With DR | 0.0679 | 0.009 | 0.093 |

Without DR | 0.0766 | 0.0119 | 0.109 |

Degree (p) | ${\mathit{m}}_{1}$ | ${\mathit{m}}_{2}$ | ${\mathit{m}}_{3}$ | ${\mathit{m}}_{4}$ | ${\mathit{m}}_{5}$ | ${\mathit{m}}_{6}$ | ${\mathit{m}}_{7}$ | ${\mathit{m}}_{8}$ |
---|---|---|---|---|---|---|---|---|

2 | 0.6061 | 0.1345 | NA | NA | NA | NA | NA | NA |

3 | −0.016 | 1.5525 | −0.936 | NA | NA | NA | NA | NA |

4 | −0.235 | 2.4303 | −2.25139 | 0.65556 | NA | NA | NA | NA |

5 | −1.458 | 9.886 | −20.92 | 21.1449 | −8.156 | NA | NA | NA |

10 | 3.8512 | −90.59 | 857.68 | −3885.2 | 10,407 | 17,572.45 | 19067.9 | 13006.7 |

15 | 20.437 | −802.9 | 13357 | −121,706 | 661,929 | −2,132,575 | 3,267,138 | 2,932,709 |

Degree (p) | ${\mathit{m}}_{\mathbf{9}}$ | ${\mathit{m}}_{\mathbf{10}}$ | ${\mathit{m}}_{\mathbf{11}}$ | ${\mathit{m}}_{\mathbf{12}}$ | ${\mathit{m}}_{\mathbf{13}}$ | ${\mathit{m}}_{\mathbf{14}}$ | ${\mathit{m}}_{\mathbf{15}}$ | c |

2 | NA | NA | NA | NA | NA | NA | NA | 0.15478 |

3 | NA | NA | NA | NA | NA | NA | NA | 0.22922 |

4 | NA | NA | NA | NA | NA | NA | NA | 0.24466 |

5 | NA | NA | NA | NA | NA | NA | NA | 0.30014 |

10 | 5113.5 | -888.6 | NA | NA | NA | NA | NA | 0.25182 |

15 | −3 × 10${}^{7}$ | 7 × 10${}^{7}$ | −1 × 10${}^{8}$ | 9.2 × 10${}^{7}$ | −5 × 10${}^{7}$ | 18132030 | −3 × 10${}^{6}$ | 0.19706 |

Polynomial Degree (p) | Training | ||
---|---|---|---|

MAE | MSE | RMSE | |

3 | 0.0973329 | 0.01732 | 0.131609177 |

4 | 0.0973174 | 0.01732 | 0.131591693 |

10 | 0.0970367 | 0.01717 | 0.131019329 |

15 | 0.0969165 | 0.01708 | 0.130697822 |

16 | 0.0968882 | 0.01708 | 0.130688064 |

18 | 0.0969342 | 0.01707 | 0.130644772 |

20 | 0.0970481 | 0.01705 | 0.130574147 |

Polynomial Degree (p) | Training | ||
---|---|---|---|

MAE | MSE | RMSE | |

3 | 0.09289 | 0.015969 | 0.12637 |

4 | 0.09276 | 0.015939 | 0.12625 |

10 | 0.09274 | 0.015889 | 0.12605 |

15 | 0.09295 | 0.015849 | 0.12589 |

16 | 0.09292 | 0.015853 | 0.12591 |

18 | 0.09308 | 0.015877 | 0.12600 |

20 | 0.09311 | 0.015900 | 0.12609 |

Regression | |||
---|---|---|---|

Model | MAE | MSE | RMSE |

SLR | 0.0939 | 0.0163 | 0.1277 |

PR | 0.0930 | 0.0158 | 0.1259 |

MLR | 0.0766 | 0.0119 | 0.1092 |

MLR with DR | 0.0679 | 0.009 | 0.093 |

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**MDPI and ACS Style**

Veeramsetty, V.; Mohnot, A.; Singal, G.; Salkuti, S.R.
Short Term Active Power Load Prediction on A 33/11 kV Substation Using Regression Models. *Energies* **2021**, *14*, 2981.
https://doi.org/10.3390/en14112981

**AMA Style**

Veeramsetty V, Mohnot A, Singal G, Salkuti SR.
Short Term Active Power Load Prediction on A 33/11 kV Substation Using Regression Models. *Energies*. 2021; 14(11):2981.
https://doi.org/10.3390/en14112981

**Chicago/Turabian Style**

Veeramsetty, Venkataramana, Arjun Mohnot, Gaurav Singal, and Surender Reddy Salkuti.
2021. "Short Term Active Power Load Prediction on A 33/11 kV Substation Using Regression Models" *Energies* 14, no. 11: 2981.
https://doi.org/10.3390/en14112981