A dynamic opportunistic maintenance model to maximize energy-based availability while reducing the life cycle cost of wind farms

A dynamic opportunistic maintenance model to maximize energy-based

availability while reducing the life cycle cost of wind farms

A. Erguido

a,b

, A. Crespo Márquez

b

, E. Castellano

c

, J. Gómez Fernández

b

a

_{Departamento de Organización Industrial y Gestión de Empresas I, Escuela Superior de}

Ingenieros, Universidad de Sevilla.

b

_{IK4-Ikerlan Technology Research Centre, Operations and Maintenance Technologies}

Area, 20500 Gipuzkoa, Spain

c

_{MIK Research Centre, Mondragon University, 20560 Gipuzkoa, Spain}

*Asier Erguido (corresponding author)

[email protected]

+34 943 712 400

Adolfo Crespo

[email protected]

+34 954 487 215

Eduardo Castellano

[email protected]

+34 943 718 009

Juan Fco. Gómez

[email protected]

+34 954 487 215

Funding

This research work was performed within both the context of the EmaitekPlus 2015-2016

Program of the Basque Government and the SustainOwner (‘Sustainable Design and

Management of Industrial Assets through Total Value and Cost of Ownership’), a project

sponsored by the EU Framework Programme Horizon 2020, MSCA-RISE-2014: Marie

Skłodowska-Curie Research and Innovation Staff Exchange (RISE) (grant agreement

number 645733 - Sustain-Owner - H2020-MSCA-RISE-2014).

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LCC W F W T F M O&M CM P M CBM CM S T T F M T vt vi vo vr GPt RP Rik(V A) SRTikj SRTikjt DRTik DRTikt V p wik SRTikj DRTik K J GRP V Ahikt ↵ik ik qpr ikj qc ik N T C cna cp cc ik cpr_ikj cteam cet N Tmax N Tc cdisp mc ik mpr_ik OT Dt Do T

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j = J j = 1 qij q = 0 q = 1 V Anewi = V Aoldi (1 qij) F (t|V Anew i ) = P [Tij t|Tij > V Anewi ] = F (t) F (V Anew i ) 1 F (V Anew i ) (↵ik) ( ik) k i

R (t_{|V A}newhik) = 1 F (t|V Anewhik) = exp

"✓ V Anew hik ↵ik ◆ ik ✓ t ↵ik ◆ ik# cdisp _cc ik c pr ik mc ik m pr ik k = 1 cna _cp N Tmax cteam _C ET cet DRTik SRTikj (Rik(V A)) DRTik

SRTikj DRTik SRTikj (V ) p V (GPt) (wik) DRTik SRTikj (GPt) (RP )

SRTikjt= SRTikj+ (2Wt 1)· SRTikj· wik· ( RP

GPt+ RP· Wt) (2Wt 1) DRTikt= DRTik+ (2Wt 1)· DRTik· wik· ( RP GPt+ RP· Wt )(2Wt 1) Wt= ( 1 Pt+p_l=t vl_p  V 0 Pt+p_l=t vl_p > V

Pt+P l=t vl p = 0 (T =_{{0, 1, 2, ..., T })} ↵ (SRTikjt, DRTikt) zhikt= 8 > < > :

1 if CM k is perf ormed in system i of W T h in period t 0 otherwise yhikjt= 8 > < > :

1 if P M j is perf ormed in F M k of system i of W T h in period t

0 otherwise

✓t= (

1 if a M T is correctively dispatched to W F in period t 0 otherwise

t= (

1 if a M T is preventively dispatched to W F in period t 0 otherwise hikjt= 8 > < > :

1 if P M j should be perf ormed in F M k of system i of W T h in period t 0 otherwise 't= 8 > < > :

1 if there are available resources f or perf orming P M in period t

(zhikt) (yhikjt) (N T, cteam_{) (ET, c}et₎ cdisp ⇣_cc ik, c pr ikj ⌘ (cna_{) (c}p₎ ⇣ mc ik, m pr ikj ⌘ (GPt) ⇣ qc ik, q pr ik,j ⌘ t (ka)

min LCC (DRTikt,SRTikjt) =

" X t ETt· cet+ X t N T · cteam₊X t ( t+ ✓t)· cdisp+ X h X i X k6=1 X t zhikt· ccik· (qcik) 2 +X h X i X k X t zhikt· mcik· (qikc ) 2 · GPt· (cna+ cp) + X h X i X k X j X t yhikjt· ⇣

q_ikjpr⌘2 ⇣mpr_{ikj· GP}t· (cna+ cp) + cprikj

⌘3

5 · (1 + ka) t

(OT ) H P_tGPt hP_hP_iP_kP_tmcik· zhikt· (qcik) 2 · GPt +P_hP_iP_kP_jP_tmpr_{ikj· y}hikjt· ⇣ q_ikjpr⌘2_{· GP}t H P_tGPt Do OT  P h P i P k P j P tm pr ikj· yhikjt· ⇣ q_ikjpr⌘2 +P_hP_iP_kP_tmc ik· zhikt· (qikc ) 2i OT vi _(vo₎ (RP ) (vr₎ GPt= 8 > > > < > > > : 0, 0 vt< vi RP_{· (a + b · v}t+ c· v2t) vi vt< vr RP vr_{ v} t< vo 0, vo  vt 8t✏T a = 1 (vi _vr₎2 " vi vi+ vr 4vivr ✓ vi_{+ v}r 2vr ◆3# b = 1 (vi _vr₎2 " 4 vi+ vr ✓_vi_{+ v}r 2vr ◆3 3vi+ vr # c = 1 (vi _vr₎2 " 2 4 ✓_vi_{+ v}r 2vr ◆3# DRTikt (Rik) (DRTikt) t (zhikt = 1) 0_{ DRT}ikt 1 8i✏I, 8k✏K, 8t✏T

t= ( 1 Rik(V Ahikt) DRTikt 0 otherwise 8h✏H, 8i✏I, 8k✏K, 8t✏T ✓t= ( 1 P_hP_iP_k6=1zhikt 1 0 otherwise 8t✏T ✓t+ t 1 8t✏T SRTikjt 0_{ SRT}ikjt 1 8i✏I, 8j✏J, 8k✏K, 8t✏T hikjt= ( 1 Rik(V Ahikt) SRTikjt 0 otherwise 8h✏H, 8i✏I, 8k✏K, 8j✏J, 8t✏T

yhikjt hikjt hik(j+1)t 8h✏H, 8i✏I, 8k✏K, 8j✏J, 8t✏T

yhikjt ✓t+ t 8h✏H, 8i✏I, 8k✏K, 8j✏J, 8t✏T X i X k X j yhikjt+ X i X k zhikt  1 8h✏H, 8t✏T ET (M Tmax) (N Ttc✏{1, 2, ..., NTmax}) X h X i X k6=1 zhikt· mcik· (qcik) 2  C · NTtc+ ETt 8t✏T

N Tc t  NTmax 8t✏T 't= ( 1 P_hP_iP_k6=1zhikt· mcik· (qikc ) 2  C · NTmax 0 Ph P i P k6=1zhikt· mcik· (qikc ) 2 > C· NTmax 8t✏T X h X i X k X j yhikjt· mprikj· ⇣ q_ikjpr⌘2_{ C · (NT}max N Ttc)· 't 8t✏T yhikjt = 1, zikht = 1 V Ahikt q_ikjpr qcik V Ahikt= (V Ahik(t 1)+ 1)· ⇣

1 zhikt· qikc yhikjt· qprikj

⌘ 8h✏H, 8i✏I, 8k✏K, 8j✏J, 8t✏T (SRTikj, DRTik) (wik, V, p) (T T F ) R T T Fhik= ↵ik "✓ V Ahik ↵ik ◆ ik ln (1 R) # 1 ik V Ahik (T T Fhik)

LCC = f [SRTikj, DRTik, wik, V, p]

LCC = f [SRTikj= 0, DRTik= 0, wik= 0, V = 0, p = 0]

LCC = f [SRTikj, DRTikwik, V, p]

q_ik1pr qpr_ik2

SRTi1j = 0.0, SRTi21 = 0.8, SRTi22 = 0.4, SRTi31 = 0.8, SRTi32 =

0.4, DRTi2= 0.2, DRTi3= 0.2, wik= 0.5, V = 2.0, p = 5

(p)

p = 3

(wik)

(wik) SRT11j SRT21j SRT41j SRT41j DRT11 DRT21 DRT31 DRT41 w11 w21 w31 w41 V V V V SRT121 SRT221 SRT321 SRT421 SRT122 SRT222 SRT322 SRT422 DRT12 DRT22 DRT32 DRT42 w12 w22 w32 w42 V V V V SRT131 SRT231 SRT331 SRT431 SRT132 SRT232 SRT332 SRT432 DRT13 DRT23 DRT33 DRT43 w13 w23 w33 w43 V V V V