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Electric Power Systems Research 104 (2013) 80– 86

Contents lists available at ScienceDirect

Electric Power Systems Research

jou rn al hom epage: www.elsev ier .com/ locate /epsr

hybrid analytical-simulation approach for maintenanceptimization of deteriorating equipment: Case study of wind turbines

alman Kahrobaee ∗, Sohrab Asgarpoorepartment of Electrical Engineering, University of Nebraska-Lincoln, 209N SEC, Lincoln, NE 68503, United States

r t i c l e i n f o

rticle history:eceived 6 March 2013eceived in revised form 18 June 2013ccepted 21 June 2013vailable online 21 July 2013

eywords:vailabilityaintenanceptimizationemi-Markov decision processesonte Carlo simulationind power

a b s t r a c t

As the power system moves toward more efficient operation, one of the main challenges for asset man-agers is to determine the optimum maintenance strategy for deteriorating equipment such as windturbines. This problem can be addressed using a variety of optimization methods including analyti-cal approaches which globally find the best strategy. However, since there are numerous factors (e.g.,resource availability, weather conditions, etc.) affecting the operation and maintenance of equipment,there is not a unique solution for all of the possible situations. While it will be complicated to includethese scenarios in an analytical model, a simulation model is more flexible and can easily handle theseconditions. In order to benefit from the advantages of both analytical and simulation models, we proposea hybrid analytical-simulation approach toward solving a maintenance optimization problem with actualsystem limitations. In the first step of this approach, the optimum maintenance policy for a wind turbineis obtained using semi-Markov decision processes. Then, this model is built and solved with a MonteCarlo simulation, and the results are compared for justification of the simulation model. In the second

step, the effects of maintenance and repair constraints on system availability and costs are studied usingthe simulation model developed. The model developed can assist the asset managers in including theirown restrictions through sensitivity analysis and performing a cost/benefit analysis to determine, forexample, how many technicians are required for a fleet of equipment, such as a wind farm. The effec-tiveness of this approach is demonstrated by the results from the case study of wind turbines where anumber of maintenance and repair restrictions are considered.

. Introduction

Deterioration of power system equipment depends on its agend operational condition [1]. In practice, there are two main pre-entive maintenance strategies aiming to increase the lifetimend reliability of equipment: time-based maintenance (TBM) andondition-based maintenance (CBM) [2]. TBM is scheduled preven-ive maintenance based on the manufacturer’s recommendationnd/or industry standards. This type of maintenance is often limitednd inflexible under different operating conditions [3]. With CBM,n the other hand, inspections or a continuous condition monitor-ng system may be employed to trigger maintenance tasks basedn the current condition of equipment or its predicted condi-ion in the future [4]. Reliability-centered maintenance (RCM) is

relatively recent philosophy which combines the previous strate-

ies and includes studies such as failure mode and effect analysisFMEA) to prioritize components and identify the best possible

aintenance options [5,6]. The goal of RCM is to facilitate minimum

∗ Corresponding author. Tel.: +1 402 937 0307.E-mail address: skahrobaee@huskers.unl.edu (S. Kahrobaee).

378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.epsr.2013.06.012

© 2013 Elsevier B.V. All rights reserved.

cost-effective maintenance that satisfies safety and reliability tar-gets [3–7]. Regardless of the type of maintenance, asset managersare required to study and develop an optimal maintenance strategywhich may even lead to a “run to failure” policy [8].

Maintenance optimization is usually subjected to several con-straints, especially in a power system where certain operationalrequirements should also be considered [9]. In addition, resourceconstraints can affect the maintenance of a system as well. In anactual system, corrective maintenance may be delayed or takelonger than initially expected due to adverse weather conditionsor unavailability of the maintenance crew, equipment, and spareparts.

This is a critical issue particularly for systems such as wind tur-bines which are typically installed in remote areas and are noteasily accessible or may require special maintenance equipment,such as a crane. In addition, maintenance may be influenced bycrew constraints. For example, in the case of simultaneous fail-ures or multiple warnings from condition monitoring systems on

a wind farm, a limited size maintenance crew can cause additionalmaintenance delays. Our research intends to model the operationand maintenance (O&M) of a deteriorating system, such as windturbines, determine the optimum maintenance, and address the

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ffect of maintenance constraints on the availability and total gainaverage revenue per unit time) of the system.

There have been numerous research studies in maintenance andts optimization [10–24]. Due to the probabilistic nature of deteri-ration and failure of equipment, stochastic models have proven toe more suitable for maintenance studies.

Among the analytical techniques, Markov models have beenidely adopted in the literature [10–17]. Markov decision pro-

esses (MDP), and semi-Markov decision processes (SMDP) haveeen used for maintenance optimization in various sections of aower system, such as traditional power plants [10,11], substa-ion equipment [12,13], and renewable energy sources [14,15].ime-based Markov models [16] are limited in the sense thathey only consider time as a deterioration factor. To solve thisroblem, “inspection” has been added to the model to incor-orate CBM as well [12]. However, current Markov modelsre still limited in modeling complex situations with deteriora-ion, inspection, and maintenance [17,18]. The model becomesven more complex by including the realistic aforementionedestricting factors affecting maintenance and repair. Simula-ion models based on Monte Carlo simulation (MCS) have alsoeen employed for maintenance studies [19–25]. MCS may beerformed to study a power system [18–21] or its individualieces of equipment [23–25]. The main goal of these studies isenerally to determine the optimum maintenance policy con-idering cost and overall reliability. MSC is favorable becauset can also be applied to system states with non-exponentialistribution times without an extra computational burden [26].owever, due to the need for a large sample size, utilizingCS for maintenance optimization could be computationally

ntensive.None of the previous research has incorporated both mainte-

ance optimization and the consequences of restricting conditions,uch as extended duration of maintenance/repair, lead time, andpportunity costs, on the availability and profit of the system. Inhis paper, we develop a hybrid of analytical and simulation meth-ds incorporating SMDP and a replicated sequential-based MCSodel for wind turbines in order to determine the optimum main-

enance strategy and, at the same time, the effect of maintenanceonstraints on the availability and gain of the system. By choos-ng a hybrid method, we benefit from the combined advantages offorementioned types of modeling.

In the first stage, it is computationally more efficient to use annalytical method, similar to the SMDP introduced in [12], to obtainhe optimum maintenance of equipment, such as a wind turbine,nder different decision policies. Then, the MCS-based model iseveloped emulating the SMDP and validated through comparisonf the results. In the second stage, the MCS-based model devel-ped is employed to analyze the effect of maintenance and repairesource constraints on the availability and cost of the wind tur-ines, through different case studies. Due to the flexibility of ourimulation-based model, wind farm operators can calculate thempact of expected delays in maintenance or the repair of equip-

ent by using cost analysis to choose the optimum option, e.g.,hether to recruit additional repair crews to the site. Although theroposed method is described as it applies to wind turbines, therocedure is general; and it can be used to optimize the mainte-ance of different parts of a wind turbine as well as any type ofeteriorating piece or fleet of equipment, subject to data availabil-

ty.The rest of the paper is organized as follows. Section 2 provides

step by step explanation of the proposed approach and describes

he SMDP and the MCS-based models used in this research. Thearameters of the model used for the wind turbines in the casetudy are presented in Section 3. This section is followed by Section

which provides the results of case studies with wind turbines

Systems Research 104 (2013) 80– 86 81

based on both SMDP and MCS. Finally, the conclusion of this paperis given in Section 5.

2. Modeling and the approach

The proposed approach is based on the analytical andsimulation-based modeling described in this section. The processcan be summarized as follows and a more detailed explanation isprovided for each model in the following sections.

1. Build a semi-Markov model for operation and maintenance ofa wind turbine, considering equipment deterioration, failure,inspection, and maintenance rates (Fig. 1).

2. Define the types of maintenance and decision options at differentdeterioration stages. Different combinations of possible main-tenance decisions determine a set of applicable maintenancescenarios.

3. Determine the optimum maintenance policy based on SMDPunder various decision frequencies. Decision frequency is therate at which the maintenance is feasible considering the actualoperational constraints. Therefore, in this step, an optimummaintenance policy is determined for each decision frequency.

4. Develop an MCS-based model according to the state diagramof Step 1 and determine the optimum maintenance policy. Inthis step, MCSs are run iteratively for each possible maintenancepolicy; and the expected gain for each scenario is determined.The optimum policy is the one with the highest expected gain.

5. Validate the MCS-based model by comparing the results fromSteps 3 and 4.

6. Study the effect of maintenance constraints, such as mainte-nance lead time and repair crew readiness, on availability andcost of a single wind turbine and a group of wind turbines (Windfarm) with the MCS model.

2.1. SMDP

The state transition diagram of the semi-Markov processesmodel is shown in Fig. 1 [12]. The model is comprised threeoperating states, Di ; i = {1, 2, 3} , representing three deteriorationstages where D1 implies “like new” condition and the conditionof equipment deteriorates by moving toward D3. Eventually, thedeterioration leads to a failure state, F1, where it would requiresubstantial repair in order to bring the equipment back to its initialworking state. There is also another type of failure due to randomevents denoted by F0. In this model, � and � represent transi-tion rates between adjacent states, where �i is a random failurerate originating from Di; and �j ; j = {0, 1} , is the repair rate afterfailure Fj. Mi and mi denote major and minor maintenance at thedeterioration stage, i, respectively. Following maintenance activ-ity, equipment should be in better condition; however, there is apossibility that its condition worsens due to defects in replacementparts or human error. Therefore, the next state after visiting an Mior mi state can be either one of the Di states or an F1 state; andtheir transition rates are denoted by �Mi or mi−Di or F1 . The ratesof leaving the major and minor maintenance states, �M and �m,are the same at each deterioration stage and can be defined usingEqs. (1) and (2), respectively. These rates are inversely related tothe duration of the maintenance.

�M =(

3∑k=1

�Mi−Dk

)+ �Mi−F1 , i = {1, 2, 3} (1)

�m =(

3∑k=1

�mi−Dk

)+ �mi−F1 , i = {1, 2, 3} (2)

82 S. Kahrobaee, S. Asgarpoor / Electric Power Systems Research 104 (2013) 80– 86

SMDP

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reward from being in Di is reduced as i increases. With the samereasoning, the cost of maintenance slightly decreases over timebecause of lower opportunity costs for an aged turbine. Table 2gives transition probabilities from the maintenance states back to

Table 1Expected reward/penalty of being in each state.

State Expected reward/penalty State Expected reward/penalty

D1 210,500 m1 −9000D 184,000 m −9000

Fig. 1. State transition diagram for

In formulating SMDP, for each level of deterioration, a decisionan be made from the three possible options: d1 (do nothing), d2 (doajor maintenance), or d3 (do minor maintenance).

The “Inspection” state in an SMDP model [12] is where the deci-ions are made; and, therefore, they are represented by “Decision”tates in our model (Fig. 1).

The policy iteration approach is used to solve this SMDP scheme27]. After selection of an initial policy, there is an iterative processith two main steps to evaluate and improve the policies until an

ptimum policy is determined.In the evaluation step, a policy is assessed by solving a set of

quations (3) which calculates the gain, g, and the relative valuesf this policy.

i + g = qiti +N∑

j=1

�ijvj, i = 1, 2, . . . , N (3)

here vi, qi, and ti are the relative value, the earning rate, and theojourn time of state i, respectively. � ij represents the transitionrobability from state i to j, and N is the total number of states.

In the policy improvement step, the relative values derived byolving Eq. (3) are utilized. For each state i, a search is performed forn alternative, a, that maximizes the test quantity, Ga

i, expressed by

q. (4).

ai = qa

i +(

1tai

)⎡⎣ N∑j=1

� aij vj − vi

⎤⎦ (4)

This alternative is set as the new decision in state i, and therocess is repeated for all states to determine the new policy.

It should be noted that the process explained above solves SMDPor a specific decision frequency, �d. However, the optimum main-enance policy may vary based on the feasibility of the maintenancerequency. To address this aspect, SMDP should be solved for dif-erent decision frequencies. This will be explored by setting up aase study and will be explained in Section 3.

.2. MCS

A replicated MCS-based model is developed based on the same

et of states described for SMDP using Rockwell Arena software28]. This software is modular and features a flowchart-style

odeling methodology enabling MCS studies and performancevaluation.

study of deteriorating equipment.

The model developed is illustrated in Fig. 2 where the wind tur-bine enters the simulation environment and travels within the statespace for a designated lifetime (e.g., 20 years). Then the simulationis repeated with the required number of replications to determineconfidence intervals. The majority of the states in the SMDP con-figuration are modeled by three components representing sojourntime, expected reward, and transition probabilities, in the Arenamodel. First, the block representing the sojourn time imposes adelay with a desired probability distribution. Next, the expectedreward associated with that state is allocated. Finally, a decisionblock is used to assign transition probabilities between the states.The failure states, F0 and F1, do not need the third component men-tioned above because the next state after a failure is always D1. Ineach iteration of the MCS, the equipment starts at D1 and travelsthrough the states based on the probabilities defined. At the end ofthe simulation, Arena calculates the expected output parameters,such as the average gain and the availability of the system.

3. Case study

The models described in the previous section are employed tostudy wind turbines as a case study. The following tables presentthe parameters used in the model based on the data for a typi-cal 3 MW direct drive wind turbine [29]. The data provided in thissection is referred to as the base case in the sensitivity analysis ofSection 4.

Table 1 provides the expected reward/penalty of being in eachstate where negative values correspond to the costs of repair andmaintenance. In this table, it is rationally assumed that as the tur-bine deteriorates, its capacity factor decreases; and as a result, the

2 2

D3 131,500 m3 −8500M1 −23,000 F0 −37,000M2 −21,500 F1 −1400,000M3 −20,500

S. Kahrobaee, S. Asgarpoor / Electric Power Systems Research 104 (2013) 80– 86 83

Fig. 2. State transition diagram for MCS-based

Table 2Transition probabilities after maintenance.

From To Probability From To Probability

M1 D1 0.99 m1 D1 0.99M1 D2 0.01 m1 D2 0.01M2 D1 0.89 m2 D1 0.4M2 D2 0.1 m2 D2 0.59M2 D3 0.01 m2 D3 0.01M3 D2 0.9 m3 D2 0.35

tei

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TT

M3 D3 0.1 m3 D3 0.65

he working states. It is assumed that major maintenance is moreffective than minor maintenance; and a small probability of 1% isncluded to account for human error.

The transition rates used to calculate the remaining transitionrobabilities are presented in Table 3. To consider the vulnerabilityf aged equipment, it is assumed that the rate of random failurencreases with deterioration. For the base case study, the durationsor major and minor maintenance are 6 and 3 days, respectively,nd the duration of repairs after deterioration and random failuresre 14 and 3.5 days, respectively.

. Results and discussion

This section provides the results for maintenance optimizationnd availability assessment of the described wind turbine (equip-ent) and a wind farm (fleet) using SMDP and MCS. In addition,

he effects of maintenance and repair constraints on availabilityf the wind turbines are investigated. The opportunity costs of the

quipment due to these constraints are used to determine the creweeded for a number of wind turbines managed on a wind farm.

able 3ransition rates of the model.

Parameter Rate (day−1) Parameter Rate (day−1)

�12 1/730 �3 1/122�23 1/365 �0 1/3.5�3F 1/365 �1 1/14�1 1/243 �M 1/6�2 1/183 �m 1/3

modeling of deteriorating equipment.

4.1. Wind turbine study with SMDP

SMDP is performed using MATLAB software. The optimum pol-icy depends on decision frequency (�d); and as the time betweenthese decisions becomes longer (less frequent maintenance), amore extensive type of maintenance will be required. Fig. 3a–cshows the optimum maintenance strategies obtained for eachoperating state of the wind turbine with different maintenancefrequencies.

The most efficient decision in D1 is always to do nothing sincethe wind turbine is in its best operating condition; however, inD2 and D3, the optimum decision may vary. Performing too manymaintenance functions is not efficient; and that is reflected in theoptimization results with a do nothing decision if the maintenancefrequency goes beyond 1.6 and 3.65 times per year for D2 and D3,respectively. On the other hand, if the maintenance is performedless frequently, the optimum decision will shift toward a do majormaintenance.

Based on the optimum maintenance decisions at each work-ing state, the availability of the wind turbine can be determined asshown in Fig. 3d. The discontinuity in the availability curve occursdue to a change in the optimum maintenance strategy which mod-ifies the transition probability matrix of the model. According tothis figure, availability of the wind turbine is decreasing as themaintenance frequency increases. However, changes in optimummaintenance policy create sudden desirable availability rises at thecorresponding points in maintenance frequency. In addition, Fig. 3dshows the gain of the system based on the SMDP model for differentmaintenance frequencies. Among these decisions, a maintenancerate of nearly once per year results in the highest calculated gainfor which the optimum maintenance decisions are do nothing, dominor maintenance, and do major maintenance in D1, D2, and D3,respectively.

4.2. Wind turbine study with MCS

The optimum maintenance policy for the case study is ana-lyzed using MCS, and the results are compared with those fromthe SMDP method. Therefore, with the previously determined opti-

mum maintenance frequency of once per year, we now run theMCS model (Fig. 2) for all 27 combinations of possible mainte-nance policies (d1, d2, d3) in D1, D2, D3, and determine the policywhich results in the highest gain (optimum policy). The simulation

84 S. Kahrobaee, S. Asgarpoor / Electric Power

Fig. 3. Optimum maintenance decisions at different operating states: (a) D1, (b) D2

and (c) D3 using SMDP. (d) Wind turbine availability and total system gain withvarious maintenance frequencies.

280.00

330.00

380.00

430.00

480.00

111

113

112

131

133

132

121

123

122

311

313

Gain

Decisions

Fig. 4. Expected gain of the wind turbine w

0.960

0.965

0.970

0.975

111

113

112

131

133

132

121

123

122

311

313

312

Avai

labi

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Decisions at D

Fig. 5. Expected availability of the wind turbi

Systems Research 104 (2013) 80– 86

duration in this study is 20 years, and the number of iterations isselected as 5000. Bases on extensive testing, this number of itera-tions satisfies the convergence of all the case studies with less thanone percent error in the expected output parameters such as thegain and availability with significance level of 0.05.

Fig. 4 shows the expected gains and the confidence intervals forall of the cases studied. Do nothing, do minor maintenance, and domajor maintenance are denoted by “1,” “2,” and “3” in this figure,respectively. The maintenance policy corresponding to the highestgain is “123” which is in agreement with the result of the SMDPmethod.

Fig. 5 displays the availability of the wind turbine with differentpolicies. The availability corresponding to the optimum mainte-nance policy (about 0.972) is not the highest in this figure. Thisavailability value is the same as the one derived from SMDP (Fig. 3)with a maintenance frequency of once per year.

Next, we study the effect of maintenance and repair restrictionson the availability and cost of the wind turbine. For this purpose, theeffects of various durations of maintenance and repair on the avail-ability of the wind turbine are captured through sensitivity analysisusing MCS. The results are shown in Figs. 6 and 7 where the basecase durations have been defined in Section 3. In addition, a relativecost analysis is performed where the opportunity cost of the windturbine in each case is compared to the base case scenario. Here,the opportunity cost is defined as the amount of expected profitthat would have been realized had the wind turbine not operatedbelow the availability of the base case study.

The opportunity cost of wind turbine k for duration of T can becalculated from Eq. (5).

OCk = �Ak · T · Poutk· CFk · PR (5)

where OCk and �Ak are the opportunity cost and relative avail-

ability compared to the base case, respectively; Poutk

is the ratedoutput power of the turbine; CFk represents the capacity factor ofthe wind turbine based on the wind resource of the area; and PRis the expected rate of profit from selling the electricity generated.

312

331

333

332

321

323

322

211

213

212

231

233

232

221

223

222

at D1 , D2 , an d D3

ith different maintenance policies.

331

333

332

321

323

322

211

213

212

231

233

232

221

223

222

1, D2, and D3

ne with different maintenance policies.

S. Kahrobaee, S. Asgarpoor / Electric Power Systems Research 104 (2013) 80– 86 85

-700-20030080013001800

0.965

0.967

0.969

0.971

0.973

0.975

Base/4 Base/3 Base/2 Base case Base*2 Base*3 Base*4

OC(

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Dura�on of Maintenance

Availability PR=2cents/kWh PR=3cents/kWh PR=4cents/kWh

Ft

Ti

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etcHpTrntlds

wAdFa

t

F

Fig. 8. Expected wait time before repair with different numbers of turbines on awind farm.

0

50000

100000

150000

200000

0.9475

0.9525

0.9575

0.9625

0.9675

0.9725

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

OC(

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Turb

ine

Avai

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Number of w ind turb ines in th e w ind f arm

Availabilit y PR= 2cents/ kWh PR= 3cents/ kWh PR= 4cents/ kWh

ig. 6. Expected availability of the wind turbine with different durations of main-enance.

hree different rates of 2, 3, and 4 cents/kWh have been consideredn these figures; and CF is assumed to be 0.35 for all of the cases.

As depicted in Figs. 6 and 7, higher values of PR result in higherpportunity costs when the durations of repair and maintenancere longer than the base case. On the other hand, slightly morerofit is expected if these durations can be reduced.

The results indicate that longer durations of repair andaintenance reduce the availability of the system, and fasteraintenance and repairs may not improve it considerably. In

ddition, since durations of repair are usually longer thanaintenance, they can influence the reliability and the oppor-

unity costs of the wind turbine more significantly, as observedrom Figs. 6 and 7.

.3. Wind farm study with MCS

In addition to delays in repairs due to weather conditions, lack ofquipment, etc., the unavailability of the repair crew can influencehe reliability of equipment. Maintenance of a fleet of equipmentan usually be planned ahead to minimize delay and lead time.owever, equipment failures are random; in a wind farm, for exam-le, simultaneous failures may occur on different wind turbines.hen, a turbine repair may be delayed due to already-scheduledepairs to other turbines. Therefore, a certain number of technicianseed to be assigned for a special fleet to avoid losing revenue dueo delays in repair of the equipment. This section studies expectedead time, availability, and costs of unavailability which are used toetermine the optimum number of crew hired for O&M of a fleet,uch as a wind farm.

This condition is modeled by simultaneous simulation of 20ind turbines representing a wind farm using the MCS model.ssuming that the wind turbines are repaired one at a time, Fig. 8epicts the expected wait time before repair, on average, in both

0 and F1 failure states. As expected, the situation is aggravated in

wind farm with more wind turbines.Fig. 9 shows the average availability of the wind turbines on

his wind farm versus the number of wind turbines, assuming the

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0.880

0.900

0.920

0.940

0.960

0.980

1.000

Base/4 Base /3 Base /2 Base case Base *2 Base *3 Base *4

OC(

$/ye

ar)

Avai

labi

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Dura�on o f Repair

Availability PR=2cents/kWh PR=3cents/kWh PR=4cents/kWh

ig. 7. Expected availability of the wind turbine with different durations of repair.

Fig. 9. Expected availability of a wind turbine based on the number of turbines ona wind farm.

repair capability of one turbine at a time. Although the availabilitydoes not change considerably with a small number of wind tur-bines, this effect becomes increasingly significant to the long-termoperation of large wind farms. Fig. 9 also presents the opportunitycosts the wind farm incurred because of the delay in repair of thewind turbines, with different expected rates of profit based on Eq.(5). A comparison of this cost with the cost of hiring an additionalrepair technician can determine the cost-effective option. For thecase study of the paper, it is assumed that a second technician canbe hired at a rate of $50,000 per year [30]. Therefore, according toFig. 9, the second repair technician becomes profitable with morethan 12, 14, and 16 wind turbines on a wind farm with a PR of 4, 3,and 2, respectively.

In the next step, the effect of two parallel repairs have beenstudied using the MCS model, and the expected availability of awind turbine in this case is depicted in Fig. 10.

Availability remains almost constant in a wind farm containingup to 20 wind turbines compared with the previous case. Fig. 10 alsoshows how the expected availability of an average wind turbinechanges if the second repair technician is employed at the site with

different rates of PR.

0.9475

0.9525

0.9575

0.9625

0.9675

0.9725

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Turb

ine

Avai

labi

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Number of wind turb ines in the w ind f arm

One repa ir crew Two repa ir crew PR= 2cents/ kWh

PR=3cents/ kWh PR= 4cents/ kWh

Fig. 10. Expected availability of a wind turbine with a cost-effective change in repaircrew based on the number of turbines on a wind farm.

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. Conclusion

In this paper, a hybrid SMDP-MCS method was proposed tobtain and validate the optimum maintenance policy for deterio-ating equipment. The goal was to not only determine the optimumaintenance policy but also include the restricting conditions

ssociated with actual maintenance and repair of deterioratingquipment such as wind turbines. The process was conducted inhe following steps: (1) a SMDP approach was employed to deter-

ine the optimum maintenance policy for a wind turbine; (2) anCS model was proposed to simulate the analytical SMDP model;

3) with the best maintenance policy applied to the replicatedCS model, further investigation was carried out to determine the

ffect of maintenance and repair restrictions on the availability andpportunity costs of the system. The consequences of equipmentnd human resource unavailability were modeled by extendedurations of repair/maintenance and lead times, and the perfor-ance of wind turbines was studied through sensitivity analysis.sing this approach, wind farm maintenance planners and assetanagers are able to (1) determine the optimum type and fre-

uency of maintenance for the wind turbines; (2) study the effectf maintenance and repair resource restrictions on the availabilitynd costs of the wind farm; and (3) run cost/benefit studies to allo-ate the proper number of technicians for maintenance and repair,aking into consideration the costs of wind farm unavailability anddditional crew employment. For example, the results of our lastase study indicated that it would be beneficial to hire repair tech-icians at a rate of one for every 12–16 turbines in a wind farm.

n addition, with the parallel work of the second technician, thevailability of each wind turbine could increase by almost 1.5% onverage.

eferences

[1] S.N. Mukerji, Deterioration of electrical equipment and its assessment by envi-ronmental testing, in: IEE-IERE Proc., vol. 8, 1970, pp. 115–120.

[2] R. Ahmad, S. Kamaruddin, An overview of time-based and condition-basedmaintenance in industrial application, Computers and Industrial Engineering63 (2012) 135–149.

[3] P. Gill, Electrical Power Equipment Maintenance and Testing, CRC, New York,1997.

[4] E. Deloux, B. Castanier, C. Berenguer, Predictive maintenance policy for a grad-ually deteriorating system subject to stress, Reliability Engineering & SystemSafety 94 (2009) 418–431.

[5] L. Bertling, R. Allan, R. Eriksson, A reliability-centered asset maintenancemethod for assessing the impact of maintenance in power distribution systems,IEEE Transactions on Power Systems 20 (2005) 75–82.

[6] H.H. Hoseinabadi, M.E.H. Golshan, Availability, reliability, and component

importance evaluation of various repairable substation automation systems,IEEE Transactions on Power Delivery 27 (2012) 1358–1367.

[7] J. Endrenyi, S. Aboresheid, R.N. Allan, The present status of maintenance strate-gies and the impact of maintenance on reliability, IEEE Transactions on PowerSystems 16 (2001) 638–646.

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Systems Research 104 (2013) 80– 86

[8] Application of reliability centered maintenance to optimize operation andmaintenance in nuclear power plants, International Atomic Energy Agency,IAEA-TECDOC-1590, 2007.

[9] D. Frost, R. Dechter, Optimizing with constraints: a case study in schedulingmaintenance of electric power units, Lecture Notes in Computer Science 1520(1998), http://dx.doi.org/10.1007/3-540-49481-2 40.

10] A. Rajabi-Ghahnavie, Fotuhi-Firusabad, Application of Markov decision processin generating units maintenance scheduling, in: International Conference onProbabilistic Methods Applied to Power Systems, 2006.

11] T.M. Welte, J. Vatn, J. Heggset, Markov state model for optimization of main-tenance and renewal of hydro power components, in: 9th InternationalConference on Probabilistic Methods Applied to Power Systems, Stockholm,2006.

12] H. Ge, C.L. Tomasevicz, S. Asgarpoor, Optimum maintenance policy with inspec-tion by semi-Markov decision processes, in: 39th North American Power Symp.,2007, pp. 541–546.

13] H. Ge, S. Asgarpoor, Reliability and maintainability improvement of substa-tions with aging infrastructure, IEEE Transactions on Power Delivery 27 (2012)1868–1876.

14] Y.R. Wu, H.S. Zhao, Optimization maintenance of wind turbines using Markovdecision processes, in: 2010 International Conference on Power System Tech-nology, 2010.

15] E. Byon, L. Ntamino, Y. Ding, Optimal maintenance strategies for wind tur-bine under stochastic weather conditions, IEEE Transactions on Reliability 59(2010).

16] C.L. Tomasevicz, S. Asgarpoor, Optimum maintenance policy using semi-Markov decision process, in: 38th North American Power Symp., 2006, pp.23–28.

17] S.V. Amari, L. McLaughlin, H. Pham, Cost-effective condition based maintenanceusing Markov decision processes, in: Proc. of Annual Reliability and maintainab.Symp., 2006.

18] Y. Haung, X. Guo, Finite horizon semi-Markov decision processes with appli-cation to maintenance systems, European Journal of Operational Research 212(2011) 131–140.

19] S.G. Gedam, Optimizing R&M performance of a system using Monte Carlo sim-ulation, in: Annual Reliability and Maintainab. Symp., 2012.

20] P. Hilber, Maintenance optimization for power distribution systems, KTH RoyalInstitute of Technology, Stockholm, 2008 (Doctoral Thesis).

21] A. Karyotakis, On the optimisation of operation and maintenance strategies foroffshore wind farms, University College London, 2011 (Doctoral Thesis).

22] F. Besnard, On optimal maintenance management for wind power systems,KTH Royal Institute of Technology, Stockholm, 2009 (Licentiate Thesis).

23] G. Lanza, S. Niggeschmidt, P. Werner, Behavior of dynamic preventive mainte-nance optimization for machine tools, in: Annual Reliability and Maintainab.Symp., 2009, pp. 315–320.

24] E. Zheng, Y. Li, B. Wang, J. Wu, Maintenance optimization of generatingequipment based on a condition-based maintenance policy for multi-unitsystems, in: Chinese Control and Decision Conference, 2009, pp. 2440–2445.

25] J. Andrawus, J. Watson, M. Kishk, Maintenance optimization of wind turbines:lessens for the built environment, in: Proc. of 23rd Annual ARCOM Conference,2007, pp. 893–902.

26] G.J. Anders, A.M.L. Silva, Cost related reliability measures for power sys-tem equipment, IEEE Transactions on Power Systems 15 (2000) 654–660.

27] R.A. Howard, Dynamic Probabilistic Systems, Semi-Markov and Decision Pro-cesses, vol. 2, John Wiley & Sons, 1971.

28] Arena Website. Available online: http://www.arenasimulation.com

29] S. Kahrobaee, S. Asgarpoor, Risk-based failure mode and effect analysis for wind

turbines (RB-FMEA), in: 43rd North American Power Symp., 2011.30] R. Poore, C. Walford, Development of an operations and maintenance cost

model to identify cost of energy savings for low wind speed turbines, in: Sub-contract Report, NREL/SR-500-40581, 2008.