Research on Risk Assessment of the Transformer Based on Life Cycle Cost

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1 ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation, Hangzhou, hina b Depatment of Electical and Electonic Engineeing, The Univesity of Hong Kong, Hong Kong, hina Abstact This pape poposes an optimization model of life cycle cost (L) of the tansfome. Fist, to build the model of L of the tansfome, the whole L of the tansfome is divided into five costs, i.e., initial cost, opeating cost, maintenance cost, fault cost and disposal cost. The whole L is calculated. Second, accoding to the data of seveal kinds of tansfomes, the elationship between the initial cost and the whole L is established by using the cuve fitting method. The optimal initial cost that minimizes the whole L is calculated. Thid, isk souces of L ae identified and associated isk index is established based on the poposed model. To quantify isks, the fuzzy analytic hieachy pocess (FAHP) method is used to establish the index of the cost of each stage. Accoding to the index, the isks can be soted based on the impotance. The degee of isks of L can also be obtained accoding to the index. Keywods: Life cycle cost, optimal cost, isk assessment, isk index. ntoduction Appopiate life cycle management [-2] is impotant to ensue the safety and efficiency of the whole tansmission systems [3-5]. The tansfome is one of the impotant components in tansmission systems. Theefoe, the optimal life cycle cost (L) of the tansfome in its life time will play an impotant ole in the whole life cycle cost management of tansmission systems. This pape poposes an optimization model of life cycle cost of the tansfome. Based on the poposed model, isk souces ae identified and associated isk index is established. Some isk management methods fo L ae established. The wok of the pape is oganized as follows. To build the model of L of the tansfome, the whole L pocess of the tansfome is divided into five costs, i.e., initial cost, opeating cost, maintenance cost, fault teatment cost and disposal cost. Each cost is analyzed, thus the whole L is calculated. Accoding to the data of tansfomes povided by Zhejiang Electic Powe opoation of State Gid opoation of hina, the elationship between the initial cost and the whole L can be simulated by using the cuve fitting method. And the optimal initial cost that makes the whole L minimum can be calculated. itical factos, which affect the cost of each stage, ae identified. The fuzzy analytic hieachy pocess (FAHP) [6-8] is employed to establish the index system of each cost to analyze the isks quantitatively. Accoding to the index, the isks can be soted based on the impotance and some isk management contol methods can be poposed to educe the cost isk. The L model and the index system have been successfully applied in the tansmission system of Zhejiang Electic Powe opoation of State Gid opoation of hina. * Manuscipt eceived July 5, 202; evised August 5, 202. oesponding autho. Tel.: ; addess: tonywangchong@63.com.

2 26 ntenational Jounal of Smat Gid and lean Enegy, vol. 2, no., Januay Optimization Model of Life ycle ost of Tansfomes 2.. Model of life cycle cost The whole L of tansfomes is divided into five costs, i.e., initial cost, opeating cost O, maintenance cost M, fault cost F and disposal cost D. nitial cost efes to the cost paid in the duation of planning and constuction of the tansfome. t includes the design cost, the tansfome puchase cost, constuction and installation cost. The design cost mainly includes the eseach cost, the cost of feasibility study, peliminay design cost, and so on. Opeating cost efes to the sum of all costs that ae needed duing the opeation peiod of the tansfome. t mainly includes the loss cost, opeating labo cost and so on. The opeating cost of each yea can be descibed as follows: O = loss + P () whee P is the opeating labo cost, loss is the cost caused by the powe loss of the tansfome, it can be calculated as: = 8760 P η a (2) loss loss whee P loss is the load loss of the tansfome, η is the load ate of the tansfome, a is the electicity pice. Maintenance cost efes to the maintenance staff cost, the epai cost and so on. The data of the cycle of epai and ovehaul and the cost of each epai and ovehaul can be povided by the manufactues, so maintenance cost can be calculated accoding to the cycle of epai and ovehaul and the cost of each epai and ovehaul. Fault cost is the economic loss cost caused by failue outage. Unplanned Outage oefficient (UO) can be used to calculate the fault cost of each yea appoximately. t can be descibed as follows: = UO P η a (3) F whee P is the ated active powe of the tansfome. Disposal cost efes to the cost needed in the decommissioning pocess. n addition to the payment of the necessay emedial teatment cost, some component salvage can be ecycled. The total disposal cost can be consideed as a popotion of the puchase cost appoximately. The whole L can be calculated as follows: L = N N N i i i N Oi Mi Fi D i= i= i= (4) whee is the inflation ate, is the annual inteest ate, N is the life cycle of the tansfome, Oi is the opeating cost of the ith yea, Mi is the maintenance cost of the ith yea, Fi is the fault cost of the ith yea Optimization model of L The whole L of the tansfome can be calculated accoding to the above analysis. Because lowe initial cost and highe cost may both esult in high L, an appopiate initial cost is impotant to make the whole L minimum. The function between the initial cost and the whole L, which can be calculated accoding to the equations () ~ (4), is built by using the cuve fitting method. Table shows the paametes of six cases povided by Zhejiang Electic Powe opoation of State Gid opoation of hina. The life cycle of the tansfome is 30 yeas. The electicity cost is 0.5 MB/kWh, the disposal coefficient is appoximately 0%, the annual inteest ate is 4% and the inflation ate is 6%.

3 Hui Zhou et al.: eseach on isk Assessment of the Tansfome Based on Life ycle ost 27 Table. Paametes of Each ase Paametes ase ase 2 ase 3 ase 4 ase 5 ase 6 ( 0 6 MB) P loss (kw) η P ( 0 6 MB) UO (%) P (MVA) ycle of epai (Yea) ost of Each epai ( 0 6 MB /Yea) ycle of Ovehaul (Yea) ost of Each Ovehaul ( 0 6 MB /Yea) (a) Fig.. (a) L cuves of case, case 5 and case 6; (b) uves of L vs. and S vs. (b) Fig. (a) shows L cuves of case, case 5 and case 6. Accoding to the Fig. (a), case 6 has the maximum initial cost, but its whole L is not the maximal. ase has the minimum initial cost, but its whole L is the maximal. So the initial cost is an impotant facto of the whole L. Accoding to the povided initial costs and the whole Ls of six cases, the elationship between the initial cost ( ) and the whole L can be simulated by: L = (5) Accoding to the equation (5), the optimal initial cost can be calculated and its value is MB. n the pactice, the initial cost which is neaest to the MB can be consideed as the optimal stategy. Fig. (b) shows the cuves of vs. L and vs. S. S can be descibed as follows: S = O + M + F + D (6) 3. Analysis of the isks of L Thee ae many uncetainties in the whole life cycle. The L of components will be affected by these uncetainties. To analyze these uncetainties quantitatively, isk esouces of life cycle cost ae identified and then the fuzzy analytic hieachy pocess is employed to establish a isk assessment model. 3.. isks of L Accoding to the five costs mentioned in section 2, the L isks (F) based on these five costs include initial cost isks (S), opeating cost isks (S2), maintenance cost isks (S3), fault cost isks (S4) and disposal cost isks (S5).

4 28 ntenational Jounal of Smat Gid and lean Enegy, vol. 2, no., Januay 203 nitial cost isks mainly include the pice isk (T), the technological pogess isk (T2), the investigation isk (T3), the load foecasting isk (T4), the component location isk (T5) and the pesonal quality isk (T6). Opeating cost isks mainly include the opeation isk (T2), the load contol isk (T22), the legal isk (T23) and the management isk (T24). Maintenance cost isks mainly include the uncetainty of maintenance isk (T3), the opeation isk (T32) and the management isk (T33). Fault cost isks mainly include the failue numbe isk (T4), the load loss isk (T42) and the pesonal quality isk (T43). Disposal cost isks mainly include the disposal application isk (T5), the disposal appoval isk (T52), the inactive facilities statistic isk (T53) and the inactive facilities disposal isk (T54) Pinciple of FAHP AHP is a multi-attibute decision-making model poposed by Saaty [6]. This method is widely used to solve decision-making poblem with uncetainties due to its advantages of integal stuctue, simple theoy and easy opeation. Howeve, AHP has a disadvantage of the ambiguity in decision making. Fuzzy analytic hieachy pocess (FAHP) is poposed by Laahoved and Pedycz [8] to ovecome this disadvantage. n the pocess of FAHP, a paied compaison matix is built by using the evaluation citeia, as shown in the judgment matix A : a2 a n a2 A [ aij ] = = an an2 whee a ij can be detemined by the -9 scale [9]. A is a ecipocal matix with a ij > 0, aij = / aji, a =. ii λ n max =, = n whee and ae the consistency index and the consistency atio espectively, n is the dimension of matix and λ max is the lagest eigenvalue of A, is the andom consistency ation shown in Table 2. When 0., the matix A should be ectified appopiately. Table 2. The Value of n (7) (8) The establishment of altenative set shows as follows: V = { v, v, v, v, v } = (vey low, low, medium, high, vey high) (9) whee v i epesents the isk degee of the citical factos. Duing the establishment of the fuzzy elationship matix, the fuzzy elationship E can be obtained though expet assessments. When evaluate the fuzzy compehensive, the second-level fuzzy compehensive evaluation vecto D can be calculated as follows: i Di = wi Ei (0)

5 Hui Zhou et al.: eseach on isk Assessment of the Tansfome Based on Life ycle ost 29 Then the compehensive evaluation matix D can be fomed by D i. The evaluation esult can be calculated by multiplying the D by the weight vecto w : H = w D () 3.3. Evaluation of isks of L Based on the isks of L, a seial of judgment matix of elative impotance between citeia can be defined as accoding to the equation (7): 3 /5 5 /3 /3 /5 3 F S = 3 /3 3, /5 /3 /5 / /5 3 /3 S2 T =, /7 /3 /3 / S4 T = /5 /3 /3 3 /3 /7 /3 /5 3 3 / S T =, 3 /3 3 5 /3 3 /3 /3 /5 /3 /5 5 3 S3 T = /5 /3, /3 3 /3 /5 /3 /5 S5 T = 3 3 / Accoding to FAHP, oveall citeia weights can be calculated and shown in Table 3: Table 3. Weights of the Evaluation ndex Level F-Level S Local weight of sub-citeia Global weight F-S Weight=0.803 F-S2 Weight= F-S3 Weight=0.945 F-S4 Weight= F-S5 Weight= T= T2= T3= T4= T5= T6= T2= T22= T23= T24= T3= T32= T34= T4= T42= T43= T5= T52= T53= T54= Accoding to expet evaluations, the fuzzy elation between evaluation factos and emaks set V can be expessed as evaluation matix E. Take the evaluation of the isk of as an example. The single facto evaluation matix E is:

6 30 ntenational Jounal of Smat Gid and lean Enegy, vol. 2, no., Januay E = The weight of the isk of is: w = (0.067, 0.390, 0.434, 0.490, 0.663, ) Then, the single-facto evaluation esult set D can be denoted as: D = we = (0.648, , 0.259, 0.253, ) Othe evaluation esults also can be calculated by the same method. D = (0.237, , , 0.697, ), D = (0.000, , 0.222, 0.740, 0.000) 2 3 D4 = (0.000, , 0.276, 0.757, 0.000), D5 = (0.565, , 0.263, 0.64, ) The compehensive evaluation can be calculated: T , , 0.259, 0.253, , , , 0.697, H = w D = , , 0.222, 0.740, , , 0.276, 0.757, , , 0.263, 0.64, = (0.62, 0.430, 0.287, 0.632, ) Accoding to the compehensive evaluation H, the maximum index is and the isk of L of the tansfome is low based on the pinciple of the maximum membeship degee. Accoding to the global weight in Table 3, the isks can be soted based on the impotance. Fo citical isks, the coesponding measues can be adopted to educe the isks of the L. 4. onclusion The pape divides the whole L into five costs, i.e., initial cost, opeating cost, maintenance cost, fault cost and disposal cost accoding to the chaacteistic of the tansfome. An optimization model of L is built. The cost of each stage is analyzed, thus the whole L can be calculated. The elationship between the initial cost and the whole L can be simulated by using the cuve fitting method. Based on the poposed model, isk souces ae identified and associated isk index is established. To quantify the isk, a fuzzy analytic hieachy pocess method is used to establish the index of the cost of each stage, and the isk degee of L of the tansfome can be obtained accoding to the index. A ealistic case study fom Zhejiang Electic Powe opoation of State Gid opoation of hina is epoted to validate the poposed method. Acknowledgements This eseach is suppoted by Zhejiang Electic Powe opoation of State Gid opoation of hina and eseach nstitute of HKU in Shenzhen. efeences [] Asset Management Pat : Specification fo the Optimized Management of Physical nfastuctue Assets, PAS 55- (UK) 2008.

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