Economic Life Prediction of Transformer Based on Repairing Profit and Decommissioning Profit

Transformer lifecycle management is an important research field that power grid enterprises pay great focus on. The economic life prediction of transformer can provide a basis for transformer equipment management and power grid planning, contribute to prolong the service time of transformer and improve the operation safety and economy of power grid. This paper proposes an economic life prediction model of transformer by analysing various economic factors of transformer and taking the maximum annual average net profit of transformer as the judging criterion, and achieves the economic life quantitative prediction of transformer by comparing the annual average net profit of repairing a transformer and the annual average net profit of decommissioning a transformer. Finally, a case study on the economic life prediction of transformer by selecting an 110kV transformer in service as an example is carried out according to the proposed model, and the results show that the proposed model can not only effectively analyse the economic factors of the transformer, but also reasonably predict the economic life of the transformer, which has a guiding significance for the decision-making of transformer management and the future planning of substation.


Introduction
The reliability of transformer is directly related to the safe operation of smart grid, and the power outage accident caused by transformer will probably bring about huge economic losses. At present, some transformers in power grid have been operating for more than 20 years and begin to enter the middle and late stage of the design life. Technically, these transformers can continue to be on service, but their failure probability will become higher and higher, which has a greater impact on the safe and reliable operation of the power grid. Economically, the operation and maintenance costs and failure probability of transformers will increase with the operation time increase and the component aging of transformer. Therefore, when to decommission these transformers to ensure the highest economic efficiency is an urgent problem to be solved. The economic life prediction of transformer is an effective method to solve the problem.
In order to make an objective life assessment of a transformer, it is necessary to clarify the life termination conditions of the transformer. Aiming at the large number of transformers in power grid, this paper selects the maximum annual average net profit as the judgement condition and presents an economic life predicting model of transformer by calculating the annual average net profit under two cases of repairing a transformer or decommissioning a transformer to help determine the economic life of the transformer and verifies the effectiveness of the proposed model with an actual case study.

Related Works
The equipment state analysis with various modern technologies has been widely researched to degrade the accident risk and improve traditional management methods. With the scale of power grid increasing, the power grid enterprises pay more focuses on the economy of equipment management [1]. The various economic information such as power supply income, operation and maintenance cost, failure repairing cost and environmental protection cost are both taken into consideration in the process of equipment lifecycle management [2]. In recent years, some research works begin to focus on the economic life evaluation of transformer [3][4][5]. Liu et al. consider that the decommissioning time of transformer is the time when its maximum annual average net income decreases to less than that of a new equipment [6]. Most of the calculation equations used in this work are empirical equations, which do not make full use of the historical information of transformers. With the technology development of online monitoring and asset management, the increase of transformer life data provides a good basis for the economic life study of transformer in power grid enterprises.
The economic life management of transformer has developed into an interdisciplinary, comprehensive and systematic subject [7]. In fact, with the advancement of digitalization power grid and the intensification of market competition, more and more attention has been paid to the economic life accurate evaluation of power transmission and transformation equipment. Therefore, broadening the research field of equipment renewal of power grid enterprises and proposing equipment renewal theories and methods suitable for the needs of power grid enterprises are not only of far-reaching theoretical value, but also of great practical significance [8].

Repairing Profit and Decommissioning Profit-Based Transformer Economic Life Prediction
The Testing of Transformer  Figure 1. Repairing profit and decommissioning profit-based transformer economic life prediction. To predict the economic life of transformer based on repairing profit and decommissioning profit, the relevant economic factors of transformer should be firstly analysed, and then the repairing profit and decommissioning profit of transformer can be calculated by considering synthetically the revenue and cost of transformer in different operation stages. When the decommissioning profit is bigger than the repairment profits, the economic life of transformer will be ended.

Economic Factors Analysis
The economic factors related to transformer include power supply income, operation and maintenance cost, accident risk cost, generalized depreciation cost, failure repairing cost, etc. The power supply income mainly refers to the income that is brought by a transformer by providing electric energy services. The operation and maintenance cost mainly include the expenses of energy consumption, daily maintenance, etc. The energy consumption expenses come from two parts: main equipment and auxiliary equipment, the daily maintenance expenses refer to the expenses of components, materials, labour and others for daily maintenance. The accident risk cost refers to the direct and indirect losses caused by a transformer accident such as outage loss, accident processing expense and social responsibility loss. The generalized depreciation cost refers to all one-time investment of a transformer from commissioning to decommissioning, including equipment purchase expense, installation and commissioning expense, decommissioning expense, decommissioning residual value and other fees. The failure repairing cost mainly includes repairing expense and downtime loss.

Model Premise Assumptions
To simplify the model without losing its generality, the following assumptions are put forward based on the investigation and analysis of various operational experience data: i. The operation and maintenance cost will increase linearly with the service age increasing.
ii. The repairing time will increase linearly with the service age increasing.
iii. All transformers have a basic failure probability curve. iv. Repairing the failure of a transformer can reduce the failure probability, but the reduction magnitude of the failure probability first increases and then decreases with the service age increasing, which can be specifically described by the equation (i) and (ii).
In the equation (i) and (ii), λ(t) is the failure probability before the repairing at time t, Δλ(t) is the reduction magnitude of the failure probability made by the repairing at time t, λ'(t) is the failure probability after the repairing at time t.
v. The failure probability after repairing will start from a new base point, but still follow the same curve. Assuming that the current time is t0, a transformer will be repaired at a certain time t after t0. According to the above assumption iv, the failure probability and the various costs will decrease after the repairing. According to the above assumption v, we can get the failure probability curve as shown in Figure 2 (1) In the equation (1), ξ is the contribution rate of the transformer in the whole power supply chain, S is the capacity of the transformer, η is the average load rate of the transformer, ΔP is the price difference between power purchase and power sale.

Operation and Maintenance
Cost. The operation and maintenance cost of a transformer can be calculated with the following equation: In the equation (2), P0 is the energy loss of the transformer with empty load, PK is the energy loss of the transformer with some load,  is the average load rate of the transformer,  is the annual loss rate, p1 is the unit power cost paid by the transformer owner. (P 0 +η 2 ×P K )×p 1 ×μ(t+Δt-t 0 )×8760 is the annual energy loss of the transformer. COb is the annual basic maintenance expense, which can be obtained according to the relevant statistical data. α1 is the linear coefficient of the maintenance expense increasing with the service age of the transformer. CO b × ∫ (1+a 1 t)dt t+∆t t 0 is the maintenance expense of the transformer.

Accident Risk Cost.
The following equation can be used to determine the accident risk cost of a transformer: is the economic loss when a transformer accident occurred and mainly includes load removing expense, accident repairing expense and personal injury compensation. S is the capacity of the transformer, cosφ is the average power factor of the transformer,  is the average load rate of the transformer, tr is the failure repairing time of the transformer, F is the load removing probability under a sudden transformer failure. θ is the value of unit power consumption. The correction factor of system accident risk includes mainly the importance of substation β11, the importance of load β12 and the importance β13 of repairing environment. Their values are listed in Table 1. S×cosφ××tr×F×θ×(β11× β12×β13) is the load removing expense of the transformer under repairing. Cf represents the statistical average value of the accident repairing expense that can be obtained according to expert experiences. The correction factor of the accident repairing expense includes mainly the influence of transformer manufacturer address β21 and the influence of transformer maintenance environment β22. Their values are listed in Table 2. Cf×(β21×β22) is the accident repairing expense. Si(i=1,2,3) represents the compensation expenses corresponding to three levels of personal injury: slight injury, serious injury and death. ri(i=1,2,3) represents the probability that a person is slightly injured, seriously injured or dead with taking the values of 2%, 0.5% or 0.1%. ∑ S i ×r i

Generalized Depreciation Cost.
According to the definition of generalized depreciation cost, its calculation equation is shown as follows: In the equation (4), CIE+CII+CIO is the initial investment expense of a transformer, including purchase expense CIE, installation and commissioning expense CII, and other related expenses CIO. CID×CCR-CDR is the decommissioning expense of a transformer that mainly includes scrapping expense and residual income. The scrapping expense CID×CCR refers to the expenses of dismantling and transporting a scrapped transformer and labor charges, the residual income CDR is the recycling income of an out-of-service transformer. Crc is the outage loss caused by changing an old transformer with a new transformer, and Tdl is the design life of a transformer provided by the manufacturer.  (5), CM1 is the failure repairing cost that mainly includes repairing expense and downtime loss. α2 is the linear coefficient of the repairing cost increasing with the service age of the transformer and generally takes 0.005 as the default value, t is the service age of the transformer, Cb is the basic expense of a single repairing, (1+α2t)×Cb is the repairing expense at time t. tb is the basic overhaul time, α3 is the linear coefficient of the repairing time increasing with the service age of the transformer and generally takes 0.02 as the default value, (tb+α3t)(S×∆p×0.02 is the downtime loss. In summary, the cost sum of a transformer under the condition of repairing is shown as follows: C 1 =CO 1 +CR 1 +CD 1 +CM 1 (6) The corresponding annual average net profit of a transformer under repairing:

The Annual Average Net Profit Model of Transformer under Decommissioning
For the case of directly replacing an old transformer with a new one, assuming that the current time is t0 and an old transformer is replaced at time t, the annual average net profit model of a transformer under decommissioning needs to know all income and cost factors during the period between t0 and t.

Power Supply Income.
The power supply income is mainly related to load rate and price difference between power purchase and power sale, and shown as follows: I p2 =ξ×S×η×ΔP×(t-t 0 ) (8) In the equation (8), all parameters have the same meaning as the equation (1).

Operation and Maintenance
Cost. The operation and maintenance cost of a transformer under decommissioning can be calculated with the following equation: In the equation (9), (P 0 +η 2 ×P K )×p 1 ×μ×(t+Δt-t 0 )×8760 is the annual energy loss of the transformer, and CO b × ∫ (1+a 1 t)dt t+∆t t 0 is the maintenance expense of the transformer. In the above three equations, all parameters have the same meaning as the equation (2).

Accident Risk
Cost. The accident risk cost of a transformer under decommissioning can be calculated with the following equation that has the same parameters as the equation (3): In the equation (11), each parameter has the same meaning as the equation (6), but the transformer design life Tdl is replaced by t.
In summary, the cost sum of a transformer under the condition of decommissioning is shown as follows: C 2 =CO 2 +CR 2 +CD 2 (12) The corresponding annual average net profit of a transformer under decommissioning:

The Economic Life Judging of Transformer
In order to objectively analysing the life of transformer, it is necessary to clarify the life termination conditions of transformer. For transformers, this paper takes the maximum annual average net profit of a transformer as the termination condition of its life. Two cases need to be considered during the economic life predicting of transformer: the transformer will be repaired when a failure occurred or the transformer will be decommissioned when a failure occurred.
If P1>P2, it means that the annual average net profit obtained by selecting the repairing plan is bigger, so it is better to repair the failure of transformer.
If P1<P2, it means that the average annual net income obtained by selecting the decommissioning plan is bigger, so it is better to replace the old transformer.

The Case Study
Taking a 110kV and 31.5 MVA transformer in a substation as an example to evaluate its economic life with the above models. The nameplate number of the transformer is SFSZ8-31500/110, and the economic life-related data are shown in Table 3. According to the above hypothesis, we can get the

The Annual Average Net Profit of the Example Transformer under Repairing
According to the data listed in Table 3, the power supply income of the example transformer under repairing is shown as follows: I p1 =1655640×(t+∆t-t 0 )