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Reasonable probability assessment of transformer failure rate (FR) is a critical reference to the transformer replacement work. At present, the lack of support theory for transformer replacement usually causes reliability and economy issues for power companies. For this reason, a transformer replacement decision method based on probability assessment of FR is proposed. Firstly, a first order model of transformer paper degradation is proposed. Then, the Weibull Distribution is used by Monte Carlo Simulation (MCS) to generate the variations of Degree of Polymerization (DP) along with time based on the historical data, and the transformer FR is determined. When the FR is higher than a pre-defined threshold value, the transformer should be replaced for reliability purpose. Finally, the effectiveness of the proposed method for the transformer replacement decision is verified by a typical engineering application.

The safe operation of power transformer is one of the important defenses to the reliability operation of power system. In order to ensure the transformer always works under a healthy operation status, it is critical to assess the failure rate (FR) of transformer and replace the old on eat a most suitable time [

At present, there usually exists two extremes in the replacement of transformer. On the one side, the old transformer in service always working exceeds its service life limitation, which may lead to a high maintenance cost. On the other side, frequently replace transformer in pursuit of the high performance of new transformers will definitely results in unnecessary waste. The old transformer still occupies a large proportion in power system at the present time, and the replacement work is very urgent. Therefore, considering the relationship between the healthy status and service life of transformer, it is critical to determine a transformer replacement decision method for providing the scientific basis for the power enterprises to carry out technology reconstruction of power transformer.

A lot of studies have already been carried out in this area. In refs [

For this reason, a transformer replacement decision method based on probability assessment of FR is proposed. A first order model of transformer paper degradation is used to depict the mathematical relationship between service life and FR, and the Weibull Distribution is used to generate the variations of Degree of Polymerization (DP) by Monte Carlo Simulation (MCS) along with time. The transformer FR is then determined. When the FR is higher than a pre-de- fined threshold value, the transformer should be replaced for high reliability purpose.

Transformer is composed of iron core, high and low voltage windings, major insulation, dielectric oil, oil tank, and drive pipe, etc. According to the refs [

where DP(t) is the DP value at time t; DP(t_{0}) is initial value of DP; E_{a} is the initial aging activation energy of insulating paper; A is the gas constant; T(t) is the absolute temperature varying with time, which is set to be 370 K in this paper.

When E_{a} = 110.942 kJ/mol, R_{g} = 8.314, DP(t_{0}) = 1000, A = 2 × 10^{8}, and T = 370 K, the ideal DP curve changes with time is shown in

As depicted in

lower than the joint stress (DP_{F}), the breakdown of the insulation paper will lead to the failure. At the same time, in the actual operation process, the life of the transformer will face a variety of uncertainties (also called unexpected stress), such as electrical stress, mechanical stress, thermal stress and chemical stress, which will significantly impact the insulation strength, just as shown in

It can be seen that under the normal condition, the insulation strength decreases with time. When the insulation strength is equal to the normal stress, the service life of the transformer is terminated. When suffered from some unexpected stresses, the insulation strength of the transformer is significantly reduced, which may lead to the reduction of the service life. Therefore, it is necessary to simulate the random effects of the unexpected stress on the insulation strength for replacement of old transformers.

The Weibull distribution is widely used to reflect the equipment failure rate changes with service age [

where

Weibull distributionin (4). Then the fitted Weibull distribution function is used by MCS to generate ΔD a teach specific time.

The steps of the proposed replacement decision method based on probability assessment of failure rate are given as follows:

Step 1: Set the Monte Carlo simulation times as N. The iteration time icount = 1. The initial prediction time is t_{0}. The aim is to predict the future service life of the transformer within n days. The simulation changing step is set to be 1 day. The transformer fault statistical vector is given in (5)

where n is the forecast time period; inum_{ti} = 0, when t_{i} = t_{0}, (t_{0} ≤ t_{i} ≤ n).

Step 2: The transformer statistical data of ΔD is fitted by the Weibull distribution with the corresponding scale and shape parameters using (4) at time t_{i}.

Step 3: The fitted Weibull distribution at time t_{i} is used to generate ΔD_{ti} (the ΔD for iteration time icount at time t_{i}).

Step 4: Using the value D_{ti} in _{i}, the DP value at time t_{i} in the icount interation (DP_{ti} = D_{ti} − ΔD_{ti}) is determined. If DP_{ti} ≤ DP_{F}, The expected service life (t_{f}) of the transformer is obtained (t_{f} = t_{i}), and the corresponding failure times at t_{i}, inum_{ti} = inum_{ti} + 1. Then, renew the iteration time icount = icount + 1. Go to step 5. Otherwise, t_{i} = t_{i} + Δt, and go to step 2.

Step 5: if icount ≤ N, go to step 2. Otherwise, go to step 6.

Step 6: According to inum, the fault ratecurve of the transformer changing with time is determined. For a specific time t_{i}, the fault ratep_{f_ti} = inum_{ti}/N, which is used to determine the service life of the transformer.

Step 7: Set the failure probability threshold (p_{fc}) for determining the service life of transformer. If p_{f_ti} ≥ p_{fc}, the transformer is considered to be replaced and reaches the termination of its service life.

In order to verify the validity of the method proposed in this paper, a distribution transformer in a power supply company was used as a test case, and the simulation parameters are shown in

Parameters | Value |
---|---|

N | 50,000 |

E_{a} | 110.94 kJ/mol |

R_{g} | 8.314 |

T | 370 K |

DP(t_{0}) | 1000 |

A | 2 × 10^{8} |

DP_{F} | 250 |

The comparison results of DP variation between the normal and unexpected stress conditions are given in _{F} = 250 days.

According to the method proposed in this paper, the failure rate in the last 25 days before the end of service life was analyzed. As seen in

25 days, the failure rate of the transformer is continuously increasing. At the end of day 1979, the failure rate is gradually approaching to 100%. It can be considered that the service life of the transformer is terminated, and the transformer should be replaced.

The service life of a transformer is significantly influenced by unexpected stresses. As a result, it is of great practical value to put forward a decision method for transformer replacement, in order to guide the transformer technical transformation process. For this reason, a transformer replacement decision method based on probability assessment of FR is proposed. A first order model of transformer paper degradation is firstly proposed. The Weibull Distribution is used by MCS to generate the variations of DP along time based on historical data, and the transformer FR is determined. When the FR is higher than a pre-de- fined threshold value, the transformer should be replaced for reliability purpose. Case studies show that the method can effectively identify the influences of various uncertainties on the service life of transformer, and improve the technical level and economic benefit of power company, which has a good engineering application prospect.

This work was supported by the project: Research on key techniques to the design of smart substation in Tianjin (KJ15-1-08).

Liang, G., Li, S.W., Qi, Y., Cao, J., Hao, Y. and Chen, W.F. (2017) A Transformer Replacement Decision Method Based on Probability Assessment of Failure Rate. Energy and Power Engineering, 9, 748-755. https://doi.org/10.4236/epe.2017.94B080