Economic Life Assessment of Power Transformers ... - IEEE Xplore

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CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 3, SEPTEMBER 2015

Economic Life Assessment of Power Transformers Using an Improved Model Jiyu Wang, Ruijin Liao, Yiyi Zhang, and Fanjin Meng

Abstract—The electric power enterprise devotes considerable attention to the reliability of power transformers particularly when it decides to either maintain these transformers or decommission them altogether from operation. Although this process has reduced the risk of transformer faults, the attendant dilemma is of excessive maintenance of transformers, or retiring them prematurely, leading to high economic waste. This paper is inspired by real-time engineering applications, and proposes an improved model to assess the economic life of power transformers. The new model offers a more efficient approach than previous methods of assessment, with a specific focus of using the annual net income as separate criteria for determining the economic indices of continuous operation, overhaul, and retirement strategies of transformers. The economic life of power transformers is divided into three sections according to different strategies to better resolve the quantification problem in this field. A case study is provided to prove the feasibility and validity of the proposed economic life model. The case study achieves the fine management goal when the electric power enterprise is required to make the maintenance and retirement strategy decision. Index Terms—Economic life model, retirement strategy, power transformer.

maintenance

and

I. INTRODUCTION

P

OWER transformers that have been in operation for over 20 years in the state grid are slowly approaching the end of their lifetime service [1]. These aged transformers may continue to serve technically; however, the safety and reliability of the power system is threatened due to the deterioration of power transformer insulation systems, and the high cost of operation and maintenance that increases over time, resulting in high risk costs [2]. Therefore, the problem of improper maintenance or premature retirement of power transformers is an ongoing research focus in the electrical power industry. Currently, most transformers are replaced based on service time. Parts of transformer that are performing well are retired in advance due to ignorance of their economic performance, Manuscript received February 10, 2015; revised May 12, 2015; accepted July 3, 2015. Date of publication September 30, 2015; date of current version July 29, 2015. This work was supported by the Funds for Innovative Research Groups of China (51021005). J. Y. Wang and R. J. Liao are with the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China (e-mail: jiyu [email protected]; [email protected]). Y. Y. Zhang is with the Electrical Engineering College of Guangxi University, Nanning 530004, China (e-mail: [email protected]). F. J. Meng is with the Tangshan Power Supply Company, Tangshan 063000, China (e-mail: [email protected]). Digital Object Identifier 10.17775/CSEEJPES.2015.00037

which in turn leads to enormous economic losses. Thus, in order to maximize the lifetime of transformers and to ensure their operational reliability, it is necessary to assess the economic life of transformers [3]–[6]. In current practice, there is not yet a unified assessment criterion to determine a power transformer’s economic life since very little research has been devoted to this area. Reference [7] has proposed a method for evaluating the economic life of power transformers that take into consideration many factors such as energy cost, social benefits and environmental benefits. It then evaluates the economic life quantitatively using an optimized index of a synthesis of economic benefits. Reference [8] divides the economic life model into two modes— a dynamic mode, which considers the time value of money, and a static mode, which does not. The dynamic mode is suitable for assessing long-term device investment strategies. Reference [9] analyzes the economics based on the operation range of transformer distributions for load adjustment and load distribution, and then proposes a load adjusting method by reducing peaks and filling up valleys. However, these works have limitations in engineering applications, because they only consider the device’s economic benefits in particular cases, and fail to conclude an economic assessment index system for power transformers. In [10] Liu analyzes the economic factors of power transformers, and establishes an economic life model based on a maintenance and retirement strategy for power transformers, which has seen favorable engineering applicability. However, accurate and efficient assessment is still a challenge due to the imperfect analysis of economic factors, which is why an economic life model based on continuous operation should be set up for comparison purposes. In this study, the economic life model of a power transformer is further analyzed. A new economic life model based on continuous operation is proposed, and more factors such as operation energy cost, system load shedding cost, fault recovery cost—all are taken into the index system. The improved economic life model complies better with the requirements of engineering applications, and is of optimal use for power transformers. The model can also provide practical value to raising the economic efficiency of the power grid while improving the management of electrical equipment. II. M ODEL E STABLISHMENT A. Factors of Economic Life The remainder life of power transformers consists of their insulation life, reliability life, and economic life. While the

c 2015 CSEE 2096-0042

WANG et al.: ECONOMIC LIFE ASSESSMENT OF POWER TRANSFORMERS USING AN IMPROVED MODEL

former two parts can be specifically assessed [11]–[14], the economic life, which is a game between revenue and cost, is difficult to assess. The common method for economic life assessment is comparing the revenue and the cost of transformers in a given period, accompanied by a retirement strategy that is acceptable only if the revenue is less than the cost in that period. Many factors must be taken into consideration in the assessment of transformer revenue and cost, making the process both subjective and random. As such, a relevant economic life model needs to be established for quantifying the various factors before the economic life assessment. The indices in the model should be consistent with the actual situation in order to satisfy the requirements of accuracy and applicability. Since there is no agreed upon index system available for economic life assessment, this paper will establish an index system for the economic life assessment of power transformers on the basis of [10], [15], as shown in Fig. 1. The revenue of power supply The operation maintenance cost Continuous operation

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transformer needs to be retired immediately. The assessment procedure is adopted as follows (Fig. 2): First, relevant economic indices of the transformer are analyzed. Second, the fault probability curve of the operational power transformer is simulated, and then benefits and cost of different strategies in the given period are calculated. Finally, the net income of each strategy is compared to obtain the economic life.

Transformer economic life

Indies analysis

Economic life model

Basic assumption

Load condition

Continuous operation

Overhaul

Retirement

Annual net income 1

Annual net income 2

Annual net income 3

The fault risk cost

Economic life assessment

The generalized depreciation cost The revenue of power supply

Fig. 2. Assessment procedure of transformer economic life.

The operation maintenance cost Index system of transformer economic life

Overhaul

The fault risk cost The generalized depreciation cost The overhual cost The revenue of power supply The operation maintenance cost

Retirement The fault risk cost The generalized depreciation cost

Fig. 1. Assessing index system of transformer economic life.

The index system is comprised of three sections: continuous operation, overhaul, and retirement. Each model comprises revenue of power supply, operation and maintenance costs, fault risk costs, and generalized depreciation costs, whose value varies with different models. In addition, the overhaul cost is considered independently in the overhaul model [16], [17]. B. Assessment Procedure In this section, the transformer economic life is divided into three sections. The indices in the respective strategies are analyzed and benefits during different periods are calculated to obtain the economic life. It is assumed that the transformer’s economic life begins to decline when the overhaul benefits outweigh the benefits of continuous operation; it is also assumed that the end of the economic life occurs when retirement benefits are greater than overhaul benefits. This means that the

C. Basic Assumptions To simplify the model without loss of generality, the following basic assumptions are proposed through an analysis of existing operating data [18]. 1) The fault probability curve of power transformers can be calculated. 2) Overhaul can decrease the fault probability of power transformers. As shown in Fig. 3, the amplitude change increases first and then decreases as the operating time extends. 3) The annual preventive maintenance cost of the transformers increases linearly with the operating time. 4) Time consumption in terms of the overhaul increases linearly with the operating time. 5) The overhaul cost increases linearly with the operating time. 6) After the overhaul, the fault probability decreases to a new point, and then follows the same fault probability curve as before.

III. A NNUAL N ET I NCOME IN C ONTINUOUS O PERATION M ODEL Assuming the current moment t0 , the transformer continues to operate at some moment t after t0 . Then, we can calculate the net income in this period.


Decrease Rate of Fault Probability (%)

70

C. Fault Risk Cost

1.0

0.4

Since the transformer is a core equipment in the power system, a fault here can easily induce a fault in other connected electrical equipment, leading to even accidents. The risk assessment can be written as follows:

0.2

CR1 = LOT F · λ(t)

0.8 0.6

where CR1 is the risk value of the transformer (Yuan), λ(t) is the occurrence probability of transformer fault, LOTF is the economic losses of transformer fault, including system load shedding cost, fault recovery cost, personnel security cost, and environmental cost.

0.0 0

5

10

15

20 25 30 Service Age (year)

35

40

45

50

Fig. 3. Influence of maintenance on the probability of failure.

LOT F = Loss1 + Loss2 + Loss3 + Loss4 .

A. Revenue of Power Supply The revenue of power supply comes from the benefits of electricity selling. This is primarily related to the load factor in the period and the price difference of electricity, which can be expressed by: IP1 = ξSη∆p(t − t0 )

(1)

where ξ indicates the contribution rate of power transformers throughout the power supply chain. ∆p is the price difference of electricity. S is the capacity of power transformers. η is the average load factor of power transformers. B. Operation Maintenance Cost The operation maintenance cost is the sum of all the costs during the entire transfomer life cycle, which can be estimated as follows: CO1 = COe1 + COm1 (2) where COe1 is the energy consumption cost of the transformer and COm1 is the preventive maintenance cost, including labor cost, environmental cost, maintenance fees, and so on. 1) Energy Consumption Cost COe1 : Energy consumption cost mainly refers to the loss of the transformer. According to the calculation method in [19], energy consumption cost COe1 can be defined as follows: COe1 = (P0 + η 2 PK )p1 µ(t − t0 )8760

(3)

where P0 indicates the no-load loss of power transformers (kW). PK indicates the load loss of power transformers (kW). η is the average load factor. µ is the annual load loss rate, which here takes 0.608 [19]. p1 is the purchase price per unit of electricity paid by users (Yuan/kWh). 2) Preventive Maintenance Cost COm1 : Based on assumption 3), the preventive maintenance cost COm1 can be estimated as follows: Zt (1 + α1 t)dt

COm1 = COb

(5)

(4)

t0

where COb is the annual basic maintenance cost obtained from statistical data. α1 is the linear dependent coefficient between the maintenance cost and the age growth, which here takes 0.004.

(6)

Loss1 , Loss2 , Loss3 , and Loss4 are the system load shedding cost, the fault recovery cost, the cost of personnel security risk and the cost of environmental impact respectively. Once a transformer breaks down, the loss of the system load shedding can be expressed by: Loss1 = SF θηβ1 tr cos ϕ

(7)

β1 = β11 β12 β13

(8)

where S indicates the transformer capacity. cos ϕ is the average power factor, here takes 0.9. η is the load factor of transformer. F is the probability of load shedding in the sudden fault, here takes 0.05. tr is the mean time to repair. θ is the value at risk per unit of electricity, here takes 10,472.1 Yuan/MWh. β1 is the corrected parameters of system risk, including the significance of substation β11 , the significance of transformer load β12 and the factor of maintenance environment β13 (shown in Table I). The fault recovery cost includes material cost, manual work cost, and other expenses. The average fault recovery cost can be estimated as follows: Loss2 = Cf β2 β2 = β21 β22

(9) (10)

where Cf indicates the statistical fault recovery cost, according to the expert advice. β2 is the corrected parameters of repair cost, which consists of the factor of manufacturer β21 and the factor of maintenance environment β22 (shown in Table I). The personnel security risk refers to the personal injury caused by fault. The severity can be assorted by the levels of minor injury, serious injury and death, and can be expressed as follows: 3 X Loss3 = Si ri (11) i=1

where Si (i = 1, 2, 3) indicates the fault cost at different severity levels, and takes 50,000 Yuan, 100,000 Yuan, 500,000 Yuan respectively. ri (i = 1, 2, 3) presents the different probability, and takes 2%, 0.5%, and 0.1% respectively. The cost of environmental impact means the risk cost of environmental pollution such as oil leaking, emission of CO2 and other poisonous gas after a transformer fault. The risk cost can be estimated by the statistical data combined with expert advice.


The corresponding annual net income is shown as follows:

TABLE I C ORRECTED PARAMETERS OF S YSTEM R ISK AND R EPAIR C OST Factors Significance of substation Significance of transformer load Maintenance environment Manufacture

The Selection of Corrected Parameters Load-center substation: β11 = 1.16. Connection substation: β11 = 1. Terminal substation: β11 = 0.8. Critical load: β12 = 1.16. Moderate load or default: β12 = 1. Outdoor substation: β13 , β22 = 1. Indoor substation: β13 , β22 = 1.16. Local: β21 = 0.9; Domestic: β21 = 1. Overseas: β21 = 1.3.

Finally, the fault risk cost can be concluded as follows: Zt λ(t)dt · LOT F

CR1 =

(18)

Assuming the current moment t0 , the transformer will be overhauled at some moment t after t0 . The fault probability and the risk cost will decrease after the overhaul based on assumption 2). The fault probability, which follows the origianl curve will increase to λ(t) after ∆t based on assumption 6), which means the related period, is extended from t − t0 to t + ∆t − t0 (shown in Fig. 4). Then, we calculate the net income in this period. Fund

Cost

Δt

Income

The generalized depreciation cost refers to the entire disposable investment of the transformer during its lifetime. It comprises equipment investment cost, installation cost, decommissioning disposal cost, retired residual, and other expenses; the expression can be presented as follows: t − t0 CD1 = (CI + CD + Crc ) (13) Td where CI is the initial investment cost, which consists of equipment procurement cost, installation cost and other expenses. CD is the decommissioning cost, which involves the disposal cost and residual value. Crc indicates the loss of outage in the period of the equipment replacement. Td is the designed life of the transformer, provided by the manufacturer. The initial investment cost can be estimated using engineering methods as follows:

t0

(15)

where the CDT is the disposal cost, which means the cost of dismantlement, transportation, and labor. CDR is the residual value based on the equipment procurement cost, which approximately equals 5% of the equipment procurement cost [16]. CDT can be calculated as follows: (16)

t

t +Δt

Time X䖤

Fig. 4. Cost income analysis of overhaul case.

A. Revenue of Power Supply The total revenue of power supply in the period after overhaul can be expressed by:

(14)

where CI E is the equipment procurement cost. CI I is the installation cost, and CI O presents the spare cost in the initial investment, which comprises the employee training cost, the debugging cost of special projects, and the cost of the condition monitoring devices. The decommissioning cost is expressed as follows:

CDT = CII · CCR

IP1 − C1 . t − t0

IV. A NNUAL N ET I NCOME M ODEL IN OVERHAUL

Y䖤

D. Generalized Depreciation Cost

CD = CDT − CDR

W1 =

(12)

t0

CI = CIE + CII + CIO

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IP2 = ξSη∆P (t + ∆t − t0 ) where the indicators are explained in Section III A. B. Operation Maintenance Cost

The operation maintenance cost in the overhaul model is expressed by: CO2 = COe2 + COm2 = (P0 + η 2 PK )p1 µ(t+∆t−t0 )8760 t+∆t Z + COb (1 + α1 t)dt (20) t0

where the indicators are explained in Section III B. C. The Fault Risk Cost

where CI D is the direct cost of equipment installation, and CCR is the rate of equipment disposal, and CCR generally takes 32% [15]. In conclusion, the total cost in continuous operations can be presented as follows:

The related fault risk cost can be presented by:

C1 = CO1 + CR1 + CD1 .

where the indicators are explained in Section III C.

(17)

(19)

Zt

Zt λ(t)dt] · LOT F

CR2 = [ λ(t)dt + t0

t−∆t

(21)

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B. Operation Maintenance Cost

D. The Generalized Depreciation Cost

The operation maintenance cost in the retirement model is expressed by:

The generalized depreciation cost is shown as follows: CD2 = (CI + CD + Crc )

t − t0 Td

(22)

where the indicators are explained in Section III D.

CO3 = COe3 + COm3 = (P0 + η 2 PK )p1 µ(t − t0 )8760 Zt (31) + COb (1 + α1 t)dt t0

E. Overhaul Cost The overhaul cost in the moment t is shown as follows, and mainly involves the overhaul expense and the cost of outage risk. CM2 = CMt + CMR (23) where CM t is the overhaul expense and CM R is the loss of the outage risk. According to assumption 5), the calculation of CM t is expressed by: CMt = (1 + α2 t)Cb (24) where Cb is the basic cost for a single overhaul, and the value is determined by the average of statistical data combined with the expert advice. t represents the transformer’s service age (year), and α2 is the linear dependent coefficient between the overhaul cost and the age growth, here taken as 0.005. The cost of outage risk can be calculated by CMR = trs · Crb

(25)

where Crb indicates the cost of outage risk per hour due to the decline of redundancy rate of the grid, and estimated by (26). trs is the overhaul time estimated by (27) based on assumption 4). Crb = S∆p20% (26) trs = tb + α3 t

(27)

where tb represents the basic time of overhaul, and α3 is the linear dependent coefficient between the overhaul time and the age growth, here taken as 0.02. The total cost in overhaul can be concluded as follows: C2 = CO2 + CR2 + CD2 + CM2 . The related annual net income is shown as follows: IP 2 − C2 . W2 = t + ∆t − t0

(28)

(29)

V. A NNUAL N ET I NCOME M ODEL IN R ETIREMENT Assuming the current moment t0 , the transformer will be decommissioned at some moment t after t0 . Then we can calculate the net income in the related period, namely t − t0 . A. Revenue of Power Supply The total revenue of power supply in the retirement strategy can be expressed by: IP3 = ξSη∆P (t − t0 ) where the indicators are explained in Section III A.

(30)

where the indicators are explained in Section III B. C. Fault Risk Cost The related fault risk cost can be presented by: Zt λ(t)dt · LOT F

CR3 =

(32)

t0

where the indicators are explained in Section III C. D. Generalized Depreciation Cost The generalized depreciation cost is shown as follows. It is important to note that the transformer designed life is replaced by the acutal service life in the denominator of the expression. t − t0 (33) t where, the indicators are explained in Section III D. The total cost in retirement can be concluded as follows: CD3 = (CI + CD + Crc )

C3 = CO3 + CR3 + CD3 + CI3 . The related annual net income is shown as follows: IP3 − C3 W3 = . t − t0

(34)

(35)

VI. E CONOMIC L IFE A SSESSMENT The transformer’s economic life is divided into three sections based on the criterion of annual net income: If the maximum of annual net income is W1 , this means the transformer ought to be continuous operation; if the maximum of annual net income is W2 , this means the economic life begins to decline, and the power transformer ought to be overhauled; finally, if the maximum of annual net income is W2 , this means the economic life has reached its end, and the power transformer ought to be decommissioned. We can also input all the relevant data of the current moment t0 to obtain the two intersections of three strategies, which represents the transformer’s economic life. VII. C ASE S TUDY A power transformer of 31.5 MVA in Chongqing substation of 110 kV is studied here. The relevant data are shown in Table II and Table III. The fault probability curve of the power transformer can be calculated as follows: m t t + 4.1 4.566 ) . (36) λ(t) = ( )m−1 = 0.1934( η η 28.65


The cost of personnel security risk and the cost of environmental impact are respectively presented as follows:

TABLE II NAMEPLATE DATA OF 110 K V T RANSFORMER Item Manufacturer Manufacturer data Product model Voltage level (kV) Manufacturer code Rated capacity (MVA) Oil origin Oil weight

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Data ABB Transformer Co., Ltd. in Chongqing 1990-08-01 SFSZ8-31500/110 AC 110 192 31.5 Karamay 15.94

Loss3 = 2000Loss4 = 130000.

(43)

The fault risk cost can be calculated according to (12): Zt λ(t)dt · 1008487.57.

CR1 =

(44)

t0

TABLE III DATA OF A P OWER T RANSFORMER (110 K V) Parameter S (MVA) ξ (%) ∆p (Yuan/kWh) P0 (kW) PK (kW) η (%) Cf (Yuan)

Value 31.5 5 0.2 21.3 139.78 60 800,000

Parameter cos ϕ p1 (Yuan/kWh) COb (Yuan)

Value 0.9 0.3 20,000

Crc (Yuan)

30,000

Cb (Yuan) tb (day)

200,000 5

The equipment procurement cost of this transformer is two million Yuan. The installation cost is CI I = 20,470 Yuan, and the spare cost CI O = 200,000 Yuan, as stated in [15]. The disposal cost CDT is 6550 Yuan, the residual value CDR is 100,000 Yuan, so the decommissioning cost CD is −934,500 Yuan, according to (15) and (16). Consequently, the generalized depreciation cost is shown as follows: t − t0 . (45) CD1 = 2157000 30

The fault probability will be decreased by the overhaul, and the amount of change can be fitted as follows: 75 (37) ∆λ(t) = λ(t) · 125 + (t − 26)2 λ(t − ∆t) = λ(t) − ∆λ(t)

(38)

where λ(t) is the fault probability before the maintenance time t, ∆λ(t) is the magnitude of decrease at maintenance time t, and λ(t − ∆t) is the fault probability after maintenance time t. A. Annual Net Income in Continuous Operation In order to compare the economic life models of different strategies, the period in the continuous operation model should correspond with that in the overhaul model, namely, the period in the calculations should be t + ∆t − t0 . According to Table III and (1), the revenue of power supply should be: IP1 = 1655640(t + ∆t − t0 ). (39) The operation maintenance cost is calculated as:

B. Annual Net Income in Overhaul The total revenue of power supply in the period after overhaul is calculated as: IP2 = 1655640(t + ∆t − t0 ).

t+∆t Z

CO2 = 149993.49(t + ∆t − t0 ) + 20000

t0

(40) The fault risk cost is needed to calculate the economic loss of the transformer fault first. Since the connection is the outdoor substation, and the load is classified as moderate loading, then β1 takes 1. The mean time to repair tr takes 17.57 h [20]. In this way, the system load shedding cost is obtained: Loss1 = 156487.57. (41) Since the transformer is a domestic product, the β2 takes 0.9, according to Table III. Then the fault recovery cost can be obtained: Loss2 = 80 · 104 · 0.9 = 720000

(42)

(1 + 0.004t)dt. t0

(47) The fault risk cost is obtained as follows: Zt t0

(1 + 0.004t)dt.

(46)

The operation maintenance cost is calculated as:

Zt λ(t)] · 1008487.57.

CR2 = [ λ(t)dt +

t+∆t Z

CO1 = 149993.49(t + ∆t − t0 ) + 20000

According to (17), (18), and (39)–(45), the annual net income and its variation with time in the continuous operation model is simulated in Fig. 5.

(48)

t−∆t

The generalized depreciation cost is obtained as follows: CD2 = 2157000

t − t0 . 30

(49)

The overhaul cost is obtained as follows: t+∆t Z

CM2 = 120000 + 200000

(1 + 0.005t)dt t0

+ 1260 · (120 + 0.48t).

(50)

According to (28), (29), and (46)–(50), the annual net income and its variation with time in the overhaul model is simulated in Fig. 5.

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C. Annual Net Income in Retirement The total revenue of power supply in the retirement strategy is calculated as: IP3 = 1655640(t − t0 ).

(51)

The operation maintenance cost is calculated as: Zt CO3 = 149993.49(t − t0 ) + 20000

(53)

t0

The generalized depreciation cost is obtained as follows: t − t0 . (54) t According to (34), (35), and (51)–(54), the annual net income and its variation with time in the retirement model is simulated in Fig. 5. CD3 = 2157000

6

x 10

X: 23.85 Y: 1.387e+006

Annual Net Incom e ( Yuan)

1.4

Continuous operation Overhaul Retirement

1.35 X: 28.39 Y: 1.356e+006

1.3

1 2 3 4 5

Voltage Level (kV) 110 110 220 220 500

Commissioning Date 2000-05-01 2008-11-18 2001-06-30 2011-11-01 2001-06-19

Testing Date 2013-12-17 2011-10-14 2014-02-20 2013-09-17 2010-12-25

Residual Economic Life 13.53 25.82 16.31 29.13 26.79

VIII. C ONCLUSION

The fault risk cost is obtained as follows: Zt CR3 = λ(t)dt · 1008487.57.

1.45

No.

(1 + 0.004t)dt. (52) t0

1.5

TABLE IV E XAMPLES OF E CONOMIC L IFE A SSESSMENT

1.25 1.2 1.15

In this paper, the economic life model of three strategies is established for the assessment of transformer economic life. First, the economic indices in the different strategies are analyzed, and the maximum average annual net income is determined as a criterion of comparison. Next, on the basis of reasonable assumptions, the revenue and the costs are calculated respectively under different situations. Finally, the transformer economic life is assessed quantitatively by comparing the annual net income of the different strategies. The proposed model is generally applicable in most cases. The fault probability curve of the power transformer can be fitted by the statistical data. Consequently, the decreased degree of fault probability after overhaul will be taken into account. The relevant parameters in the model can be obtained by the manufacturer’s information and operation data. The residual economic life of testing the transformer will be achieved ultimately by comparing the different strategies. The case study proves preliminarily the feasibility and validity of the proposed economic life model and its ability to provide the electric power enterprise with a reference method to develop a more profitable plan for the maintenance and retirement of power transformers.

1.1

ACKNOWLEDGMENT

1.05 1 10

15

20

25 30 35 Service Age (year)

40

45

50

Fig. 5. Annual net income for three strategies.

The current service time of the power transformer is 25 years. This can be obtained from Fig. 5 where before T = 28.39, the strategy of overhaul has a higher net income, and the strategy of retirement will be accepted for more benefits after T = 28.39. We may safely conclude that the economic life of this transformer is about 3.39 years based on the principle of the maximum annual net income. If we assume the current service age is 15 years, then it will be profitable to adopt the strategy of continuous operation; in other words, the economic life of this transformer will begin to decline after 8.85 years. In order to prove the validity of the proposed model, 5 different transformers in Chongqing have been assessed, and the results are revealed in Table IV. According to the results presented in Table IV, the proposed model can assess the residual economic life of a power transformer effectively. Results show the total economic life is basically around 30 years, which corresponds to the operational situation.

The authors would like to thank Dr. Yiyi Zhang and M.S. Fanjin Meng for their kind support in the research. R EFERENCES [1] “The 2010 annual professional summary report of transformer equipment in State Grid,” China Electric Power Research Institute, Beijing, China, 2011. [2] H. B. Zheng, “Study on condition assessment and fault diagnosis approaches for power transformers,” Ph. D. dissertation, School of Electrical Engineering, Chongqing University, Chongqing, China, 2012. [3] W. Cao, B. S. He, and W. Shen, “An approach for economic assessment on oil-paper insulation diagnosis through accelerated aging experiments,” IEEE Transactions on Dielectrics and Electrical Insulation, vol. 21, no. 4, pp. 1842–1850, Aug. 2014. [4] E. I. Amoiralis, M. A. Tsili, and A. G. Kladas, “Power transformer economic evaluation in decentralized electricity markets,” IEEE Transactions on Industrial Electronics, vol. 59, no. 5, pp. 2329–2341, May 2012. [5] A. E. B. Abu-Elanien, M. M. A. Salama, and R. Bartnikas, “A technoeconomic method for replacing transformers,” IEEE Transactions on Power Delivery, vol. 26, no. 2, pp. 817–829, Apr. 2011. [6] Y. Y. Zhang, “Study on life cycle cost based maintenance decision making for power transformers considering condition assessment and insulation life assessment,” Ph. D. dissertation, School of Electrical Engineering, Chongqing University, Chongqing, China, 2014. [7] J. L. Yu, C. F. Wang, and B. Zhang, “Economic life evaluation of power transformer in service,” Proceedings of the CSU-EPSA, vol. 22, no. 3, pp. 86–90, Jun. 2010.


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Jiyu Wang was born in Anhui Province, China on 22 January 1992. He received his bachelor’s degree in electrical engineering from Chongqing University, Chongqing, China, in 2013. His major field of study is the assessment and fault diagnosis of power transformers. He has been a Ph.D. candidate in the State Key Laboratory of Power Transmission Equipment & System Security and New Technology at Chongqing University, Chongqing, China since 2013. He has published the “Experimental investigations on surface discharge characteristics over oil/pressboard interface based on a rodto-plane electrode” in the international conference journal of ICHVE 2014, Poland. His major research interests include condition assessment of power transformers, life cycle management of power transformers, and maintenance and retirement decision making of power transformers.

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Ruijin Liao received his M.S. and Ph.D. in electrical engineering from Xi’an Jiaotong University, Xi’an, China, and Chongqing University, Chongqing, China, respectively. Since 1999, he has been a Professor at the Electrical Engineering School, Chongqing University, China. His research activities lie in the field of online monitoring of insulation conditions and fault diagnosis for high-voltage apparatus, space charge measurement of high-voltage transmission lines, mechanism and characteristic of corona discharge in air, modification of Kraft paper and mineral oil for transformers, anti-icing technology of outdoor insulators, as well as aging mechanisms and diagnosis for power transformers. He is the author/coauthor of 3 books and over 130 journals and international conferences.

Yiyi Zhang received his bachelor’s degree and Ph.D. in electrical engineering from Guangxi University, Nanning, China, in 2008 and Chongqing University, Chongqing, China, in 2014, respectively. From 2009 to 2014, he was a Ph.D. candidate in the Electrical Engineering School, Chongqing University. In 2014, he joined Guangxi University. His major research interests include aging mechanisms, aging evaluation, and fault diagnosis of transformer oil-paper insulation systems.

Fanjin Meng received his master’s degree in electrical engineering from Chongqing University, Chongqing, China, in 2014. In 2014, he joined Tangshan Power Supply Company in Tangshan, Hebei, China. His major research interests include aging evaluation and fault diagnosis of transformer oilpaper insulation systems.