Stochastic optimization for condition based opportunistic maintenance for offshore wind farms with multiple turbines

Stochastic optimization for condition based opportunistic

maintenance for offshore wind farms with multiple turbines

University of Groningen

Master Thesis: Supply Chain Management

Abstract

Contents

1 Introduction 3

2 Theoretical Background 5

2.1 Opportunistic maintenance for offshore wind farms . . . 5

2.2 Condition based opportunistic maintenance for offshore wind farms . . . 6

3 Methodology 7 3.1 Model Description . . . 7

3.2 Model formulation . . . 10

3.3 Constraints . . . 10

3.4 Rolling horizon framework . . . 15

3.5 Sensor driven deterioration methodology . . . 15

3.6 Performance metrics . . . 16

3.7 Parameter setting . . . 17

3.8 Benchmark policies . . . 18

3.8.1 Preventive time based maintenance . . . 18

3.8.2 Corrective Maintenance . . . 18

4 Computational Results 19 4.1 Influence of crew deployment cost on policy performance . . . 19

4.2 Effect of electricity price on policy performance . . . 23

4.3 Effect of maintenance crew capacity on policy performance . . . 26

4.4 Effects of wind farm accessibility on policy performance . . . 29

5 Discussion 32

6 Conclusion 33

7 Limitations and further research 34

1

Introduction

Renewable energy production systems are considered to be the future in energy supply due to the increasing concerns of green house emissions and the limited resources of fossil fuels. The contribution of offshore wind power supply has gained popularity among countries with access to open water (Sarker & Faiz, 2016). In recent times, there is a significant growth in production capacity for offshore wind farms due to the abundance of wind potential and the available open space at sea. Therefore, the installed capacity for offshore wind power in the European Union alone has expanded from 532 megawatts (MW) in 2003 to 18499 MW in 2018 (Wind Europe, 2018), which is equal to an annual growth of 26%. Predictions estimate that this annual growth will proceed with the same trend for the coming years (Shafiee, Finkelstein, & B´erenguer, 2015).

Although the future of the offshore wind power looks promising, the operations & maintenance (hereafter; O&M) for the offshore wind farms is estimated to account upon one-third of the total costs which is significantly higher compared with onshore wind farms where the total cost of O&M activities are ranging between 5% and 10% of the total expenditures (Maples, Saur, Hand, van de Pieterman, & Obdam, 2013). Until this day offshore wind farm projects are still dependent on subsidies since it is simply not financially feasible for private companies to plan and build offshore wind farm projects without governmental support (Nicolini & Tavoni, 2017). The reason for the significant high O&M costs lies in the fact that offshore wind farms are located in a harsh marine environment with rapid changing weather conditions which negatively affect the systems availability and reliability resulting in more failures and downtime compared with onshore wind farms (Scheu, Matha, Hofmann, & Muskulus, 2012). Onshore wind farms can reach a system availability between 95% and 99%. Meanwhile the systems availability for offshore wind energy systems stagnates between 60% to 70% (Le & Andrews, 2015). To be able to compete with other renewable energy sources the pressure to reduce O&M costs for offshore wind farms is increasing (Shafiee & Sørensen, 2017). In an attempt to reduce these O&M expenditures, a suitable O&M policy should be de-veloped to make the offshore wind farm projects economically independent and competitive with other renewable energy sources. In spite of its importance, O&M policies have not been optimized in practise (Erguido, Crespo M´arquez, Castellano, & G´omez Fern´andez, 2017). Currently the most applied maintenance strategies are preventive time-based maintenance and corrective maintenance in which maintenance actions are performed at fixed time intervals or after a failure occurs (F. Ding & Tian, 2011). In addition to these two dominant O&M policies, Condition Based Maintenance has been proven to be cost effective compared with the two aforementioned by enhancing condition monitoring systems to prevent failures based on the component condition, rather than the predeter-mined estimated lifetime (Amirat, Benbouzid, Al-Ahmar, Bensaker, & Turri, 2009). Only a limited number of studies addressed alternative maintenance strategies such as opportunistic maintenance as an advisable maintenance policy for offshore wind farms.

and need to be replaced together with other maintenance actions on wind turbines. Grouping maintenance actions act as an opportunity to exploit economic dependencies by reducing indirect costs due to production losses, shutdowns, traveling and set-up expenditures (Koochaki, Bokhorst, Wortmann, & Klingenberg, 2012). Expectations show that the economic dependencies will increase in the near future due to a rise in electricity prices, higher production capacity of wind farms to an increasing number of wind turbines at each wind farm and the increasing capacity of each wind turbine, and limited accessibility due to increasing variation in weather conditions (Wind Europe, 2018; Garc´ıa M´arquez, Tobias, Pinar P´erez, & Papaelias, 2012; Y. Ding, Ntaimo, & Byon, 2010). Therefore an optimal maintenance strategy should be implemented to deal with these changes.

Multiple studies have showed the benefits of implementing an opportunistic maintenance strat-egy for offshore wind farms by demonstrating that cost reductions can be achieved by diminishing maintenance costs, production losses and travelling expenditures (Abdollahzadeh, Atashgar, & Ab-basi, 2016; Besnard, Patriksson, Str¨omberg, Fischer, & Bertling, 2011; Sarker & Faiz, 2016; Tian, Jin, Wu, & Ding, 2011). However, these previous studies are primarily focusing on jointly optimizing corrective maintenance and time-based preventive maintenance activities assuming each component has the same remaining lifespan with the results that preventive maintenance actions are executed after the lifespan has exceeded a certain threshold (Bachant, Goude, & Wosnik, 2016). This leads to maintenance actions that are performed either too early, not fully exhausting the component life time, or performing maintenance actions too late which increases the chance of failure leading in higher downtime of the wind turbine and higher maintenance costs due to corrective maintenance actions. A limited number of studies considered condition based maintenance in combination with opportunistic maintenance strategy. Tian (2011) and Perez (2015) studied condition based mainte-nance in combination with opportunistic maintemainte-nance but both narrowed their studies to a single wind turbine, whereas Yildirim et al., (2017) excluded multiple components for each wind turbine. When the dependencies are grouped within and between wind turbines we expect that maintenance activities can be scheduled more precise at the wind turbines that oppose the highest risk of failure, reducing unexpected failures and downtime.

Therefore, this study will function as an extension of the current offshore wind farm maintenance literature by developing a Mixed Integer Programming model which is able to test the effectiveness of implementing a condition based opportunistic maintenance policy with real life sensor data together for an offshore wind farm with multiple wind turbines and multiple components. The objective of the model is to maximize the operational revenue which is subject to operational O&M aspects such as the maximum production capacity at each time period, stochastic degradation process of com-ponents based on actual sensor data, limited maintenance resources and maintenance capabilities in a harsh marine environment. To evaluate the effectiveness, the CBOM policy is bench-marked over a periodic time-based maintenance policy (PM) and a strictly corrective maintenance policy (CM).

2

Theoretical Background

The following section provides an overview of previous research considering condition based tunistic maintenance strategies for offshore wind farms. At first, the literature regarding oppor-tunistic maintenance and their limitations are discussed. Hereafter the literature that have studied condition based opportunistic maintenance will be presented.

2.1

Opportunistic maintenance for offshore wind farms

Opportunistic maintenance refers to the common practice of reducing the number of maintenance visits to offshore wind farms by performing jointly maintenance activities (F. Ding & Tian, 2011). Appropriately implementing an opportunistic maintenance policy is considered to be an efficient strategy to reduce maintenance expenditures by taking full advantage of the maintenance crew ca-pacity by grouping maintenance actions together, either preventive and/or corrective tasks, in order to reduce maintenance set-up costs (Besnard, Patriksson, Str¨omberg, Wojciechowski, & Bertling, 2009). In the study of Besnard (2011) the author extended this model by calculating the effects over a longer period and increased the number of turbines whereby the accessibility for the mainte-nance crew was dependent on weather conditions. The model showed that scheduling maintemainte-nance tasks in an opportunistically fashion were able to decrease the maintenance expenditures with 32% compared with a strictly time-based preventive maintenance policy. However the model applied solely preventive maintenance actions on components based on the estimated lifespan neglecting corrective maintenance actions after a component has failed. The study of Atashgar et al. (2016) incorporated a combination of deployment possibilities allowing maintenance crews to perform pre-ventive maintenance and corrective maintenance actions at the same time epoch. The study of Erguido et al. (2017) extended this model by scheduling maintenance activities based on the time-varying weather conditions which limits the accessibility of the offshore wind farm when weather conditions were too harsh.

2.2

Condition based opportunistic maintenance for offshore wind farms

Condition based maintenance systems are constantly monitored on their actual condition using sen-sors (e.g. temperature, vibration, noise, lubrication and corrosion)(McMillan & Ault, 2007). When the condition of the sensor exceeds a predetermined threshold it gives the operator an opportunity to act upon this information before the component completely fails. However not every systems condition can be monitored. The condition holds that it has to be measurable and it must correlate to the moment of failure (De Jonge, Klingenberg, Teunter, & Tinga, 2015). Since the mechanical construction of wind turbines is relatively simple, the condition of wind turbines components are easy to monitor through the use of integrated sensors (Hameed, Hong, Cho, Ahn, & Song, 2009). The first studies that included a condition based policy for offshore wind farms mainly focused on justifying the extra monetary expenses compared with the traditional periodic time-based main-tenance policy (Nilsson & Bertling, 2007). In the study of McMillan et al. (2008) the authors compared different types of condition monitoring strategies, namely continuous condition monitor-ing, periodic condition monitormonitor-ing, and visual inspection. In terms of maintenance cost reduction the strategy of continuous condition monitoring resulted in the most suitable solution. Condition based maintenance has been proven to be a beneficial approach for reducing maintenance costs com-pared with the periodic time-based maintenance policy. However in the aforementioned studies, maintenance activities are solely performed during a planned interval dependent on the components lifespan which was predetermined. When condition based maintenance is combined with oppor-tunistic maintenance the foremost expected benefit is that the component with the highest failure probability has the highest priority to undergo preventive maintenance rather than the oldest com-ponent. Therefore the number of corrective maintenances can be reduced since the actual status of the component provides information for the ideal maintenance interval. For offshore wind turbines the component state is heavily influenced by the variable load due to harsh weather conditions (Bachant et al., 2016; Wilson & McMillan, 2014). The study of Yildirim et al. (2017) stated that the deterioration process for identical machinery can create considerable differences. This results in more failures if the actual conditions are not monitored, which comes at a cost if more corrective maintenance actions are required (Garc´ıa M´arquez et al., 2012).

ca-3

Methodology

In this section the establishment of the methodology, including the key features, are proposed. A Mixed Integer Programming (MIP) will be formulated to assess the effectiveness of the condition based opportunistic maintenance policy. The model’s objective is to maximize profit while con-sidering the inter-dependencies such as turbine failure risk, feasibility of maintenance activities, wind power output influenced by weather conditions and limited capacity of the maintenance crew. These inter-dependencies are mathematically characterized by a set of constraints. Furthermore, a rolling horizon framework is proposed for assessing O&M activities over a longer planning horizon. At each instance the parameters and deterioration data of the operational components and failed components will be updated according to the results obtained from the previous instance.

This chapter is structured as follows. First the model is formulated that will provide a de-scription of the problem that is represented by the MIP-model. Hereupon the model’s objective function will be introduced followed by the set of constraints to conform the models formulation. Hereafter, the methodology to compute the sensor remaining lifetime and failure probabilities are discussed. Furthermore, a description of the rolling horizon framework is made that allows to test the performance of maintenance policies over a longer time period. This section concludes with the parameter setting.

3.1

Model Description

crew’s lead-time to reach the wind turbine is negligible. It is assumed that in the case a component has been maintained by a maintenance crew, either preventive or corrective, it will not fail again during the remainder of the planning horizon. In table (1) the variables which are used in the model are described. The following indices are used in the model during the planning horizon:

• t Index for maintenance epochs for set T • i Index for turbine for set G

• k Index for component for set K • Go set of operational turbines

• Gf set of operational turbines

• Ko set of operational components

Variables Description

yti Generated power for turbine i.

πt Price for electricity.

qit The maximum power turbine i can produce during time epoch t.

xt When binary variable is equal to 1 a maintenance crew has been deployed

during maintenance epoch t.

zi,kt When binary variable is equal to 1 preventive maintenance has been executed

on component k in turbine i during maintenance epoch t.

v_ti,k When binary variable is equal to 1 corrective maintenance has been executed on component k in turbine i during maintenance epoch t.

ui,k_t When binary variable is equal to 1 maintenance has been executed on component k in turbine i before the end of the planning horizon t. ws,ti,k When binary variable is equal to 1 when no maintenance actions have been

executed between sub-period s and time period t on component k in turbine i. δit,1 Generated power for turbine i during time epoch t before maintenance actions zi,kt .

δit,2 Generated power for turbine i during time epoch t maintenance actions zti,k.

pi,kt Failure probability of component k in turbine i.

Ri,kt Remaining life of component k in turbine i.

ρit Failure probability of turbine i during time period t.

ηth Binary variable dependent on the maintenance status h at time epoch t.

Ctv Crew deployment costs.

C_ti,ko

k,t Costs of maintenance for operating component k in turbine i. C_if Failure penalty if wind turbine i has not been maintained before

the end of the planning horizon.

3.2

Model formulation

The objective of the model is to maximize profit by considering operational aspects and maintaining the wind farm to ensure it is in good condition. The variables used for formulating the MIP model are summarized in table 1. The first term of this equation entail the revenue that can be generated by production from each operational wind turbine which is denoted by yi

tmultiplied with the energy

price πt. The second term holds the crew deployment costs where, every time a maintenance crew

is dispatched xt. The third term calculates the cost C i,k to

k,t for conducting preventive maintenance

actions zi,k_t on component k in turbine i in time period t. The fourth term evaluates the costs which are incurred if the wind turbine state is ’failed’ with the failure probability ρi

tof wind turbine

i during time epoch t. C_if represents the penalty of failure which is incurred when turbine i has failed based on the failure probabilities of the components within the turbine before the end of the planning horizon. max X i∈G X t∈T yi_t· πt | {z } operational revenue −X t∈T xt· Cvt | {z }

crew deployment cost

−X i∈Go X k∈Ko X t∈T zi,k_t · C_toi,k k,t | {z }

component maintenance cost

− X i∈Go X t∈T ρi_t· C_if | {z }

failure penalty cost

(1)

3.3

Constraints

1.) Linking failure uncertainty to operations

Constraints (2-6) establishes the link between the uninterrupted operational production qi tand

the expected operational production yi

tfor operational turbine i in Go. The relationship is

decom-posed into two cases. Case I considers the time before the preventive maintenance has been executed and is described in constraint (3). For example if the sensor-driven failure probability pi,k_t is 20% the expected production of turbine i, before preventive maintenance has been executed, is equal to 80% of the uninterrupted production qi

t. Case II considers the time after preventive maintenance

has been performed and is described in constraint (4). Hereby it is assumed that wind turbine i is able to produce the uninterrupted operational production which is equal to qi

t. Constraints (5

& 6) ensure that at most one of the [δ_t,ji : j ∈ (1, 2)] variables can be non-zero for any i and t. If a component k fails before the scheduled preventive maintenance action, the failed component is going to be scheduled for corrective maintenance. In constraints (7 & 8) the link between binary variable z_ti,k and binary variable w_s,ti,k is made. For example, z_ti,k = 1 if wi,k_s,t = 0 meaning that a maintenance crew visits a wind turbine i between sub-period s and time epoch t. In the scenario whereby z_ti,k= 0, and the binary variable w_s,ti,k= 1 no maintenance crew has visited wind turbine i between sub-period s and time period t.

yi,t= δit,1+ δ i

δi_t,1≤ 1 − t X s=1 h pi,ko f · (1 − w i,k s,t) i ! · qi t, ∀i ∈ Go, ∀t ∈ T (3) δ_t,2i ≤ qi t, ∀i ∈ Go, ∀t ∈ T (4) δ_t,1i ≤ T X k=t+1 zi,k_t ! · M, ∀i ∈ Go, ∀t ∈ T (5) δit,2≤ t−1 X s=1 zsi ! · M, ∀i ∈ Go, ∀t ∈ T (6) w_s,ti,k≤ 1 − zτ, ∀i ∈ Go, ∀t ∈ T , ∀τ ∈ {s, s + 1, ..., t − 1}, ∀s ∈ {1, ..., t − 1} (7) wi,ks,t ≥ t−1 X τ =s (1 − zτ) − (t − s − 1), ∀i ∈ Go, ∀t ∈ T , ∀s ∈ {1, ..., t − 1} (8)

Constraint (9) ensures that the expected production yi

tshould not exceed the weather dependent

production capacity qi t.

y_ti≤ qi

t, ∀i ∈ G, ∀t ∈ T (9)

2.) Linking turbine failure to failure probabilities

In constraint (10 & 11) the links between ui,k_t , vi,k_t & zi,k_t are shown. Binary variable ui,k_t = 1 if component k within turbine i has been maintained, either preventive (z_ti,k) or corrective (vi,k_t ), and remains equal to 1 to ensure that the failure probability of a component remains equal to zero before the end of the remaining time epochs. Variable ui,k_t is linked to the binary variables z_ti,k or vi,k_t , which depends on the type of maintenance action that has been performed.

t−1

X

s=1

z_si,k= ui,k_t , ∀i ∈ G, ∀k ∈ Ko (10)

t−1

X

s=1

Decisions regarding maintenance operations are linked to all possible scenarios and are made by use of a so-called ’no good cut’ policy (constraint 12 & 13). According to the study of Kruize (2019), maintenance scenarios can be regarded as a set of all possible scenarios, which is denoted by the set of M. For each wind turbine there are 2n _{maintenance scenarios possible whereby n denotes the}

number of components within the turbine. For example: in the scenario whereby a turbine consist of two components there are 22= 4 possible maintenance scenarios, wherein each component can be either maintained or not. The first scenario is that both components are maintained, in the second scenario only component 1 is maintained, in the third scenario solely component 2 is maintained, and in the last scenario both components are not maintained. The binary variable ηht is defined for

each maintenance status h at each maintenance epoch t. This variable is subject to constraint 12 wherein for the of turbines during each maintenance epoch t For all turbines, during all maintenance epochs all scenarios in which at most n–1 components are maintained this variable is subject to constraint (12). Binary variable ηh

t is subject to constraint (13) for all the possible scenarios in

which all the n components are maintained. This ensures that the binary variable ηh

t ≥ 1 when

ut= ˆu h

t, and ηth are not bounded otherwise. The index set k ∈ K(ˆu h

t) represents the components

that have been maintained and the index set of k ∈ F(ˆuh_t) represents those components that have been left unattended.

η_th≥   X k∈K( ˆuh t) ui,k_t − X k∈F( ˆuh t) ui,k_t − K( ˆu h t)   + 1   (12) ηth≥   X k∈K( ˆuh t) ui,kt − X k∈F( ˆuh t) ui,kt −   K( ˆu h t)      (13)

The failure probability of the turbine φh

t in constraint (14) that is required for the fourth term in

the objective function (1) can be computed for each scenario based on the reliability series systems equation Moskowitz (1956) in constraint (15).

3.) Maintenance coordination

Constraint (16) ensures that preventive maintenance is performed on operational components within the time limit ζi,k_{, which is defined as the first time that its sensor-updated reliability falls}

below a control threshold η. Constraint (17) limits the number of corrective maintenance to at most one per component during the planning horizon. Here vi,kt = 1 if component k of turbine i is

maintained corrective during time epoch t.

ζi,k X t=1 zi,k_t = 1, ∀ i ∈ Go, ∀t ∈ T , ∀k ∈ Ko (16) X t∈T υti,k≤ 1, ∀ i ∈ Gf, ∀t ∈ T , ∀k ∈ Kf (17)

Constraints (18 and 19) ensure that the maintenance crew visit the wind turbine if the wind turbine is scheduled for preventive maintenance (18) or corrective maintenance (19).

zi,k_t ≤ xt, ∀ i ∈ G, k ∈ Ko, t ∈ T (18)

υi,kt ≤ xt, ∀ i ∈ G, k ∈ Kf, t ∈ T (19)

4.) Maintenance crew coordination

Constraint (20) ensures that the number of maintenance actions at each time epoch t do not exceed the limit of the maintenance crew capacity, which is defined as: Mt.

X

i∈Go

z_ti,k+X

i∈Gf

υ_ti,k≤ Mt, ∀ i ∈ G, t ∈ T , k ∈ K (20)

Constraint (21) prevents any maintenance visits when the weather conditions are unfeasible. Weather conditions are considered unfeasible when the wind-speed threshold ws is exceeded. The

wind speed is denoted as vt at time period t and is obtained from the weather data set (KNMI,

5.) Operating decisions

In the next constraint, being constraint (22), the decision variable vi,k_t is coupled with the opera-tional variable y_ti. Constraint (22) indicates whether a turbine generates electricity or is forced to stop due to a failure or when the wind-speed is too low to generate power. Constraint (22) ensures that turbine i generates electricity during maintenance epoch t. In the scenario whereby a turbine has failed it is not capable of producing electricity until it has been maintained correctively.

yi_t≤ qi t· t−1 X j=1 υ_ti,k, ∀ i ∈ G, ∀k ∈ Kf, ∀t ∈ T (22)

6.) Wind power delivery

The production capacity of each wind turbine at time epoch t is based on weather data originat-ing from the KNMI North Sea Wind Atlas project (KNMI, 2014). The data set contains the hourly wind speed measurements on 8 different height levels (10, 20, 40, 60, 80, 100, 150 and 200 meters) over a time period starting in January 2014 and ending in January 2017. The maximum production capacity for each operational turbine Gois dependent on the wind speed during that particular time

epoch. The uninterrupted produced power in mWh is denoted by qi

tand will be modelled by taking

the average wind speed (meters per second) during the time period, which is retrieved from the weather containing data set, multiplied with the weather dependent production capacity during that time epoch. The mathematical relation between power output and wind speed is defined in constraint (23) (Karki & Patel, 2009). Wind turbines are only able to produce electricity when the wind speed is between a minimum cut-in and a maximum cut-out which are denoted as vin and vout. In the scenario whereby the wind speed vtat time epoch t is less than vin, wind turbine

i is not able to produce electricity during that time epoch t. In the scenario whereby the wind speed exceeds the limit of vout the wind turbine shuts down to prevent unnecessary strain on the components. The turbine power production increases non linearly until the wind speed reaches the rated power (RP) and corresponding wind speed vr_{. It is assumed if the wind speed falls between}

the rated power and the cut-out wind speed, wind turbine i is able to produce the maximum turbine production capacity until the cut-out point. Parameters a, b and c for the abc-formula in constraint (23) are obtained according to constraints (24, 25 and 26).

b = 1 (vi− vr₎2  4(vi+ vr) (v i_{+ v}r 2vr ) 3 _{− (3v}i_{+ v}r₎  (25) c = 1 (vi− vr₎2  2 − 4(v i_{+ v}r 2vr ) 3  (26)

3.4

Rolling horizon framework

In this study, a rolling horizon framework has been developed to extend the stochastic optimization time horizon in order to test the effectiveness of the results over a longer period of time. The method of a rolling horizon framework is to split the model into I intervals resulting in lower computational effort made by the model, which reduces the running time to solve the model while allowing to increase the time horizon within a reasonable time-span and model the behavior of the policy over a longer time horizon. Initially the model is solved for a planning horizon period denoted by T number of time maintenance epochs. Hereafter, a specified number of n maintenance epochs at the beginning are frozen. After solving the stochastic optimization problem of an interval, the obtained values are passed on to the next interval. The components that have been maintained within this interval will be selected and updated with new deterioration data and the corresponding dynamic maintenance costs will be captured. Those components that have not been maintained during this frozen interval will also be updated and initialized for the next run.

3.5

Sensor driven deterioration methodology

The degradation patterns of real life degeneration signals are used to reproduce real life scenarios. Based on the degradation pattern, the Remaining Life Distribution (RLD) can be calculated ac-cording to the method as described by Yildirim et al. (2017) and is illustrated in constraint (27). Hereby pi,k_t represents the sensor-driven prediction on the probability that component k will fail during time period t. The remaning life of the component is denoted by Ri,k_t . These probabilities are updated with new sensor data after each time period. Based on these RLD’s the maintenance costs for each component at each time period are calculated in the form of dynamic maintenance costs. Incorporating these dynamic maintenance costs in the MIP-model allows the model to continuously make the trade-off between incurring costs to perform preventive maintenance or to postpone pre-ventive maintenance activities with the associated costs and production losses due to the increased risk of failure for each component. Each component randomly selects a single degradation process sample from the deterioration data sample. Components that have been maintained during the time epoch will receive a new deterioration sample for the next time instance.

pi,kt = P (t − 1 ≤ R i,k

3.6

Performance metrics

In table 2 the performance metrics are presented which are used to compare the CBOM policy with the benchmark policies. The averages results of the performance metrics will be calculated over the entire planning horizon of all instances.

Metric Description

Revenues

Operational Revenue (AC ) Total revenue of the wind farm based on generated power and the electricity price.

Net Profit (AC ) Revenue minus the expenditures for maintenance and crew deployment costs.

Expenditures

Maintenance Costs (AC ) Total costs incurred for turbine maintenance.

Preventive maintenance costs (AC ) Total costs related to preventive maintenance actions. Failure costs (AC ) Total costs related to corrective maintenance actions. Crew deployment costs (AC ) Total costs for crew deployment.

Performance Metrics

Corrective maintenance actions (#) Total number of corrective actions conducted. Preventive maintenance actions (#) Total number of preventive actions conducted.

Crew deployment frequency (#) Total number of times the maintenance crew has been dispatched.

Availability Average time the wind turbines are operational.

Downtime Total time expressed in maintenance epochs during turbine failures.

Maintenance cap. utilization Total utilization by the maintenance capacity crew during each maintenance epoch.

3.7

Parameter setting

Table 3 provides the parameter settings that will be used as the default setting in the MIP-model for the numerical experiments. Within the numerical experiments it will be mentioned when parameters are modified with respect to the values in table 3.

Parameter Value

Wind Farm characteristics

Turbines 75

Components 2

Energy price per mW/h AC 20

Turbine capacity (Mw/h) 2 Cut-in (m/s) 4 Rate (m/s) 12 Cut-out (m/s) 25 Maintenance characteristics PM costs AC 4K Failure costs AC 16K

Maintenance labor capacity 8 tasks per maintenance epoch

Crew deployment costs AC 48K

Wind speed threshold for wind farm accessibility (m/s) 14 Rolling horizon characteristics

Runs 50 Intervals 8 Warm-up period 5 Iterations 8 Time periods 50 Sub-periods (hours) 48 Policy characteristics PM interval (T Ii_{) 4} T Ii _0.8 M T T F 250

3.8

Benchmark policies

In this section the maintenance policies are presented which will act as a benchmark to evaluate the performance of the suggested CBOM policy. The results of the CBOM policy are placed into perspective by comparing the performance against a Preventive time-based Maintenance policy (PM) and a Corrective Maintenance policy (CM). The general goal of the benchmark study is to study how the CBOM policy exploits the financial dependencies as stated in table (2) in comparison with the benchmark policies. Hereafter the adaptions in the MIP-model for the characteristics of each benchmark policy are discussed.

3.8.1 Preventive time based maintenance

Within preventive time based maintenance, activities are scheduled based on the components lifes-pan meaning that the deterioration sensor data is not applied resulting in C_ti,ko

k,t = 0. Components

are allowed to undergo preventive maintenance when the components lifespan is within a certain interval of [ti _{· M T T F}i _{− T I}i_{, t}i _{· M T T F}i_{] where t}i _{is the time threshold in which preventive}

maintenance has to be executed and T Ii _{denotes the length of the interval. To enforce the time}

based planning for preventive maintenance, constraint (16) is adjusted to constraint (28) where bk,l

and bk,uare the lower- and upper-bound of the time interval where preventive maintenance actions can be executed for component k in turbine i. Components with ages below this threshold will not be maintained preventively. Components that have exceeded the time threshold will also not be maintained preventively but will eventually fail from which they can be maintained correctively. The procedure to determining the optimal value for ti _{is described by Kruize (2019). In this study}

the author calculated the ti _{multiple times from which he obtained an optimal value of t}i _{= 0.8}

(ti _{· M T T F}i_{) whereby interval T I}i _{consists of 5 maintenance epochs.}

bk,u

X

bk,l

zti,k≤ 1, ∀ i ∈ G, ∀k ∈ Ko (28)

3.8.2 Corrective Maintenance

Within corrective maintenance, components maintenance actions are only performed after they have failed. Therefore constraint (16) is adjusted to constraint (29) which enforces the MIP-model to ensure that no preventive maintenance actions can be scheduled and/or executed.

X

t∈T

4

Computational Results

The results of the MIP-model for the policies are analyzed in this section. At first the effects of the crew deployments costs on each policy performance are analyzed. Secondly the effects on different electricity prices are tested for each policy. The third section discusses the influences of maintenance crew capacity on each policy. This section concludes with analyzing the effects of different wind farm accessibility thresholds on each policy.

4.1

Influence of crew deployment cost on policy performance

In figure 4.1 the net profit of the three policies under a range of different crew deployment costs Ctv starting from AC 0K towards AC 112K with intervals of AC 16K are shown. Other values that

were presented in table 3 remain identical. Based on figure 4.1 the CBOM policy surpasses the performance in comparison with the PM and CM policy. This means that the CBOM policy is less affected as the crew deployments costs increase. Hereby encounter the CBOM an average decrease of 12% in the profit as the crew deployment costs increase fromAC 0K towardsAC 112K, whereas the other policies experience a decrease of approximately 20% in profit.

0 20 40 60 80 100 18

20 22 24

Crew. Dep Cost (KAC )

Net

profit

(M

AC

)

Fig 4.1 Effect of crew deployment cost on net profit

CBOM PM CM

while the corrective maintenance costs associated to the failure costs experience a small increase, which forms a trend showing when Cv

t increase a shift occurs in the maintenance actions from

preventive maintenance tasks towards corrective maintenance actions. This trend also explains the increase in maintenance costs since corrective maintenance actions (AC 16K) are significant more expensive than preventive maintenance costs (AC 4K). The focus of the model is no longer to schedule maintenance actions at the optimal moment but rather group maintenance tasks together each deployment to utilize the maintenance crew capacity more efficient. However this deviating from performing maintenance at the optimal moment leads to more components failures and longer wind turbine downtimes. In total the downtime increases with 13% when Ctv increases from 0K till

112K. However, this has a positive effect on the crew maintenance utilization whereas the utilized capacity is more efficiently scheduled, which reduces the number of deployments of the maintenance crews. For example the average utilization of the grouped crew maintenance actions when Cv

t = 0

corresponds to 31% whereas this is 95% when Cv

t = 112K. Although the maintenance activities are

grouped more efficiently, the increase in maintenance costs have a negative effect on the net profit for the CBOM policy. In conclusion, the focus of implementing a CBOM policy is changed towards grouping maintenance actions more efficient in order to lower the frequency of the maintenance crew deployments and their associated costs.

Cv,`t (AC ) 0K 16K 32K 48K 64K 80K 96K 112K Revenues Op. rev. 26.2M 26.4M 26.3M 26.3M 26.2M 26.3M 26.3M 26.3M Net profit 24.3M 23.9M 23.2M 22.5M 22.1M 21.5M 20.7M 21.0M Expenditures Expenditures 1.87M 2.46M 3.11M 3.67M 4.20M 4.70M 5.34M 5.3M Maint. exp. 1.85M 1.80M 1.82M 1.76M 1.79M 1.76M 1.93M 1.76M Failure costs 944K 930K 920K 866K 911K 896K 1.04M 976K PM costs 911K 866K 904K 893K 882K 861K 889K 854K Crew dep. costs 5.95K 665K 1.29M 1.92M 2.41M 2.94M 3.41M 3.89M Performance Metrics Crew dep. 119.0 41.6 40.2 40.0 37.6 36.8 35.5 34.7 C. act. 56.9 65.2 53.4 54.4 59.8 54.0 56.3 61.4 P. act. 236.0 232.5 230.4 216.5 227.8 224.0 206.4 201.2 Availability 0.96 0.95 0.95 0.95 0.95 0.95 0.95 0.95 Downtime 1190.4 1244.6 1270.2 1244.6 1269.4 1301.8 1324.3 1345.8 Maint. Cap. Ut. 0.31 0.88 0.89 0.85 0.94 0.96 0.95 0.95

Results regarding the PM policy are presented in table 5. First it is noticeable that the shift from preventive maintenance actions towards corrective maintenance actions, as it was with the CBOM policy, does not apply for the PM policy. This observation can be explained since PM activities are conducted based on the predetermined component estimated lifespan, instead of the failure probability based on the actual components condition. Therefore PM activities are conducted according solely to the predetermined lifespan, meaning that the crew deployments costs have no influence on planning the PM tasks. Moreover, apart from the crew deployment when C_tv = 0, the increase of Ctv has no influence on the number of crew deployments since the moment of

conducting preventive maintenance is fixed as well. The number of corrective maintenance actions are significantly higher compared with the CBOM policy. This change in number is caused by the varying deterioration patterns for components, meaning that components have already failed before reaching the preventive maintenance threshold. This underlines the importance of considering identical components as unique as it was stated by Yildirim (2017). As the downtime of the PM policy when Cv

t = 0 is comparable to the CBOM policy, this number increases rapidly along with

grow of Cv

t towardsAC 112K. This is reached by leaving components in their failed state until the next

preventive maintenance actions are planned and executed to lower the frequency in maintenance crew deployments and their increasing associated costs.

Cv t (AC ) 0K 16K 32K 48K 64K 80K 96K 112K Revenues Op. rev. 26.2M 26.4M 26.3M 26.3M 26.2M 26.3M 26.3M 26.2M Net profit 23.9M 22.9M 22.3M 21.5M 20.8M 20.3M 19.6M 18.9M Expenditures Expenditures 2.21M 2.85M 3.47M 4.35M 4.92M 5.45M 6.14M 6.84M Maint. exp. 2.21M 2.16M 2.13M 2.20M 2.21M 2.17M 2.15M 2.23M Failure costs 16.4M 1.58M 1.58M 1.63M 1.63M 1.61M 1.58M 1.65M PM costs 570K 576K 556K 578K 571K 563K 574K 571K Crew dep. costs 5.95K 691K 1.33M 2.14M 2.71M 3.28M 3.99M 4.61M Performance Metrics Crew dep. 119.6 43.2 41.6 44.6 42.4 41 41.6 41.2 C. act. 102.4 98.8 98.6 101.8 102 100.6 98.5 103.4 P. act. 142.6 144.2 139.2 144.4 142.8 140.8 143.5 142.7 Availability 0.96 0.94 0.94 0.93 0.95 0.94 0.95 0.95 Downtime 1180.4 1494.8 1498 1582.8 1629.4 1653.8 1721.7 1788.7 Maint. Cap. Ut. 0.26 0.70 0.71 0.69 0.72 0.74 0.73 0.75

In table 6 the results for the CM policy are shown. It clearly demonstrates that maintenance actions are only carried after a component has failed. The most important observation for the CM policy is the significant high downtime compared with the other policies, for example the downtime is 81% higher compared with the CBOM policy if Cv

t =AC 112K. The high downtime has

a negative influence on the wind turbine availability, which is 7% lower and diminishes the generated revenue in comparison with the CBOM policy. This observation can be explained by the fact that components are failing more frequently and failed components have to wait longer before they are maintained in comparison with the CBOM policy, since maintenance actions are only grouped with other corrective maintenance actions. Therefore the CM policy has more difficulties to schedule corrective maintenance actions efficiently which results in higher maintenance expenditures and lower energy production due to the increased downtime, meaning that the turbine is not able to generate power until the failed components within are maintained.

Cv t (AC ) 0K 16K 32K 48K 64K 80K 96K 112K Revenues Op. rev. 25.8M 25.1M 25.0M 24.9M 25.0M 24.9M 24.8M 24.9M Net profit 22.1M 20.9M 20.3M 19.7M 19.5M 18.6M 18.4M 17.9M Expenditures Expenditures 3.72M 4.24M 4.72M 5.22M 5.54M 6.24M 6.32M 6.96M Maint. exp. 3.71M 3.67M 3.64M 3.62M 3.46M 3.64M 3.26M 3.33M Failure costs 3.71M 3.67M 3.64M 3.62M 3.46M 3.64M 3.26M 3.33M PM costs 0 0 0 0 0 0 0 0

Crew dep. costs 9.87K 569.6K 1.08M 1.61M 2.09M 2.60M 3.05M 3.63M Performance Metrics Crew dep. 197.4 35.6 33.8 33.5 32.6 32.5 31.8 32.4 C. act. 232 229.6 227.3 226.0 216.7 227.6 204.4 208.4 P. act. 0 0 0 0 0 0 0 0 Availability 0.95 0.94 0.92 0.91 0.91 0.90 0.89 0.88 Downtime 1263.4 2085.8 2091.2 2165.0 2235.0 2347.6 2437.2 2489.6 Maint. Cap. Ut. 0.15 0.81 0.84 0.84 0.83 0.83 0.80 0.80

4.2

Effect of electricity price on policy performance

Electricity prices are assumed to increase in the future (Wind Europe, 2018). Therefore the per-formance of the electricity prices is analyzed to determine what the effect is for each policy. To evaluate the performance, the energy prices πtare tested over a range of (AC 10 -AC 50 per mWh).

Beside the energy price πtother parameters with respect to the values in table 3 remain unchanged.

In table 7 the results of the energy prices for the CBOM policy are shown. The operational revenue and the net profit are increasing practically linearly each instance the energy price πt

in-creases with AC 10. Further it can be observed that the number of preventive maintenance actions declines as the electricity price rises. On the contrary the number of corrective maintenance actions increases. This indicates that scheduling preventive maintenance opportunistically to exploit eco-nomic dependencies becomes less urgent as πtincreases. This is moreover supported by the increase

in frequency of maintenance crew deployments. For example, if the energy price isAC 10 per mWh the average number of deployments is 39.8, but in the scenario where the price of electricity is equal toAC 50 per mWh then the average number of crew deployments increases towards 48.6. This has a negative effect on the maintenance crew utilization since the focus of the model has shift from effectively grouping maintenance actions towards minimizing the downtime. Based on this information it can be remarked that maintenance tasks that are scheduled to minimize production losses outweigh the cost advantage of minimizing the costs that are associated with the frequency in maintenance crew deployments.

Table 8 provides the results showing the effects on the electricity price regarding the PM policy. The effects on operational revenue and net profit are comparable to the CBOM policy, whereby the increase is practically linearly with each electricity price πtenlargement. However the frequency in

crew deployments remains approximately the same. Based on the results in table 8 it can be seen that not making use of actual condition data in order to anticipate on the electricity prices reduces the increase in net profit in comparison with the CBOM policy.

πt (AC ) 10,- 20,- 30,- 40,- 50,-Revenues Op. rev. 13.2M 26.4M 39.6M 52.8M 66M Net profit 5.65M 19.0M 32.1M 44.9M 57.9M Expenditures Expenditures 7.57M 7.43M 7.48M 7.9M 8.02M Maint. exp. 1.56M 1.68M 1.84M 2.01M 2.03M Failure costs 659K 794K 992K 1.14M 1.17M PM costs 902K 883K 853K 859K 826K Crew dep. costs 6.01M 5.75M 5.64M 5.9M 6.02M Performance Metrics Crew dep. 125.2 119.8 117.5 123.0 125.4 C. act. 41.3 49.6 62.0 71.2 73.2 P. act. 225.4 220.8 213.3 214.7 206.4 Availability 0.96 0.96 0.96 0.96 0.96 Downtime 1094.5 1094.4 1105.6 1119.9 1118.4 Maint. Cap. Ut. 0.27 0.28 0.29 0.29 0.29

The effects of electricity pricing on the CM policy are presented in table 9. Hereby the frequency in the deployment of the maintenance crew increases at each enlargement of the electricity price πt. However, the number of corrective maintenance actions remains approximately identical if the

electricity prices rise. This observation indicates that achieving a high utilization of maintenance actions at each deployment becomes less urgent, meaning that as the electricity price πt increases,

the focus is more pointed towards minimizing production losses rather than diminishing maintenance expenditures. This shift in focus can be explained by the increasing value for the availability of wind turbines and the decreasing value of the maintenance capacity utilization.

πt (AC ) 10,- 20,- 30,- 40,- 50,-Revenues Op. rev. 12.4M 25.1M 37.9M 50.6M 63.5M Net profit 7.32M 19.8M 32.3M 45.2M 57.7M Expenditures Expenditures 5.09M 5.24M 5.53M 5.44M 5.72M Maint. exp. 3.62M 3.64M 3.73M 3.57M 3.64M Failure costs 3.62M 3.64M 3.73M 3.57M 3.64M PM costs 0 0 0 0 0

Crew dep. costs 1.47M 1.6M 1.8M 1.87M 2.08M Performance Metrics Crew dep. 30.6 33.3 37.4 39.1 43.4 C. act. 226.3 227.6 233.1 223.0 227.7 P. act. 0.0 0.0 0.0 0.0 0.0 Availability 0.91 0.92 0.93 0.93 0.94 Downtime 2379.0 2041.0 1951.2 1816.0 1738.8 Maint. Cap. Ut. 0.92 0.85 0.78 0.71 0.65

Table 9: influence of electricity price on CM policy performance

In this section the effects of increasing electricity prices πt, which are assumed to increase in the

future, are demonstrated. However the influence of each policy is predominantly comparable to each other, although the CBOM policy is capable to exploit economic dependency more beneficially by grouping maintenance actions more efficient. This reduces the crew deployment costs in comparison with the other policies. This leads to the observation that as πtincreases, the share of net profit

4.3

Effect of maintenance crew capacity on policy performance

In the following section the influence of the maintenance crew capacity Mton the performance of

each policy is analyzed. The CBOM policy has proven that it is able to utilize maintenance capacity more efficiently compared with the benchmark policies in the previous sections. In this section the effects on the capacity utilization for the policies are analyzed by increasing and decreasing Mt

during a single maintenance period over a range from 2-18 tasks. The remaining values for the parameters in table 3 are unchanged. In tables 10, 11 & 12 the results are presented for the CBOM, PM and CM policies.

When the maintenance crew capacity is low (Mt = 2), the difference in performance for the

policies are minimal since the capacity of the maintenance crew is insufficient and the maintenance crew is not able to perform all the necessary maintenance actions at once. This is due to the fact that failed components are left unattended which increases the downtime. The increasing downtime has a negative effect on the operational revenue because at each time period the number of components that are failing is greater than the number of components that can be maintained, resulting in less operational wind turbines that are able to produce electricity. From figure 2 it can be obtained when Mt ≥ 6 the benefits of the increasing Mt reduces in respect to the net profit.

Moreover, when the maintenance crew is above a capacity of 10, the performance of the policies is not influenced anymore. This means that on average at most 10 maintenance tasks are performed each time period. Expanding the crew capacity after Mt≥ 10 does not create financial advantages.

Based on the results in figure 3, the CBOM is more capable of utilizing the maintenance capacity when it is compared with the benchmark studies. The advantage of utilizing the maintenance capacity better in comparison with the PM and CM policy is that the maintenance expenditures are decreased. However with the CM policy the crew deployments costs are lower compared with the crew deployments costs of the CBOM policy. However,this disadvantage in costs is counterbalanced by the lower maintenance expenditures. This is achieved by performing preventive maintenance actions avoiding failures for the components that have to undergo costly corrective maintenance. The CBOM policy is able to schedule maintenance activities more efficiently when Mt increases

Mt 2 4 6 8 10 12 14 16 18 Revenues Op. rev. 21.8M 25.5M 25.9M 26.1M 26.1M 26.3M 26.2M 26.1M 26.1M Net profit 13.2M 19.2M 20.8M 21.7M 22.2M 22.9M 22.9M 22.9M 22.9M Expenditures Expenditures 8.65M 6.35M 5.07M 4.38M 3.86M 3.4M 3.21M 3.21M 3.21M Maint. exp. 2.51M 2.59M 2.43M 2.35M 2.17M 1.85M 1.88M 1.87M 1.86M Failure costs 1.98M 1.86M 1.58M 1.51M 1.3M 896K 971K 917K 949K PM costs 525K 725K 844K 839K 871K 953K 913K 951K 908K Crew dep. costs 6.14M 3.76M 2.64M 2.03M 1.7M 1.55M 1.33M 1.34M 1.23M Performance Metrics Crew dep. 128.1 78.2 55.3 42.6 35.7 32.3 27.6 28.0 25.7 C. act. 124.2 116.3 99.0 94.3 81.1 56.2 60.8 57.2 59.1 P. act. 131.3 181.3 211.1 209.8 217.6 238.4 228.3 237.7 227.0 Availability 0.76 0.92 0.94 0.95 0.95 0.95 0.95 0.95 0.95 Downtime 6487 2035 1583 1415 1409 1281 1376 1374 1393 Maint. Cap. Ut. 1.00 1.00 0.92 0.91 0.90 0.88 0.87 0.86 0.86

Table 10: influence of maintenance crew capacity on CBOM policy performance

Mt 2 4 6 8 10 12 14 16 18 Revenues Op. rev. 21.6M 25.6M 25.7M 25.8M 25.7M 25.6M 25.8M 25.7M 25.5M Net profit 12.6M 19.1M 20.7M 21.3M 21.6M 21.6M 21.8M 21.8M 21.7M Expenditures Expenditures 8.94M 6.46M 4.97M 4.52M 4.12M 4.06M 3.93M 3.82M 3.82M Maint. exp. 2.84M 2.86M 2.43M 2.4M 2.4M 2.43M 2.2M 2.34M 2.43M Failure costs 2.46M 2.4M 1.87M 1.82M 1.84M 1.89M 1.6M 1.81M 2M PM costs 380K 456K 556K 580K 556K 544K 596K 528K 432K Crew dep. costs 6.1M 3.6M 2.54M 2.11M 1.73M 1.63M 1.63M 1.49M 1.39M Performance Metrics Crew dep. 126.9 75.1 53.2 44.1 36.0 33.9 33.8 31.2 29.1 C. act. 154.2 150.7 117.1 114.1 115.3 118.2 114.1 113.0 125.3 P. act. 95.4 114.3 139.1 145.5 139.3 136.2 134.1 131.9 108.4 Availability 0.71 0.91 0.92 0.93 0.94 0.94 0.94 0.94 0.94 Downtime 4917 1876 1634 1532 1604 1676 1580 1639 1815 Maint. Cap. Ut. 0.98 0.88 0.80 0.74 0.71 0.63 0.56 0.49 0.45

Mt 2 4 6 8 10 12 14 16 18 Revenues Op. rev. 19M 24.3M 24.6M 24.6M 24.7M 24.6M 24.7M 24.8M 24.8M Net profit 11.3M 17.4M 18.8M 19.2M 19.5M 19.8M 19.9M 20M 20.2M Expenditures Expenditures 7.67M 6.86M 5.81M 5.48M 5.11M 4.81M 4.77M 4.76M 4.6M Maint. exp. 3.07M 3.88M 3.78M 3.87M 3.72M 3.61M 3.64M 3.66M 3.51M Failure costs 3.07M 3.88M 3.78M 3.87M 3.72M 3.61M 3.64M 3.66M 3.51M PM costs 0 0 0 0 0 0 0 0 0

Crew dep. costs 4.61M 2.98M 2.03M 1.62M 1.39M 1.2M 1.14M 1.1M 1.09M Performance Metrics Crew dep. 96.2 62.3 42.3 33.7 29.0 25.0 23.8 23.1 22.7 C. act. 191.6 242.8 236.0 241.5 232.3 225.8 227.2 228.6 219.1 P. act. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Availability 0.67 0.90 0.91 0.91 0.91 0.91 0.91 0.91 0.91 Downtime 8738 2497 2363 2410 24785 2498.0 2441 2466 2440 Maint. Cap. Ut. 1.00 0.97 0.93 0.90 0.80 0.75 0.68 0.62 0.54

4.4

Effects of wind farm accessibility on policy performance

When the wind speed at sea level is above 14 m/s for the North sea, offshore wind turbines are considered inaccessible for maintenance activities (McMillan & Ault, 2008). In the scenario where the wind speed is expected to exceed this accessibility threshold during the planned maintenance period, maintenance crews are not able to perform maintenance actions. In this section the effects on the performance under a varying range of wind speed thresholds (starting at 6m/s to 18m/s) are tested to determine how the CBOM policy is affected when the wind speed threshold for wind farm accessibility is in- and decreased. It is expected that the CBOM policy is better able to schedule maintenance activities when the accessibility threshold is low. In this scenario it is assumed that when the wind speed during a time period exceeds the wind speed threshold, the maintenance crew is not allowed to perform maintenance tasks on the failed components. The values of the parameters in table 3 are unmodified.

Accessibility threshold(m/s) 6 8 10 12 14 16 18 Revenues Op. rev. 3.3M 15.3M 24.9M 25.9M 26.3M 26.3M 26.2M Net profit 2.71M 12.6M 20M 21M 21.9M 22.5M 22.3M Expenditures Expenditures 590K 2.78M 4.97M 4.87M 4.32M 3.77M 3.89M Maint. exp. 398K 1.82M 3M 2.64M 2.21M 1.82M 1.9M Failure costs 360K 1.58M 2.35M 1.81M 1.3M 920K 1.02M PM costs 38K 246K 646K 832K 912K 902K 876K Crew dep. costs 192K 960K 1.97M 2.23M 2.11M 1.94M 1.99M Performance Metrics Crew dep. 4.0 19.9 41.1 46.3 44.0 40.7 41.4 C. act. 22.5 98.5 147.0 113.0 81.0 57.5 64.0 P. act. 9.5 61.5 161.5 208.0 228.0 225.5 219.0 Availability 0.14 0.56 0.88 0.93 0.95 0.95 0.95 Accessibility 0.05 0.11 0.17 0.34 0.52 0.66 0.74 Downtime 23198 11796 3158 1816 1342 1260 1274 Maint. Cap. Ut. 1.00 1.00 0.94 0.86 0.88 0.87 0.85

Table 13: influence of wind farm accessibility on CBOM policy performance

Accessibility threshold(m/s) 6 8 10 12 14 16 18 Revenues Op. rev. 3.3M 15M 23.7M 25.1M 25.3M 25.6M 25.8M Net profit 2.71M 11.9M 18.2M 20M 20.3M 20.4M 21.0M Expenditures Expenditures 596K 3.08M 5.49M 5.14M 5.01M 5.21M 4.79M Maint. exp. 404K 2.12M 3.66M 3.13M 2.49M 2.4M 2.05M Failure costs 368K 1.98M 3.42M 2.7M 1.89M 1.9M 1.5M PM costs 36K 146K 238K 422K 604K 506K 550K Crew dep. costs 192K 960K 1.82M 2.02M 2.26M 2.02M 1.97M Performance Metrics Crew dep. 3.9 20.0 38.0 42.0 47.0 42.0 41.0 C. act. 23.0 123.5 214.0 169.0 118.0 118.5 93.5 P. act. 9.0 36.5 59.5 105.5 151.0 126.5 137.5 Availability 0.15 0.57 0.85 0.92 0.94 0.94 0.94 Accessibility 0.05 0.11 0.17 0.34 0.52 0.66 0.74 Downtime 23078 11568 3924 2252 1596 1664 1486 Maint. Cap. Ut. .99 .99 0.90 0.82 0.72 0.73 0.70

Table 14: influence of wind farm accessibility on PM policy performance

Accessibility threshold(m/s) 6 8 10 12 14 16 18 Revenues Op. rev. 2.67M 16.3M 23.6M 24M 24.6M 24.9M 25.1M Net profit 1.97M 12.8M 17.9M 18.2M 19.3M 19.6M 19.9M Expenditures Expenditures 704K 3.52M 5.66M 5.86M 5.27M 5.26M 5.22M Maint. exp. 512K 2.56M 4.01M 4.13M 3.74M 3.68M 3.63M Failure costs 512K 2.56M 4.01M 4.13M 3.74M 3.68M 3.63M PM costs 0M 0M 0M 0M 0M 0M 0M

Crew dep. costs 192K 960K 1.66M 1.73M 1.54M 1.58M 1.58M Performance Metrics Crew dep. 4.1 20.1 34.6 36.4 32.1 33.1 32.9 C. act. 32.4 160.5 250.4 258.6 233.3 230.6 227.1 P. act. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Availability 0.03 0.13 0.62 0.87 0.89 0.91 0.92 Accessibility 0.05 0.11 0.17 0.34 0.52 0.66 0.74 Downtime 23603 10205 3621 2882 2429 2255 2067 Maint. Cap. Ut. 1.00 1.00 0.92 0.90 0.91 0.87 0.86

5

Discussion

Integrating the proposed CBOM policy has demonstrated to be an economically efficient strategy when it is compared with the traditional periodic time-based maintenance policy and corrective maintenance policy. According to the results obtained in section 4, the performance of the CBOM policy was superior in all scenarios in comparison with the benchmark policies. When crew de-ployment costs increase, the CBOM is capable to group maintenance activities more efficiently by minimizing the maintenance expenditures and maximize the maintenance crew capacity utilization which allows the model to reduce the frequency of maintenance deployments and their associated costs. Grouping maintenance activities more efficiently is achieved by deviation from the optimal moment, from an operational perspective to conduct maintenance tasks which allows the model to postpone maintenance activities on components, so they can be grouped together and the crew deployments are minimized.

In section 4.1 when the crew deployment costs increase the CBOM policy is capable to achieve a respective 9.0% and 15.1% higher net profit when Ctv=AC 112K in comparison with the PM and

CM policy. From a costs perspective the expenditures of the CBOM policy were able to decrease the costs with 19.6% and 21.7% when it is compared with the benchmark studies. Therefore, the CBOM policy is more efficient to deal with the increasing deployment costs in terms of net profit and minimizing maintenance expenditures by effectively postpone maintenance actions in comparison with the benchmark policies. This makes that the performance of the CBOM policy is less affected in terms of net profit by the increasing maintenance crew deployments costs when compared with the benchmark studies.

For the varying electricity prices in section 4.2 the focus for the CBOM policy moves if πt

in-creases from minimizing expenditures, by reducing maintenance crew deployment costs, towards reducing production losses by increasing the frequency of maintenance crew deployments to lower the downtime of a failed component. The costs associated when maintenance actions are deviating from the ideal moment of performing maintenance tasks are outweighed by the higher energy pro-duction if the wind turbine is at an operational state. However the number of scheduled corrective maintenance actions increases as the price for electricity rises. This can be explained since the priority of the model is to maximize the time in which the wind turbines are able to produce energy whereas preventive maintenance actions will lead to a temporary stop of the operational turbine, whereby it is not possible to produce energy which is not favorable. The revenue that the wind turbines can produce by postponing preventive maintenance actions and with the possibility that a component will fail counterbalance, the extra revenue that is obtained by defusing the probability of failure and the associated costs of executing preventive maintenance actions. The shift in focus for the CBOM policy creates more financial benefits in terms of net profit when it is compared with the benchmark studies. This can be explained since the benchmark studies are not capable to change their point of focus of postpone maintenance actions and thus are not able to take advantage when the energy prices are increasing. For example if the energy price πt= 50, the CBOM policy

In section 4.3 whereby the maintenance crew capacity is increasing, the CBOM policy showed it is capable of utilizing the available capacity more effectively compared with the benchmark studies which reduces the frequency in maintenance crew deployments, resulting in decreasing the associated costs. For example when the maintenance capacity is equal to 14, the CBOM policy is able to reach a utilization of 87% whereas the PM and CM policies are reaching a utilization of 56% and 68% which results in a decrease of 22% in maintenance expenditures when it is compared with the PM policy and 49% in maintenance expenditures when it is compared with the CM policy. In the scenarios where the Mt ≥ 6 the positive effect of increasing the capacity are diminishing.

After the maintenance crew has a capacity of performing 10 maintenance task in each time period the performances remain approximately the same for each policy, meaning that further expansion of the crew capacity for the policies does not improve the performances.

In section 4.4, the CBOM policy has proven it is least affected by the influence of the wind speed on the accessibility for the maintenance crew to visit the wind farm by scheduling maintenance activities more efficiently in comparison with the benchmark studies. This results in obtaining higher net profit due to the reduction of the downtime and decreasing maintenance expenditures by effectively balancing preventive and corrective maintenance actions to reduce the downtime of components and maintenance expenditures while maintaining the operational state of the wind turbines to generate revenue.

6

Conclusion

In conclusion, applying a CBOM policy has proven to be an effective policy in multiple com-parative experiments in reducing maintenance expenditures resulting in a higher profit compared with the benchmark policies. In all aspects of the performance the CBOM policy was superior to the Periodic time-based Maintenance policy and Corrective Maintenance policy. The results demonstrate the advantage of planning maintenance actions based on an economical perspective in comparison with make maintenance tasks decisions based from an operational point of view. The CBOM policy demonstrated it is capable of generating 18% more net profit under the increasing crew deployment costs. Applying a CBOM policy allows decision makers to consider a constant trade-off between deploying the maintenance crew and postponing maintenance activities. Although initially postponing maintenance tasks is not the optimal decision since the downtime and turbine failures increases. The negative effects are outweighed by the cost savings obtained with grouping the maintenance crew activities and its associated costs. To conclude the CBOM demonstrated it is capable to effectively deal with changing operational aspects by shifting their focus from decreasing maintenance expenditures towards maximizing the production of the wind turbines if the costs of lost production counterbalance the maintenance expenditures.

7

Limitations and further research

The present study has some limitations that need to be addressed. The results are subject to some simplifications and assumptions that were needed in order to model the policies within a reasonable bound of computation time. In this study each turbine consists of two identical components and it was assumed the components within a wind turbine had no influence on each other in reality this number is greater and inter-dependencies between components exists, whereby the condition of component x has influence on the condition of component y. Furthermore, the electricity prices and maintenance costs as well as the duration of performing maintenance actions were fixed for the entire planning horizon while these values are in reality subject to variation due to changes in the supply and demand patterns.

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