# Digitalization of Distribution Transformer Failure Probability Using Weibull Approach towards Digital Transformation of Power Distribution Systems

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Failure-Rate Model

#### 2.2. Reliability Function

#### 2.3. Bathtub Curve

#### 2.4. Parametric Lifetime Models

#### 2.4.1. Exponential Distribution

#### 2.4.2. Weibull Distribution

#### 2.4.3. Other Parametric Distributions

#### 2.4.4. Goodness of Fit

#### 2.5. Reliability Indices

_{a(i)}U

_{i}

#### 2.6. Digitization, Digitalization, and Digital Transformation

## 3. Case-Study Methodology and Development

#### 3.1. Use of Case-Study Methodology

#### 3.2. Weibull Cumulative-Distribution Function and Reliability Function

#### 3.3. Methodology and Analysis

## 4. Results and Discussion

## 5. Conclusions

#### Future Works

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Graphical relationship between failure and fault for (

**a**) for discrete variables and (

**b**) continuous variables [19].

**Figure 2.**Bathtub-curve failure rate versus time [18].

**Figure 3.**Digital-transformation pyramid [16].

Apparent power (kVA) category | 100 | 160 | 250 | 400 | 630 |

Apparent power (kVA) category | 100 | 160 | 250 | 400 | 630 | 800 | 1000 |

Transformer Category | No. of Failures | Parameter | Point Estimate | Standard Error | Lower CI | Upper CI |
---|---|---|---|---|---|---|

11 kV to 400 V 100 kVA | 4 | Alpha | 11.4954 | 4.41194 | 5.41794 | 24.3902 |

Beta | 1.37384 | 0.555899 | 0.621607 | 3.0364 | ||

11 kV to 400 V 160 kVA | 3 | Alpha | 12.7236 | 3.20768 | 7.7628 | 20.8546 |

Beta | 1.48876 | 0.410304 | 0.86743 | 2.55515 | ||

11 kV to 400 V 250 kVA | 18 | Alpha | 20.573 | 2.40769 | 16.3562 | 25.8771 |

Beta | 2.10485 | 0.426645 | 1.41477 | 3.13153 | ||

11 kV to 400 V 400 kVA | 7 | Alpha | 22.1934 | 2.19919 | 18.2758 | 26.9508 |

Beta | 4.01613 | 1.28084 | 2.14951 | 7.50373 | ||

11 kV to 400 V 630 kVA | 3 | Alpha | 28.1318 | 3.12802 | 22.623 | 34.9819 |

Beta | 5.52089 | 2.44696 | 2.31601 | 13.1607 | ||

33 kV to 400 V 100 kVA | 37 | Alpha | 15.2267 | 1.41542 | 12.6905 | 18.2696 |

Beta | 1.8654 | 0.229805 | 1.46525 | 2.37485 | ||

33 kV to 400 V 160 kVA | 44 | Alpha | 16.3943 | 1.33623 | 13.9738 | 19.234 |

Beta | 1.9358 | 0.240369 | 1.51763 | 2.46919 | ||

33 kV to 400 V 250 kVA | 42 | Alpha | 17.9555 | 1.20517 | 15.7422 | 20.48 |

Beta | 2.41537 | 0.303852 | 1.88757 | 3.09075 | ||

33 kV to 400 V 400 kVA | 19 | Alpha | 15.2044 | 2.49815 | 11.0183 | 20.981 |

Beta | 1.46352 | 0.28023 | 1.00557 | 2.13002 | ||

33 kV to 400 V 630 kVA | 8 | Alpha | 16.9269 | 3082971 | 10.8641 | 26.3731 |

Beta | 1.62459 | 0.49219 | 0.897143 | 2.94189 | ||

33 kV to 400 V 800 kVA | 4 | Alpha | 10.4237 | 3.3206 | 5.5829 | 19.4618 |

Beta | 1.66328 | 0.639442 | 0.782936 | 3.53352 | ||

33 kV to 400 V 1000 kVA | 6 | Alpha | 16.7628 | 2.74205 | 12.1649 | 23.0986 |

Beta | 2.62885 | 0.880714 | 1.36332 | 5.06914 |

Beta Value | Alpha Value | Typical Failure Mode | Interpretation of Cause of Failure |
---|---|---|---|

>4 | Low compared with standard values for failed parts (less than 20%) | Old age, rapid wear-out (systematic, regular) | Poor machine/material design |

Between 1 and 4 | Low compared with standard values for failed parts (less than 20%) | Early wear-out | Poor system design |

Between 1 and 4 | Low | Early wear-out | Construction problem |

<1 | Low | Infant mortality | Production problems, design problems, misassembled, quality control, overhaul problems |

Between 1 and 4 | Between 1 and 4 | Less than manufacturer-recommended preventive maintenance cycle | Inadequate preventive-maintenance schedule |

Around 1 | Much less | Random failures with definable causes | Inadequate operating procedure |

Transformer Category | Log Likelihood | AIC | BIC | AD |
---|---|---|---|---|

11 kV to 400 V 100 kVA | −13.1355 | 42.2709 | 29.0435 | 2.91429 |

11 kV to 400 V 160 kVA | −26.59 | 59.5801 | 12.7236 | 2.25092 |

11 kV to 400 V 250 kVA | −65.1467 | 135.093 | 136.074 | 1.48386 |

11 kV to 400 V 400 kVA | −22.1699 | 51.3398 | 48.1316 | 2.2968 |

11 kV to 400 V 630 kVA | −9.18554 | NA | 20.5683 | 3.76559 |

33 kV to 400 V 100 kVA | −19.3341 | 46.6682 | 42.2517 | 2.17347 |

33 kV to 400 V 160 kVA | −151.298 | 306.889 | 310.165 | 0.627865 |

33 kV to 400 V 250 kVA | −141.136 | 286.58 | 289.747 | 0.655464 |

33 kV to 400 V 400 kVA | −67.2275 | 139.205 | 140.344 | 1.05074 |

33 kV to 400 V 630 kVA | −28.8044 | 64.0089 | 61.7678 | 1.92899 |

33 kV to 400 V 800 kVA | −12.2087 | 40.4173 | 27.1899 | 2.99284 |

33 kV to 400 V 1000 kVA | −19.3341 | 46.6682 | 42.2517 | 2.17347 |

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**MDPI and ACS Style**

Attanayake, A.M.S.R.H.; Ratnayake, R.M.C. Digitalization of Distribution Transformer Failure Probability Using Weibull Approach towards Digital Transformation of Power Distribution Systems. *Future Internet* **2023**, *15*, 45.
https://doi.org/10.3390/fi15020045

**AMA Style**

Attanayake AMSRH, Ratnayake RMC. Digitalization of Distribution Transformer Failure Probability Using Weibull Approach towards Digital Transformation of Power Distribution Systems. *Future Internet*. 2023; 15(2):45.
https://doi.org/10.3390/fi15020045

**Chicago/Turabian Style**

Attanayake, A. M. Sakura R. H., and R. M. Chandima Ratnayake. 2023. "Digitalization of Distribution Transformer Failure Probability Using Weibull Approach towards Digital Transformation of Power Distribution Systems" *Future Internet* 15, no. 2: 45.
https://doi.org/10.3390/fi15020045