# A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers

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## Abstract

**:**

## 1. Introduction

## 2. Integrated Assessing Approach

#### 2.1. Framework for HVDC Converter Transformer Condition Assessment

_{1}, P

_{2}, P

_{3}}. The factors are subdivided into indices. For instance, P

_{2}= {P

_{21}, P

_{22}, P

_{23}, P

_{24}, P

_{25}} represents the five indices selected in this paper, which are included in the DGA.

#### 2.2. Weight of Factors and Indices

Factors | P_{1} | P_{2} | P_{3} | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} |
---|---|---|---|---|---|---|---|---|

Weights | 0.3034 | 0.3760 | 0.3206 | 0.3475 | 0.3148 | 0.1348 | 0.1172 | 0.0858 |

Factors | Corresponding Index Weights |
---|---|

P_{1} | 0.20; 0.13; 0.27; 0.20; 0.20 |

P_{2} | 0.27; 0.13; 0.20; 0.20; 0.20 |

P_{3} | 0.18; 0.18; 0.18; 0.18; 0.12; 0.18 |

C_{1} | 0.15; 0.10; 0.15; 0.15; 0.15; 0.15; 0.15 |

C_{2} | 0.17; 0.17; 0.17; 0.17; 0.17; 0.17 |

_{i}, which represents the relative importance of sub-index, is obtained by the formula:

_{i}is the index that represents the value of variation. The initial static weight ω

_{i}is modified after ε

_{i}is calculated. According to [18], index weight ω

_{i}is modified in two ways. First, by allowing ω

_{i}to fulfill the requirements of the punishing formula, and second, by making it satisfy the requirements of the award formula. For condition assessment of HVDC converter transformer, the penalty formula is adopted to modify the index weights. The corresponding formula is as follows:

#### 2.3. Two-Dimensional Cloud Model (TDCM)

_{x}, entropy E

_{n}and hyper entropy H

_{e}[19]. Figure 3 illustrates the image of “about 20” TDCM.

#### 2.4. Overall Assessment Based on TDCM

_{ri}is the normalized value of index e

_{ri}(i = 1,2,…,n). Its values will be in the interval [0, 1], and n is the number of indices, X

_{rm}is the normalized value of an index, X

_{attention}is the attention value, which is decided by transformer tests and operation standards. X

_{ri}is the field testing data. When the indicator threshold is at the warning value, it should be converted to the attention value according to the following formula [11]:

_{warning}is the warning value which is decided by the transformer testing results and operation standards.

_{r}is the assessment result of the rth factor based on the TDCM method. Y

_{r}represents the index membership degrees of the rth factor, which can be seen in Figure 4. μ

_{ri}represents the weight of index e

_{ri}which belongs to the rth factor.

_{r}represents the weight of the rth factor. The overall TDCM assessment approach is implemented in Matlab.

## 3. Experimental Results

Test Dates | CH_{4} | C_{2}H_{6} | C_{2}H_{4} | C_{2}H_{2} | H_{2} | CO |
---|---|---|---|---|---|---|

20100120 | 17.3 | 0.5 | 14.0 | 2.4 | 7.1 | 300 |

20091102 | 14.0 | 4.3 | 13.1 | 2.5 | 2.1 | 183 |

20091020 | 15.4 | 3.7 | 16.0 | 2.3 | 6.0 | 215 |

Tested Items | Testing Dates (Year) | Change/% | |
---|---|---|---|

2008 | 2010 | ||

Resistance of winding (GΩ) | 130.69 | 132.07 | 1.06 |

Core insulation resistance (GΩ) | 6.16 | ||

Bushing capacitance (pF) | 1044.9 | 1054 | 0.87 |

Bushing dielectric loss | 0.460 | 0.577 | 25.43 |

Bushing insulation resistance (GΩ) | 154 |

Factors | Membership Value for Indices |
---|---|

P_{1} | 0.3110; 1.0; 0.8260; 0.0383; 1.0 |

P_{2} | 0; 0.9527; 0.7720; 0.9997; 0.9660 |

_{ij}calculated by TDCM is an uncertain value. Therefore, to enhance the credibility of the assessment, the fuzzy comprehensive assessment value C

_{i}(i = 1,2,…,N) are calculated repeatedly for N times under different conditions of membership. Finally, the average value is obtained by the formula:

Factors | ω_{r} | Corresponding Index Weights μ_{ri} |
---|---|---|

P_{1} | 0.4466 | 0.2088; 0.2000; 0.2498; 0.1414; 0.2000 |

P_{2} | 0.5534 | 0.0594; 0.2266; 0.0128; 0.3505; 0.3507 |

Factors | M_{r} | |||
---|---|---|---|---|

H_{1} | H_{2} | H_{3} | H_{4} | |

P_{1} | 0.5345 | 0 | 0.0855 | 0.1938 |

P_{2} | 0.9299 | 0 | 0 | 0.0594 |

M | Assessing Results | |||||
---|---|---|---|---|---|---|

H_{1} | H_{2} | H_{3} | H_{4} | |||

0.7533 | 0 | 0.0382 | 0.1194 | H_{1} |

_{1}, which reaches a very high value of 0.7533. The transformer condition is good and maintenance strategy is normal. However, the bushings of the transformer required immediate checking. The factual situation proves that the transformer operation is stable. After the examination, the junction box of bushing Tap 3.11 (No. M2141171) was found to be full of water. This can lead to serious internal corrosion of this bushing, necessitating replacement. This result coincides with the TDCM analysis presented in this paper.

## 4. Conclusions

- (1)
- The assessment index system, which includes the DGA, electrical testing, and oil testing data, is established to facilitate the approach.
- (2)
- An integrated approach based on TDCM and the entropy weights method was established to assess the condition of HVDC converter transformers.
- (3)
- The integrated approach can serve as an effective tool for the assessment of the condition of HVDC converter transformers, and the final evaluation provides valuable information for the provision of maintenance schemes.
- (4)
- Moreover, factors, such as the previous working history of the HVDC converter transformers and working states of the on-load tap-changer (OLTC), can be incorporated as parameters to assess the working states of HVDC converter transformers.

## Acknowledgments

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## Share and Cite

**MDPI and ACS Style**

Li, J.; He, Z.; Wang, Y.; Lv, J.; Zhao, L.
A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers. *Energies* **2012**, *5*, 157-167.
https://doi.org/10.3390/en5010157

**AMA Style**

Li J, He Z, Wang Y, Lv J, Zhao L.
A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers. *Energies*. 2012; 5(1):157-167.
https://doi.org/10.3390/en5010157

**Chicago/Turabian Style**

Li, Jian, Zhiman He, Youyuan Wang, Jinzhuang Lv, and Linjie Zhao.
2012. "A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers" *Energies* 5, no. 1: 157-167.
https://doi.org/10.3390/en5010157