# The Correlation of Transformer Oil Electrical Properties with Water Content Using a Regression Approach

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Work

#### 2.1. Experiment Preparation

#### 2.2. Method of Physical Treatment

## 3. Correlation and Regression Analysis

- b(i) is the vector containing the regression model parameters a and b;
- x(i) are the water content values;
- y(i) are the experimental values of each electrical property; and
- f(b(i),x(i)) is the exponential given in Equation (1).

- y${}_{i}$ are the experimental values of each electrical property,
- $\widehat{{y}_{i}}$ are the correlated values obtained by the regression analysis for each electrical property,
- and
- $\overline{{y}_{i}}$ are the mean of the six test values for each point.

## 4. Results and Discussion

#### 4.1. Breakdown Voltage

#### 4.2. Resistivity

#### 4.3. Dielectric Dissipation Factor

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**SESCO physical treatment mobile station (1, Degassing chamber, 2, Electric heater bloc, 3, Filtration oil system, 4, Control unit).

Property | Standard | Unit | New Sample | Regenerated Sample | Used Sample |
---|---|---|---|---|---|

Acidity | IEC 62021 | mg KOH/g | 0.012 | 0.03 | 0.21 |

Water content | IEC 60814 | ppm | 23.4 | 31.59 | 69 |

tan $\delta $ (×10${}^{-4}$) (90 ${}^{\circ}$C) | IEC 60247 | — | 27 | 31.15 | 1832 |

Permittivity | IEC 60247 | — | 2.11 | 2.12 | 2.19 |

Resistivity (90 ${}^{\circ}$C) | IEC 60247 | G$\mathsf{\Omega}$·m | 200 | 153.2 | 1.353 |

Breakdown voltage | IEC 60156 | k V | 42.3 | 33.6 | 18.4 |

Viscosity (40 ${}^{\circ}$C) | ISO 3104 | mm${}^{2}$/s | 6.78 | 6.78 | 9.91 |

Density (20 ${}^{\circ}$C) | ISO 3675 | g/mL | 0.875 | 0.875 | 0.862 |

Color index | ISO 2049 | — | <0.5 | 0.5 | 5 |

The Oil Sample | The Exponential Model BDV = a·exp$(\mathit{b}\xb7\mathit{WC})$ + c·exp$(\mathit{d}\xb7\mathit{WC})$ | R${}^{2}$ | SS |
---|---|---|---|

New | BDV = 437·exp$(-0.9676\xb7WC)$ + 60.71·exp$(-0.0144\xb7WC)$ | 99.24% | 11.43 |

Regenerated | BDV = −5.85 × 10${}^{5}$·exp$(-0.0607\xb7WC)$ + 5.851 × 10${}^{5}$·exp$(-0.0607\xb7WC)$ | 92.05% | 62.94 |

Used | BDV = 75.56·exp$(-0.09457\xb7WC)$ + 23.44·exp$(-0.003706\xb7WC)$ | 99.77% | 1.33 |

**R**

**${}^{2}$**: residual sum of squares or correlation coefficient,

**S**

**S**: sum of squares.

The Oil Sample | The Exponential Model $\mathit{\rho}$ = a·exp$(\mathit{b}\xb7\mathit{WC})$ + c·exp$(\mathit{d}\xb7\mathit{WC})$ | R${}^{2}$ | SS |
---|---|---|---|

New | $\rho $ = 6.49 × 10${}^{6}$·exp$(-3.548\xb7WC)$ + 263.1·exp$(-0.01124\xb7WC)$ | 98.38% | 371.58 |

Regenerated | $\rho $ = −5.038 × 10${}^{5}$·exp$(0.02811\xb7WC)$ + 5.041 × 10${}^{5}$·exp$(0.02811\xb7WC)$ | 90.25% | 1.1406 × 10${}^{3}$ |

Used | $\rho $ = 0.2096·exp$(-0.004624\xb7WC)$ + 1.199·exp$(2.546\times {10}^{-5}\xb7WC)$ | 95.59% | 6.4305 × 10${}^{-5}$ |

The Oil Sample | The Exponential Model tang$\mathit{\delta}$ = a·exp$(\mathit{b}\xb7\mathit{WC})$ + c·exp$(\mathit{d}\xb7\mathit{WC})$ | R${}^{2}$ | SS |
---|---|---|---|

New | tang$\delta $ = 24.36·exp$(0.004135\xb7WC)$−3.369 ×${}^{7}$·exp$(-4.813\xb7WC)$ | 95.55% | 7.4048 |

Regenerated | tang$\delta $ = 9.508 × 10${}^{4}$·exp$(0.003997\xb7WC)$−9.506 × 10${}^{4}$·exp$(0.003994\xb7WC)$ | 91.16% | 7.2310 |

Used | tang$\delta $ = 17.71·exp$(0.0005016\xb7WC)$−7.414·exp$(0.9475\xb7WC)$ | 99.25% | 0.0444 |

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**MDPI and ACS Style**

Abdi, S.; Harid, N.; Safiddine, L.; Boubakeur, A.; Haddad, A.
The Correlation of Transformer Oil Electrical Properties with Water Content Using a Regression Approach. *Energies* **2021**, *14*, 2089.
https://doi.org/10.3390/en14082089

**AMA Style**

Abdi S, Harid N, Safiddine L, Boubakeur A, Haddad A.
The Correlation of Transformer Oil Electrical Properties with Water Content Using a Regression Approach. *Energies*. 2021; 14(8):2089.
https://doi.org/10.3390/en14082089

**Chicago/Turabian Style**

Abdi, Sifeddine, Noureddine Harid, Leila Safiddine, Ahmed Boubakeur, and Abderrahmane (Manu) Haddad.
2021. "The Correlation of Transformer Oil Electrical Properties with Water Content Using a Regression Approach" *Energies* 14, no. 8: 2089.
https://doi.org/10.3390/en14082089