Incorporating wind in maintenance planning decisions for offshore wind turbines

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Incorporating wind in maintenance planning decisions for

offshore wind turbines

Simonas Mockus s1452587 First supervisor: dr. Bram de Jonge Second supervisor: dr. Jasper Veldman

Abstract

Maintenance of offshore wind turbines is a complicated process that is heavily impacted by weather conditions. This paper will investigate how to account for wind behaviour in maintenance strategy decisions and determine what cost savings can be expected from this. Several critical factors that are unique to wind turbines such as weather conditions, long lead times, larger deterioration increments on harsher wind conditions and production losses are considered. In order to model wind behaviour, wind probability matrix will be developed from the dataset and it will be included in the simulation, which will allow to investigate different scenarios and determine optimal maintenance strategies for them. We have concluded that maintenance strategies that account for seasonality in wind conditions deliver the best performance and can provide a significant maintenance cost reduction. As a result, adapting each decision variable to a specific season is optimal.

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List of figures

Figure 1. Wind speed distribution by year ... 11

Figure 2. Wind speed distribution by month ... 11

Figure 3. Distribution of wind categories in the dataset ... 12

Figure 4. Average wind speed versus failure rate (Carroll et al., 2015) ... 14

Figure 5. Relationship between wind category and costs of lost capacity due to maintenance and failure ... 16

Figure 6. PM threshold versus MCUT for 20-year simulation runs ... 18

Figure 7. PM threshold versus MCUT for 50-year simulation runs ... 18

Figure 8. PM threshold versus MCUT for 100-year simulation runs... 19

Figure 9. PM threshold versus MCUT ... 19

Figure 10. Deterioration level and PM execution points for the first 10 years of MPM = 40 simulation ... 20

Figure 11. PM threshold versus MCUT of winter and summer seasons ... 21

Figure 12. Deterioration level and PM execution points for the first 10 years of MPM = 40 winter season simulation ... 22

Figure 13.Deterioration level and PM execution points for the first 10 years of MPM = 50 summer season simulation ... 23

Figure 14. PM threshold versus MCUT versus for different maximum lengths of maintenance campaign ... 24

Figure 15. Minimalized PM threshold versus MCUT versus for different maximum lengths of maintenance campaign ... 24

Figure 16. PM threshold versus MCUT versus for tMAX = 2 ... 25

Figure 17. Deterioration level and PM execution points for the first 10 years of MPM = 40 and tMAX = 2 simulation ... 26

Figure 19. PM threshold versus MCUT for different maximum lengths of maintenance campaign in winter season ... 27

Figure 20. PM threshold versus MCUT for different maximum lengths of maintenance campaign in summer season ... 28

Figure 21. Deterioration level and PM execution points for the first 10 years of MPM = 40 and tMAX = 5 winter season simulation ... 28

Figure 23. Optimal PM threshold versus scale parameter ... 31

Figure 24. MCUT versus scale parameter ... 31

Figure 25. Optimal PM threshold versus maximum wind category that allows for maintenance ... 32

Figure 26. MCUT versus maximum wind category that allows for maintenance ... 32

List of tables

Table 1. Beaufort wind force scale ... 12

Table 2. Summer season wind probability matrix ... 13

Table 3. Winter season wind probability matrix ... 13

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Table 5. optimal tMAX values of different strategies ... 29

Table 6. Yearly wind data insights ... 37

Table 7. Monthly wind data insights ... 37

Table 8. MCUT for different PM thresholds ... 37

Table 9. MCUT in summer and winter seasons for different PM thresholds ... 38

Table 10. MCUT at different PM thresholds and tMAX ... 39

Table 11. MCUT for winter season at different PM thresholds and tMAX ... 40

Table 12. MCUT for summer season at different PM thresholds and tMAX ... 41

Abbreviations

PM – Preventive maintenance; CM – Corrective maintenance; CTV – Crew transfer vessel; MCUT – Mean cost per unit time; CS – Current strategy

MS1 – Maintenance strategy 1 MS2 – Maintenance strategy 2 MS3 – Maintenance strategy 3

Nomenclature

CPM – total cost of corrective maintenance action (€) CCM – total cost of preventive maintenance action (€) CH – costs of equipment hire (€)

CCL – cost of lost capacity (€/day)

tMAX – maximum duration of maintenance campaign (days) VIN – cut in speed of a turbine

VOUT – cut out speed of a turbine

VMAX – maximum wind speed to perform any maintenance activity MPM – preventive maintenance threshold value

MCM – Failure level ∆𝑑

̅̅̅̅ – average deterioration increment k – shape parameter

α – constant in shape parameter k θ – scale parameter

𝑣_𝑝

̅̅̅ – average wind speed of current wind category

Commented [S1]: Only those cost parameters that are

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1. Introduction

With the increasing demand for energy and recognized negative environmental impact of traditional energy sources, more and more energy is being obtained from renewable sources. Wind energy is the second largest form of renewable power generation capacity in Europe (WindEurope, 2018) and judging by the relatively steady power generation from gas, wind may soon be in the lead. Due to more consistent and higher wind speeds as well as no visual impact or physical restrictions, the role of offshore wind energy is increasing (WindEurope, 2018). However, offshore wind farms are expensive to maintain and since they are relatively recent developments, there is still lack of knowledge on how to reduce those costs to a minimum. This is a very important aspect that limits current investments and electricity generated by offshore wind farms. As a result, a variety of improvements to increase the competitiveness of this type of energy have been proposed by researchers. There are several factors that impact the effectiveness of maintenance and one of the key shortcomings of current maintenance strategies is that they do not take wind into account. IT is not possible to perform wind turbine maintenance when the wind speed is above a certain threshold, which is dependent on the type of maintenance used (Windcarrier, 2012). Since offshore wind turbines require additional assets and considerable amount of time and investment to be reached, this is a very important aspect in maintenance planning and decision making.

Niels and Sorensen (2011) state that operation and maintenance (O&M) account for up to 30% of the total cost of energy from offshore wind turbines and this is partly due to the fact that current maintenance strategies for offshore wind turbines are similar to those on land. Apart from more difficult and more expensive installation process of offshore wind turbines compared to the onshore ones, placing the turbines away from the land significantly reduces accessibility. In some cases, offshore wind farm might be inaccessible by boat for a period in excess of a month because of weather conditions (G. J. W. van Bussel & Schöntag, 1997). If this period coincides with failure of a turbine, the costs of downtime are excessive. Current maintenance strategies do not account for this risk and fail to accommodate weather conditions in the decision making process. On the contrary, current policies are mostly time-based and outdated. For example, one of the strategies is to perform preventive maintenance twice a year when weather conditions are good and perform corrective maintenance whenever repair crew and equipment are available, and the weather conditions are acceptable (G. Van Bussel et al., 2001). Since O&M has a lot of influence on overall competitiveness of a wind turbine, there has been a considerable number of researchers that addressed various problems that could lead to maintenance cost reduction. Vast majority of researchers agreed that condition-based maintenance policy is optimal and performs better than time-based maintenance policiy (Millan and Ault, 2007). However, the potential of improving condition based maintenance strategy by incorporating the effect of wind and its seasonality have not been discussed in the literature yet. There are some papers that consider weather windows or equipment to be used in various conditions (Rademakers et al., 2003; Silva and Estanqueiro, 2013) and some papers that employ the seasonality in wind speed by proposing to do maintenance in summer (Rademakers, Braam, Obdam, & Pieterman, 2008).

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In order to be able to account for wind in maintenance planning, the behaviour of wind over time based on wind data from Fino1 platform will be modelled first. Then, wind speeds will be subdivided into categories and the data mentioned above will be used to estimate probabilities of wind speed transitioning from one category to another. Here, season of the year will be taken into account as well. Results of this analysis will be implemented in simulation. Deterioration of wind mill will be modelled by gamma processes which also depend on the current wind speed that the turbine is facing. Several different strategies will then be investigated, starting from current strategy which relies on the same maintenance decisions throughout the year. Then we will explore the effect of having different preventive maintenance thresholds for each season and the effect of having different maximum lengths of maintenance campaign for each season. Finally, we will combine the findings from previous strategies to produce optimal maintenance strategy where each decision variable is season specific. This process will allow us to make certain conclusions regarding maintenance planning decisions that are aimed towards highest lowest costs. This paper will therefore answer the question how the maintenance decisions for offshore turbines should be affected by wind to achieve optimal cost.

In the next chapter of this paper we will provide a literature review, which will be followed by problem description and research questions. The fourth chapter will cover methodology and the fifth chapter will present numerical analysis, which will cover parts associated with setting up the simulations and gathering results from those simulations. review the literature in the field. The final chapter will provide a conclusions and directions for future extensions.

2. Literature review

We begin this section by reviewing maintenance policies in general, we proceed by reviewing optimal maintenance policies for wind turbines. Then we cover studies that take weather conditions into account and finish this section by specifying main points that are needed to model weather conditions reliably.

The first step of maintaining any equipment is deciding what type of maintenance policy to use. Wang (2002) provides an overview of maintenance policies of deteriorating one-unit systems. Any of the policies described by Wang could in theory be used for turbine maintenance but currently, it is very common to preventively maintain turbine at fixed time intervals, which is known as time-based or periodic PM policy. Of course, there is an option to do no preventive maintenance at all, which was investigated by Bussel and Schöntag (1997) and showed that availability levels in such cases are unacceptable and this approach is clearly not optimal. Academics generally argue in favour of condition based maintenance policy over others. Yang et al. (2016) argued that condition monitoring is more critical to offshore wind turbines because of stronger winds, longer repair and replacement downtimes, higher costs and harsher environments. Millan and Ault (2007) quantified the benefit of condition based maintenance policy compared to time based maintenance for offshore wind turbines and found that adapting condition based maintenance policy results in higher availability and higher revenue. However, in order to be able to implement condition based maintenance policy, condition monitoring system is needed. Marquez et al. (2012) have provided an overview of condition monitoring techniques for wind turbines and discussed which techniques are applicable for which components, while Yang et al. (2016) investigated the challenges associated with each condition monitoring technique.

Because maintenance of wind turbines is highly affected by weather conditions, we will now review maintenance optimisation studies that take weather conditions into account. There are several common methods to incorporate weather conditions in analyses and we will try to review them in an

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and discuss maintenance policies in general, for offshore wind, and the ones that take weather into account. Discuss weather forecasting for maintenance in a separate section.

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order of increasing complexity. Some researchers dedicate parts of their research to cover weather windows that allow to perform required actions (transport, repair, etc.). Rademakers et al. (2003) describe and compare two models used for modelling O&M of offshore wind farms and propose several ways how O&M strategy can be optimised. One of the key contributions towards maintenance optimisation in this paper is determining the most effective weather windows (in terms of availability) for accessing wind turbines. The next logical step is to make wind conditions occur randomly, which is done by Ntaimo, Ding, & Byon (2010). They developed a decision model for onshore wind turbines for which they assumed that bad weather conditions occur randomly and when they occur, maintenance cannot be performed. Nielsen and Sorensen (2011) have compared the use of condition-based and corrective maintenance in their paper. In order to do that, they needed to generate pseudo-random wind conditions for the whole lifecycle of the turbine. G. J. W. Van Bussel (1999) analysed availability and O&M costs of offshore wind farm using simulation, where wind conditions were represented by probability of wind getting stronger than 10.48 m/s. However, this probability was very general and depended heavily on assumptions made. Moreover, this probability did not account for the fact that wind differs significantly between the seasons. Since random or pseudo-random wind conditions might not represent any real case scenario, there is an option to use real past data such as done by Silva and Estanqueiro (2013) when investigating what accessibility values can be achieved using different equipment throughout all four seasons in offshore wind farm location in Portugal. Real wind data of the location in Portugal was used for that analysis. Past data can also be used to model wind in simulation. Kranenbarg (2018) proposed a maintenance optimisation policy for offshore wind turbines by executing simulation that was based on real data. In this paper, wind was modelled with the help of wind probability matrix, where probabilities of wind category of the next were defined based on the current wind category. However, wind conditions that were modelled in this simulation were only needed to determine capacity losses, while the effect of wind on execution of maintenance was completely excluded. Rademakers et al. (2008) have made a high complexity calculator that calculates O&M costs for offshore wind farm and allows to determine optimal maintenance strategy but this report does not provide any insights regarding the effect that each of those parameters might have and does not offer any recommendations or conclusions to achieve optimal maintenance strategy for offshore wind turbines.

Based on previous reviews, it can be stated that there are several main points that can be used to add significant amount of reliability into study which incorporates wind into maintenance analyses or simulation. These include using real data, accounting for seasonality and returning total maintenance costs so that different strategies, policies and conditions could be compared as suggested by Rademakers H. Braam, M. B.Zaaijer, G. J. W. Van Bussel (2003). Most of the papers discussed above have at least one of those key points covered but even though all of them acknowledge the importance of wind in maintenance of offshore wind turbines, there is no study that would use real data to develop a wind pattern for different seasons which could then be used to calculate total costs based on different parameters of simulation and make conclusions regarding optimal maintenance strategy.

3. Problem description

The optimal condition-based maintenance policy is being considered for a single offshore wind turbine with a single critical component and the continuous degradation process that depends on wind conditions. It is assumed that failure of the critical component occurs when the deterioration level exceeds a fixed threshold MF. It is further assumed that crew transfer vessels are suitable to carry out the repairs of this critical component. This means that major repairs or replacements that require larger vessels (field support vessel or heavy-lift (jack-up) vessel) will not be required. Focusing on crew

Commented [S4]: Cut in cut out speeds

Introduce scenarios

Maximum maintenance period

Remove cancelled maintenance costs

Explain that maintenance can be interrupted and there is no max duration

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transfer vessels only allow us to assume that such vessel is always available and consider maintenance policies that can be easily implemented in real life cases. Similar to the paper of De Jonge et al. (2016), we also assume that maintenance activities make the turbine as-good-as-new and that sufficiently accurate condition monitoring technique (such as vibration monitoring) is available. Since no monitoring data or expert opinion is available for this analysis, the deterioration of a turbine over time will be modelled by stochastic process that does depend on the wind speed. Gamma processes have proven to be applicable for modelling temporal variability of deterioration (van Noortwijk, 2009), thus we will model the deterioration by a gamma process and let the shape parameter α depend on the wind speed.

To simplify wind implementation in simulation, we will categorize wind speed based on the Beaufort wind scale. This scale allows to assign any wind speed to one of 13 categories (Beaufort numbers). The behaviour of the wind speed over time is based on wind data from the Fino1 platform in the North Sea. Modelling will be done by determining probabilities of wind switching from one category to any other such that knowing the wind category of the present day we can simulate wind category for the next day.

Both preventive and corrective maintenance actions are being performed on the turbine and both take a single time period to be completed. A preventive maintenance threshold MPM will be used, which means that once the deterioration level exceeds this threshold value, a preventive maintenance action is planned. This threshold level can differ between seasons and will be one of the decision variables in the simulation. A planning time of tPL will be needed to plan maintenance activity, while there will be a maximum length of maintenance campaign tMAX that represents the amount of time in which CTV is made available to execute planned maintenance activity. If maintenance is not performed during that time, it has to be planned again.

Both preventive and corrective maintenance actions can only be performed if the wind speed is below certain level (VMAX). Moreover, wind turbine is only operational when current wind is above cut in (VIN) and below cut out (VOUT) speed. Wind turbines normally operate in a wind range from 3 m/s to 25 m/s (Markou & Larsen, 2009), therefore there would be no downtime cost and no increase in the deterioration level at speeds below or above operational wind range. However, in a case where maintenance activity was planned but the wind happened to be too strong to perform it, maintenance does not have to be planned again and can be executed as soon as the weather allows it only if maximum length of maintenance campaign was not exceeded at that point. Naturally, increasing tMAX also increases costs but reduces risk of downtime. Similarly to preventive maintenance threshold MPM, tMAX is another decision variable that can depend on season.

The total cost of preventive (CPM) and corrective (CCM) maintenance come from multiple cost components such as vessel hire, labour and materials. Corrective maintenance has one additional cost component which accounts for larger costs of repairing a failure than preventively maintaining it and will be called failure penalty. Naturally, some of these cost components depend on the time it takes to perform maintenance action. Besides actual costs of maintenance, preventive and corrective repair activities cannot be performed when turbine is running, thus costs of lost capacity (CCL(V)) are taken into account as well. Lost capacity cost depends on wind speed and is also incurred for the whole duration of turbine failure. Lost capacity cost and corrective maintenance penalty cost are the key elements that make corrective maintenance less cost effective than preventive maintenance in this context.

The main goals of this study are to compare different maintenance strategies, to show what effect different decision variables have on mean maintenance costs per unit time (MCUT) and to find the

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best performing maintenance strategy. In order to achieve this, four strategies will be investigated. First, we will look into a benchmark case to which we refer to as current strategy. Here we have a single PM threshold value MPM and singe maximum length of maintenance campaign tMAX, irrespective of whether there is seasonality or not. Then, we will introduce different MPM for different seasons but will still keep tMAX fixed at single value. Next, we will do the opposite and use single MPM, while introducing different tMAX values for different seasons. Finally, we will combine these and make both MPM and tMAX season dependent. After optimal maintenance strategy is found, sensitivity analysis will be performed on parameters of gamma processes and on maximum wind speed.

3.1. Research goal and research questions

The main goal of this paper is to contribute to the current literature and assist practitioners in the field of offshore wind turbine maintenance by investigating how wind condition can be incorporated in maintenance decision making, whether adapting maintenance strategies to weather conditions can result in cost reduction and by exploring how optimal maintenance strategies are influenced by various factors and changes in parameters.

The following research questions will be answered: 1. How should wind behaviour be modelled? 2. How does wind speed influence deterioration rate?

3. How should maintenance decisions for offshore wind turbines be affected by wind speed to achieve optimal cost?

4. Is there an apparent seasonal pattern for optimal maintenance strategy due to seasonality of wind?

4. Methodology

To best answer research questions derived in previous section, it is useful to split this research in two main parts. First part is about modelling wind behaviour, while the second part is about using the results of the first part to aid in making better maintenance strategy decisions.

Based on the insights from literature review, it was decided that wind behaviour is modelled with better accuracy when real data is used. Appropriate secondary wind data source was needed, based on which, wind behaviour could be modelled. The key criteria points for appropriate data source were reliability, size, usefulness and applicability of such dataset. Since the dataset that we used had 14 years of data obtained from Fino1 platform, which is in the middle of offshore wind farm, this dataset proved to be sufficient size and otherwise a perfect match for our application. To progress from wind data to wind behaviour model, it was important to simplify the dataset, which was done by introducing wind categories. Then, data from different seasons was separated and probabilities of wind switching from one category to another were determined. This allowed to produce a wind probability matrix. This matrix shows the probability of wind switching from one category to any other.

As previously mentioned, for the next part of our study we needed to use wind behaviour model to improve maintenance strategies. Simulation study was chosen for this purpose because as combined with wind probability matrix it can simulate a stochastic weather behaviour for unlimited amount of time. Additionally, the key strength of simulation study is the ability to investigate what difference does every change of each parameter bring, which helps to understand why certain maintenance strategies can be better than others. Another significant advantage of simulation is its capability of being run for a long amount of time. It would be impossible to determine optimal maintenance strategies for offshore wind turbine only taking into consideration one or a few operational years.

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Based on these advantages and on the research of Karlsson (2016), simulation proved to be optimal choice for this application.

In order to execute simulation study successfully, we first needed to model a deterioration process. Since no data or expert opinion was available, we have used gamma processes for this application as these have proven to be suitable for modelling temporal variability of deterioration (van Noortwijk, 2009). Data or expert knowledge was not available in other fields as well, thus academic literature was consulted to obtain full image of maintenance costs, constrains, maintenance times and other parameters. After all the parameters were defined, the length of simulation runs had to be determined so that results would be sufficiently stable and accurate. When that was achieved, we needed to come up with maintenance strategies that could be tested against current strategy. This was done by referring back to the fact that wind data is seasonal and that seasonality has a significant effect on maintenance cost. Next logical step from here was to optimise each maintenance decision variable individually for each season. Combining all those optimised decision variables proved us with optimal maintenance strategy.

5. Numerical analysis

5.1. Wind data analysis

Wind data that is under investigation was captured from Fino1 platform in the North Sea and shows hourly wind speed at altitudes between 33 and 100 meters from 2004 to 2017. Fino1 platform is located approximately 70 kilometres from the shore and is surrounded by several operating wind farms, thus data captured here represents real life wind conditions for offshore wind turbines. Since hub of the turbine is usually located approximately 100 meters above the sea level, only wind data that was captured at that altitude will be analysed. First, general insights obtained from the data will be discussed, then wind speed will be categorized according to Beaufort wind force scale and finally, wind probability matrix that shows probabilities of wind switching from one category to another will be calculated.

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Figure 1. Wind speed distribution by year

Figure 2. Wind speed distribution by month

To calculate a wind probability matrix that indicates the probability of wind of one category switching to a wind of any other category, daily wind speed averages had to be obtained from hourly wind data. Then those averages were categorized into wind categories based on Beaufort wind force scale, which is presented in Table 1. The results of categorization showed that wind data follows the shape of Bell curve as represented by Figure 3. As it can be seen categories 4, 5 and 6 occurred most frequently, while there were no instances of wind getting below category 2 or above category 10. This means that categories 0, 1, 11 and 12 will not be present in our wind matrices. As previously mentioned, seasonality had to be accounted for, thus summer and winter season data was separated. Then, the probabilities of wind transferring from one category to another for each of the two seasons were calculated to determine wind probability matrixes. Summer wind probability matrix is shown in Table 2, while winter wind probability matrix is shown in Table 3. In those tables, current wind category is represented vertically, while next category is represented horizontally. For instance, the probability of wind switching from category 4 to 7 is equal to 0.036 in the summer and 0.062 in the winter. Clear differences in probabilities can be seen between these two matrixes, hereby confirming that seasonality is of significant importance.

0 5 10 15 20 25 30 2004 2006 2008 2010 2012 2014 2016 Wi nd spe ed (m /s ) Year 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 10 11 12 Wi nd spe ed (m /s ) Month

Average monthly speed Daily wind speed

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Table 1. Beaufort wind force scale

Beaufort category

(Beaufort number) Wind speed

0 <0.5 m/s 1 0.5 - 1.5 m/s 2 1.5 - 3.3 m/s 3 3.3 - 5.5 m/s 4 5.5 - 7.9 m/s 5 7.9 - 10.7 m/s 6 10.7 - 13.8 m/s 7 13.8 - 17.1 m/s 8 17.1 - 20.7 m/s 9 20.7 - 24.4 m/s 10 24.4 - 28.4 m/s 11 28.4 - 32.6 m/s 12 >32.6 m/s

Figure 3. Distribution of wind categories in the dataset

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Table 2. Summer season wind probability matrix To From 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 0.077 0.436 0.41 0.077 0 0 0 0 0 3 0.055 0.255 0.335 0.248 0.087 0.016 0.003 0 0 4 0.013 0.183 0.313 0.315 0.139 0.036 0.002 0 0 5 0.016 0.11 0.257 0.337 0.212 0.063 0.006 0 0 6 0 0.043 0.171 0.289 0.329 0.136 0.03 0.002 0 7 0 0.014 0.14 0.227 0.319 0.237 0.058 0.005 0 8 0 0.028 0 0.139 0.361 0.306 0.111 0.056 0 9 0 0 0 0 0 1 0 0 0 10 0 0 0 0 0 0 0 0 0 11 12

Table 3. Winter season wind probability matrix

To From 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 0 0.267 0.4 0.2 0 0.133 0 0 0 3 0.049 0.213 0.293 0.262 0.152 0.03 0 0 0 4 0.012 0.166 0.234 0.322 0.186 0.062 0.018 0 0 5 0.006 0.079 0.187 0.269 0.293 0.135 0.03 0.002 0 6 0 0.038 0.133 0.244 0.261 0.249 0.064 0.01 0 7 0 0.006 0.057 0.165 0.286 0.294 0.157 0.03 0.004 8 0 0 0.018 0.06 0.189 0.346 0.267 0.115 0.005 9 0 0 0 0.039 0.118 0.314 0.412 0.059 0.059 10 0 0 0 0 0 0 0.667 0.333 0 11 12

5.2. Deterioration level

To determine optimal maintenance decisions using simulation, the deterioration process of the wind turbine has to be modelled. Gamma processes have proven to be applicable for modelling temporal variability of deterioration (van Noortwijk, 2009). Since there is no data available based on which we could model deterioration levels, we are going to sample gamma distributed increments, thereby simulating a gamma process (similar to De Jonge et al., 2017). However, we also have to acknowledge the analysis of Carroll et al. (2015) and Arwade et al. (2011), which prove that increased average wind speed leads to more turbine failures. Figure 4 shows how the yearly failure rate of a turbine increases depending on average wind speed that year. Based on this, it could be argued that increased failure rate on higher wind speeds also mean that deterioration increments should also increase with wind speed. To account for that in our analysis, we are going to obtain shape parameter k by multiplying average wind speed of current wind category 𝑣𝑝̅̅̅ by constant α. Concurrently, scale parameter θ will be held constant.

Commented [B9]: This is how you implement the

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Figure 4. Average wind speed versus failure rate (Carroll et al., 2015)

Fixed values are needed for α constant of shape parameter and scale parameter θ. In order to estimate reasonable values for these parameters, we have to acknowledge that multiplication of shape and scale parameters should result in average deterioration increment. Since our shape parameter varies depending on wind category, we have to use average wind speed of the whole simulation when estimating average deterioration increment. Average wind speed for the whole simulation is approximately 10 m/s. Now we only need to obtain an estimate for average deterioration increment that we are aiming to have in our simulation and select appropriate values for parameters to result in average deterioration increment approximately equal to our aim.

Average deterioration increment can be determined using failure rate data from Carroll et al. (2015). Based on the information provided in this paper, we estimated a failure rate value of critical component of our turbine to be equal to 7 per year. This means that failure should happen every 50 days on average. Consequently, when no maintenance is performed, failure level of our turbine MF should be reached in 50 days. To make the simulation easily understandable, the as-good-as-new deterioration level is set to 0, and the failure level of a turbine MF was set to 100. This means that we should have an average deterioration increment of 2 in order to reach our defined MF in 50 days. Therefore, such alpha and beta parameters that would result in average deterioration increment of 2 were needed. Desired result was achieved by choosing α value of 0.25 and θ value of 0.75. It must be kept in mind, however, that many different combinations of those parameters can result in average increment being equal to desired number. Already defined set of parameters was chosen such that these would represent relatively steady deterioration increments but with increasing value of θ, increments become less stable.

5.3. Costs

5.3.1. Corrective and preventive maintenance costs

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average repair times, material costs, failure rates, number of technicians required for repairs and other parameters that would aid in O&M cost and resource modelling as well as decision making. Based on this paper, average material cost of the repair activities that we are interested in (those that can be carried with CTV) can be approximated to be equal to 200 euros. Such maintenance actions should require 3 technicians and take up to 12 hours of time (including travel time). Assuming that technicians earn 20 euros per hour, labour cost is 240 euros. Finally, vessel hire costs have to be considered. According to Dinwoodie et al. (2015), crew transfer vessel hire should cost around 2450 euros per day. Total cost of vessel hire per maintenance action depends on the length of maintenance campaign and will vary between strategies. For first and second maintenance strategies we have defined maximum length of maintenance campaign to be equal to 3 days, thus total vessel hire cost will be 7350 euros. Last cost component is a failure penalty for CM, which we assume to be equal to 1000 euros. Summing those numbers up for maintenance strategies 1 and 2, we get that PM action costs CPM = 7790 euros, while CM action costs CCM = 8790 euros. The main differences between costs of preventive and corrective maintenance will occur because of lost capacity. Corrective maintenance actions generally result in more downtime, thus larger downtime cost is incurred and overall cost of corrective maintenance activity becomes significantly higher.

5.3.2. Capacity losses

The last significant cost component of this simulation is associated with capacity loss (CCL). Cost of lost capacity can be calculated by multiplying power output of the turbine by time (t) and price of electricity (p). Power output of the wind turbine is given by 𝑃 = 1₂𝜌𝐴𝑣3_𝐶

𝑝, where 𝜌 is air density (1.23 kg/m3_{), v is wind speed (we will use the average wind speed of the current category 𝑣}

𝑝

̅̅̅), A is the sweep area of the blades (defined by blade length) and 𝐶𝑝 is the power coefficient. For safety reasons, turbines cannot produce more power than they were designed to, thus this formula is only needed when the generated power is below rated power output of a turbine. Additionally, wind turbines are not operational at all when wind is below cut in speed or above cut out speed, which means that there are no downtime costs when wind is lower than category 3 and or above category 9.

The turbine under investigation is assumed to have blade length equal to 50 metres, power coefficient of 0.4 and maximum power output of 4 MW. We also assume fixed electricity price of 0.2 Euros per KWh. Inserting these values into the equation we get that 𝑃 = 1950𝑣3_{. Aligning units and adding} time and price to the equation we get that 𝐶𝐶𝐿= 1.95𝑣̅̅̅𝑝3𝑡𝑝, where t represents the downtime hours, 𝑣_𝑝

̅̅̅ represents the average wind speed of current category and p represents the electricity price. Since electricity price is assumed to be equal to 0.2 €/kWh, the amount of downtime hours per maintenance activity is 12, while the amount of downtime hours per day in case of failure is 24, we have two functions of 𝐶𝐶𝐿, one for maintenance and one for failure. For maintenance, we have 𝐶𝐶𝐿𝑀(𝑣) = 4.68𝑣̅̅̅𝑝3 and for downtime we have 𝐶𝐶𝐿𝐹(𝑣) = 9.36𝑣̅̅̅𝑝3. These lost capacity cost functions are applied until wind reaches category 7, from which point rated power output is reached and we have fixed power output of 4 MW, which means that the costs from this point onward stay fixed as well. Relationship between wind category and lost capacity costs for maintenance and downtime can be seen in Figure 5.

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Figure 5. Relationship between wind category and costs of lost capacity due to maintenance and failure

5.4. Maximum wind speed allowed for maintenance

The maximum wind speed that allows for maintenance activity depends on what type of equipment is used to perform maintenance. We assumed that crew transfer vessels are the only type of vessel that is going to be needed to perform maintenance activity. According to the literature (Dalgic et al., 2014), crew transfer vessels are mostly limited by wave height rather than wind speed. However, it has been proven that wind speed and wave height are strongly correlated and we will therefore use wave height estimations that are based on Beaufort wind force scale provided by MetOffice (2015). Maximum wave height that allows for the operation of CTV is between 1.5 and 1.7 meters (Dalgic et al., 2015). Based on the Beaufort wind force scale, this means that maximum wind category that allows for maintenance is category 4.

5.5. Simulation input data

We are going to analyse four different maintenance strategies in our analyses. Table 4 summarizes simulation inputs and decision variables for those strategies.

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Table 4. Summary of input parameters for all strategies Input parameters Current strategy (CS) Maintenance Strategy 1 (MS1) Maintenance Strategy 2 (MS2) Maintenance Strategy 3 (MS3) MPM – PM threshold Decision variable Decision variables Decision variable Decision variables – Season specific PM

threshold No Yes No Yes

tMAX

– Maximum duration of

maintenance campaign (days) 3 3

Decision variables

Decision variables – Season specific maximum

duration of maintenance campaign

No No Yes Yes

CPM – Total cost of corrective

maintenance action (€) 8790 8790 440+2450 tMAX 440+2450 tMAX CCM – Total cost of preventive

maintenance action (€) 7790 7790 1440+2450 tMAX 1440+2450 tMAX CH – – Costs of vessel hire (€) 2450 2450 2450 2450 CCLM – Cost of lost capacity due to

maintenance (€/day) 4.68𝑣̅̅̅𝑝

3 _4.68𝑣

𝑝

̅̅̅3 4.68𝑣̅̅̅𝑝3 4.68𝑣̅̅̅𝑝3 CCLF – Cost of lost capacity due to

failure (€/day) 9.36𝑣̅̅̅𝑝 3 _9.36𝑣 𝑝 ̅̅̅3 _9.36𝑣 𝑝 ̅̅̅3 _9.36𝑣 𝑝 ̅̅̅3 tPL – Time required for planning

(days) 3 3 3 3

VIN – Cut in wind category 3 3 3 3

VOUT – Cut out wind category 10 10 10 10

VMAX – Maximum wind speed

category (Beaufort number) 5 5 5 5

MF – Failure level 100 100 100 100

p – Electricity price (Eur/kWh) 0.2 0.2 0.2 0.2

tShift – Shift length (hours) 12 12 12 12

α – Shape parameter constant

alpha 0.25 0.25 0.25 0.25

θ – Scale parameter 0.75 0.75 0.75 0.75

5.6. Simulation run length

The run length of the simulation will be determined practically by inspecting the relationship between run length and stability of the results. This will be done by plotting PM threshold versus average cost per day curve for several run lengths. We will choose minimum simulation length that offers relatively smooth and stable curve across the runs, so that approximately the same conclusion could be made from any run. Due to stochastic nature of the model, this curve is not expected to be completely smooth.

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noticeable differences between runs, especially in the PM threshold ranges from 40 to 45 and from 75 to 90. Since these two runs have a MCUT difference of up to 20% for some PM threshold values, it was decided to test a simulation run length of 100 years. The results of two runs of 100 years can be found in Figure 8. It is evident that such simulation run length smoothened out most of the fluctuations and resulted in relatively smooth and stable curves for both runs. This suggest that simulation run length of 100 years should deliver sufficiently consistent and accurate results to draw conclusions from. Consequently, simulation run length of 100 years will be used to investigate performance of different maintenance strategies.

Figure 6. PM threshold versus MCUT for 20-year simulation runs

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5.7. Current maintenance strategy

Current maintenance strategy (CS) is our benchmark scenario, since it represents the most common practise in the industry, which does not account for wind data analysis and relies on settled decisions throughout the year. This means that we have a single PM threshold and single maximum length of maintenance campaign for both seasons. The length of maintenance campaign was chosen to be equal to 3 days for this strategy, but this value is not backed up by any data or expert opinion and will be varied in maintenance strategy 2.

A simulation run of 100 years was done to determine optimal PM threshold value for input settings previously defined in Table 4. As it can be seen from Figure 9, the optimal PM threshold value is in the range between 40 and 55. Actual values used to plot this graph can be found in Table 8 in Appendix B. Based on this table, it can be seen that PM threshold value of 40 returns the lowest MCUT value. However, the difference of cost in a PM threshold range from 40 to 55 is a mere 3.5%, which means that instead of giving one fixed value we can say that optimality for this particular strategy lays in a PM threshold value range from 40 to 55.

Figure 9. PM threshold versus MCUT

Next, it would be beneficial to investigate why the optimal PM maintenance level is only at 40 to 55 percent of failure level. For that, we will look deeper into the results of our simulation run with a PM threshold value set to 40. As it can be seen from the deterioration level over first ten years of simulation time graph displayed in Figure 10, significant amount of time might pass before weather conditions allow for execution of maintenance. Such conclusion can be made by visually inspecting

0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 MC U T (Eur) PM Threshold Run 1 Run 2 0 500 1000 1500 2000 2500 0 20 40 60 80 100 MC U T (Eur) PM Threshold

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dots and the amount of time the deterioration level curve stays at 100 in Figure 10. Dots in this figure represent PM actions and the deterioration level at which those preventive maintenance actions were executed range from below 50 to above 90. In fact, considering the whole length of simulation, we have an average deterioration level at which PM action is executed equal to 57.3. Even though this value is nearly 50% larger than PM threshold level, it is still far away from failure. Surprisingly, even with PM threshold value being 40% of failure level, we still have approximately 0.6 failures per year, which shows that maintenance actions are heavily dependent on weather.

Clearly, these results do not appear to be optimal and better maintenance strategies can definitely be found. The fact that this simulation run showed an average wind category for winter being higher than 5, while being below 5 for summer suggests that different PM threshold values for different seasons could indeed improve the results, especially since maintenance cannot be performed when wind reaches category 5. Additionally, based on average deterioration level at which maintenance is performed, we can estimate that it takes slightly more than 5 days to perform PM maintenance activity after it is planned. Since maximum length of maintenance period is set to 3, increasing this number should reduce MCUT as well.

Figure 10. Deterioration level and PM execution points for the first 10 years of MPM = 40 simulation

5.8. Maintenance strategy 1

Maintenance strategy 1 (MS1) is meant to investigate the benefit of assigning different PM threshold values for each season. For this strategy maximum length of maintenance campaign will remain fixed at three days, since this will allow to determine the cost benefit that comes from seasonal PM threshold values alone. It can be expected that the PM threshold values for winter should be below the optimal level defined in current strategy (40), while the PM threshold value for summer should be above that number.

For this strategy we will use the same input parameters as for current strategy and the only difference will be an introduction of two preventive maintenance thresholds – one for each season. Because summer and winter PM threshold do not depend on each other, these two seasons can be separated into two simulations, one for summer season and one for winter season. This will simplify the simulation process and will also allow to add more decision variables without compromising simulation processing time in later stages. In Figure 11 we have plotted the relationship between

0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 2500 3000 3500 D ete ri o rat io n Le ve l Days

PM Action Det. Level

Commented [S12]: Add total number of maintenance

actions?

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MCUT and PM threshold for summer and winter seasons. As expected, MCUT is significantly lower for summer season than it is for winter. However, even though summer season benefits from lower average wind speed, optimal PM threshold for this season has not increased by much compared to the winter season or current strategy and is in the range from 50 to 65. Similarly, optimal PM threshold for winter season has not decreased much compared to CS and is between 35 and 40. By choosing optimal PM value for each season, overall MCUT can be obtained and compared to one obtained in CS. Data with exact values of MCUT for different PM thresholds for both seasons can be found in Table 9 in Appendix C. As this table suggests, it is the most cost effective to choose summer PM threshold equal to 50 and winter PM threshold equal to 40. Combination of these two results in overall MCUT value of approximately 763 euros, which results in a saving of 6% compared to current strategy.

Figure 11. PM threshold versus MCUT of winter and summer seasons

Now we will more closely inspect what kind of changes did this seasonal PM threshold policy bring compared to the previous strategies. We will set winter PM threshold to be equal to 40 and summer PM threshold value to be equal to 50 as these values were determined to be optimal. Figure 12 shows deterioration level over first ten years of simulation time and preventive maintenance execution points for winter season. Similarly to current strategy, preventive maintenance is executed at wide range of deterioration level values and failures are still present. Since PM threshold for winter season is the same as PM threshold in current strategy, both average deterioration level at which PM is performed and average failures per year should increase and this is exactly what happens. Considering the whole simulation, average deterioration level at which PM is performed is equal to 60.4, which is slightly higher compared to CS (57.3). Higher average deterioration level at which PM is executed has a significant impact on average number of failures per year, which increased from 0.6 in CS to 1.2. It must be noted that these values are expected to be higher compared to CS, since we are looking at continuous winter season here and they are only compared because the same PM threshold value was used and that allows to clearly show the effect of seasonal wind conditions.

0 500 1000 1500 2000 2500 3000 3500 0 20 40 60 80 100 MC U T (Eur) PM Threshold

MCUT Summer MCUT Winter

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Figure 12. Deterioration level and PM execution points for the first 10 years of MPM = 40 winter season simulation Looking at deterioration level and PM execution points over time for the first 10 years of simulation time in summer season as shown in Figure 13, we can see that most PM actions are being completed at similar deterioration level and there is significantly less fluctuation compared to winter season. Additionally, it is worth noting that no failures happened in those 10 years of simulation time, which together with relatively steady PM execution points suggest that weather conditions are significantly less harsh in summer season. Considering the whole time frame of simulation, we have an average deterioration level at which PM is performed equal to 62.7 and an average of 0.2 failures per year. Average deterioration level at which PM is performed is only slightly larger in summer than in winter, which also indicates that less time passes between planned and executed maintenance activity in summer than in winter. This conclusion can be made considering the fact that noticeably larger PM threshold value was used for summer season. Taking both, summer and winter seasons into consideration, we have an average deterioration level at which PM is completed equal to 61.5 and an average of 0.7 failures per year. Even though these values have increased compared to current strategy, higher PM threshold value for summer season also means that maintenance is executed less frequently. In fact, number of maintenance activities was reduced by 80 compared to CS and that is the key factor that allowed to reduce MCUT value by 6%. The analysis of this strategy clearly indicated significant importance of wind seasonality and financial benefit of addressing it, but the main shortcoming of this strategy is still the same as it was in current strategy - weather conditions are rather harsh and deny repairs frequently, especially in winter season, which result in high risk of failures or a need of very low PM threshold value.

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Figure 13.Deterioration level and PM execution points for the first 10 years of MPM = 50 summer season simulation

5.9. Maintenance strategy 2

Maintenance strategy 2 (MS2) is designed to investigate the benefit of changing the maximum length of maintenance campaign, while still neglecting seasonality for both, PM threshold and tMAX. Increase of maintenance campaign length means that vessel is hired for longer period of time and there is higher probability that vessel will be available when maintenance is needed and wind conditions allow to perform it. In this strategy, we want to investigate relationship between MCUT and tMAX for different tMAX values for single PM threshold only. This means that we will go back to current strategy, but instead of having fixed tMAX value, we will explore the relationship between MCUT and tMAX for different PM threshold values.

We will use the same input parameters as for current strategy and will only add another decision variable - maximum length of maintenance campaign tMAX,. Introducing this variable also means that maintenance costs are now dependent on tMAX as shown in Table 4. In this strategy, decision variables MPM and tMAX depend on each other. We expect to see optimal PM threshold increasing as maximum length of maintenance campaign increases. Figure 14 shows how MCUT depends on MPM for tMAX values of 1, 3, 5, 7 and 9 days. Clearly, maximum maintenance length of 1 day is out of context due to being unreliable choice, that can only perform well when good weather conditions align with maintenance activities. Maximum maintenance length of 9 days is also slightly out of context because of being more expensive. Consequently, we will eliminate those from the graph and only analyse tMAX values of 3, 5, and 7 days as shown in Figure 15. From this figure, we can see that optimal PM threshold level increases as maximum length of maintenance campaign increases such that optimal value of MPM is equal to 40 for tMAX of 3 days and 60 for tMAX of 7 days. Additionally, we can see that smoothness and consistency of the curves increases with higher value of tMAX and that is because higher values of tMAX make MCUT less weather dependent. Lowest MCUT value in the graph is achieved when maximum length of maintenance campaign is set to 3 days. However, to find the optimal value, tMAX of 2 and 4 days have to be investigated as well. Further analysis showed that costs are minimalized when tMAX is set to be equal to 2 days, but as previously discussed, such low value can cause unstable results. To account for that, three independent simulation runs were performed and the results of those were plotted together in Figure 16. The graph shows that there are some more fluctuations and irregularities compared to larger tMAX values, but these are not major and do not have an impact on

PM executed Det. Level

Commented [S14]: Word scenario

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conclusions since all three runs with tMAX set to 2 performed better compared to tMAX value of 3. Nevertheless, we will average results of all three runs and derive conclusions from those as this will result in improved accuracy of the results. For tMAX= 2, the lowest average MCUT value across all three runs is 760 euros and it is achieved when PM threshold is equal to 40. Such MCUT value results in a saving of 6% compared to CS and is almost identical to the lowest MCUT value achieved in MS1. Actual MCUT values for different tMAX values as well as MCUT values for different runs of tMAX = 2 can be found in Table 10 in Appendix D.

Figure 14. PM threshold versus MCUT versus for different maximum lengths of maintenance campaign

Figure 15. Minimalized PM threshold versus MCUT versus for different maximum lengths of maintenance campaign

500 700 900 1100 1300 1500 1700 1900 2100 2300 0 20 40 60 80 100

tMAX = 1 tMAX = 3 tMAX = 5 tMAX = 7 tMAX = 9

500 700 900 1100 1300 1500 1700 1900 2100 2300 0 20 40 60 80 100

tMAX = 3 tMAX = 5 tMAX = 7

Commented [S16]: Questionable

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Figure 16. PM threshold versus MCUT versus for tMAX = 2

We will now inspect simulation runs where maximum length of maintenance period was set to be equal to 2 and 7 days. First run will be inspected for tMAX = 2. Only these simulations will be considered since one of those values is optimal, while the other one should allow to investigate what effect does an increased value of tMAX have on the results. Additionally, we have already investigated the results of simulations where tMAX was set to 3 days in Sections 5.7 and 5.8. Figure 17 shows deterioration level over first ten years of simulation time for tMAX = 2 and MPM = 40. We can see that deterioration level at which PM is executed varies and that failures are slightly more common than in current strategy. Otherwise, there are no noticeable differences in this graph compared to the one in CS, where tMAX = 3. Considering the whole simulation time, we have an average deterioration level at which PM is executed equal to 56.9 and an average failure level of 0.7 per year. Compared to tMAX = 3, this shows that failures are slightly more common for tMAX = 2 which is due to lower availability of vessels, but maintenance in this particular scenario is also executed at earlier stage, which was not expected. The most likely explanation for this comes from the wind probability matrix. It is unlikely that wind will quickly switch from high category to low as it usually increases and decreases step by step, mostly one to two categories per time period. Consequently, in the instances where wind is high and tMAX is not large, it might be beneficial to have shorter tMAX, since it is unlikely that maintenance will be possible in this campaign. In such case, shorter tMAX will allow to begin planning next maintenance activity sooner. However, this only works in very specific instances. Otherwise, we can see that failure rate increased which means that the turbine could not be maintained to the same level with shorter value of tMAX. Nonetheless, reduced cost of vessel hire per each maintenance activity planned justifies slightly increased failure rate in terms of mean cost per day.

500 1000 1500 2000 2500 0 20 40 60 80 100 MC U T (Eur) PM Threshold

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Figure 17. Deterioration level and PM execution points for the first 10 years of MPM = 40 and tMAX = 2 simulation

We will now investigate how there results differ for longer periods of maximum length of maintenance campaign. In this simulation, tMAX was set to 7, while MPM was set to 40. PM threshold value of 40 instead of optimal value of 60 was chosen in order to clearly see the differences between maximum length of maintenance period set to 7 and 2 days. Deterioration level and PM execution points for the first ten years of simulation are shown in Figure 18. We can see that there is less fluctuation in deterioration level at which PM action is executed but there are still some failures. Considering the whole duration of simulation, average number of failures per year has still decreased to 0.5, while average deterioration level at which maintenance is performed is 55. Presence of failures verifies previously discussed point, that wind conditions do not change quickly and may stay above the limit that allows for maintenance for several weeks. In turn, this means that long maximum length of maintenance period is not cost effective for our input parameters.

Figure 18. Deterioration level and PM execution points for the first 10 years of MPM = 40 and tMAX = 7 simulation 0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 2500 3000 3500 D ete ri o rat io n Le ve l Days

PM executed Det. Level

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5.10. Maintenance strategy 3

Maintenance strategy 3 (MS3) is meant to combine findings of previous three strategies into one. Such strategy should deliver the best performance, since both, PM thresholds and maximum length of maintenance campaign will be optimised individually for each season.

As discussed in MS1, optimal decision variable values for winter and summer seasons do not depend on each other, which means that we can set up one simulation for winter season and another one for summer season. We will use the same input parameters as in MS2, as previously indicated in Table 4. Figures 19 shows the relationship between PM threshold and MCUT for different maximum lengths of maintenance period for winter season. As before, we can see that when the maximum length of maintenance period is equal to 1, the results are very unstable, while we observe the most stability when maximum length of maintenance campaign is highest (9 days). At both of those values MCUT is noticeable higher. Since minimum MCUT was achieved at tMAX value of 5, maximum maintenance period length of 4 or 6 days could perform better and should be simulated. After simulating that, it can be verified that tMAX value of 5 results in the lowest cost as it can be seen from the results of all the simulations that were run for winter seasons which are shown in Table 11 in Appendix E. It is also evident from this table and Figure 19 that with increasing tMAX value, optimal PM threshold value also increases. However, winter season suffers from harsher and less stable wind conditions, thus this concept can be seen much more clearly in Figure 20, which shows the relationship between PM threshold and MCUT for different maximum lengths of maintenance period for summer season. Here, we can see that optimal PM threshold value varies from 35 for tMAX = 1 to 70 for tMAX = 7. Minimum MCUT in summer season is equal to 288 euros and is achieved when maximum length of maintenance campaign is set to 2, while PM threshold is set to 50 as shown in Table 12 in Appendix E. Combining optimal decision variables for both seasons, we get MCUT value of 706 euros, which offers a saving of 13% compared to CS, where seasonality was not accounted for at all, and a saving of 7% compared to MS1 and MS2, where seasonality was only partly accounted for.

Figure 19. PM threshold versus MCUT for different maximum lengths of maintenance campaign in winter season

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Figure 20. PM threshold versus MCUT for different maximum lengths of maintenance campaign in summer season

Now we will investigate what allowed to accomplish such cost reduction for this strategy. We will look at optimal simulation strategies for summer and winter seasons independently. For the simulation of winter season, PM threshold is set to 40 and maximum length of maintenance campaign is set to 5. Deterioration level over first ten years of simulation time as well as PM execution points are shown in Figure 21. We can see that deterioration level at which PM is executed does not fluctuate as much as in MS1, where all input parameters were the same except for tMAX, which was set to 3 days. Some failures are still present in this simulation, but this is expected since failures could not be avoided when tMAX was set to 7 days for both seasons in the analysis of MS2. Considering the whole simulation time, we have an average deterioration level at which PM is executed equal to 59.2 and an average of 1.1 of failures per year. As expected, both of these values lay in the middle between already investigated strategies with tMAX values of 3 and 7. It can be concluded that for the input parameters that were used, it is economically beneficial to have longer maximum maintenance period length in order to have less failures.

Figure 21. Deterioration level and PM execution points for the first 10 years of MPM = 40 and tMAX = 5 winter season simulation Considering summer season, we have set PM threshold to 50 and maximum length of maintenance campaign to 2. From the plot of first ten years of simulation time, we can see that most PM actions were executed at similar deterioration level as shown in Figure 22. Additionally, it can be seen that

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tMAX = 1 tMAX = 2 tMAX = 3 tMAX = 5 tMAX = 7

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deterioration level increased above 90 only once and there were no failures in this ten-year period at all. These results are very similar to those of MS1, where tMAX was set to be equal to 3 days. Considering the whole length of simulation, we have an average deterioration level at which PM was executed equal to 62.5 and an average of 0.1 failures per year. Compared to MS1, both of these values decreased, which, as argued in MS2, might be due to the fact that wind conditions change slowly and in some cases it might be beneficial to begin planning next maintenance activity sooner and allow wind conditions to change during that planning time. Consequently, for the input parameters that we have considered, taking more risk and decreasing maximum length of maintenance period not only reduces vessel hire costs per each maintenance activity, but also allows to reduce average number of failures, which, in turn, results in lower mean maintenance cost per day.

Figure 22. Deterioration level and PM execution points for the first 10 years of MPM = 50 and tMAX = 2 simulation

5.11. Sensitivity analyses

In this section, we are going to investigate how MCUT and optimal PM threshold changes when input variables are changed. As before, the results obtained in this section are based on a 100-year long simulation and only one variable is changed at a time, which means that other variables are left the same as previously shown in Table 4. To simplify sensitivity analysis, we will use previously determined optimal lengths of maintenance campaigns in the strategies where tMAX is a variable as shown in Table 5.

Table 5. optimal tMAX values of different strategies

Strategy tMAX (days)

Current strategy 3

Maintenance strategy 1: summer 3 Maintenance strategy 1: winter 3

Maintenance strategy 2 2

Maintenance strategy 3: summer 2 Maintenance strategy 3: winter 5 0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 2500 3000 3500 D ete ri o rat io n Le ve l Days

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5.11.1. Parameters of gamma process

As elaborated in Section 5.2., gamma processes were used to model deterioration process of a turbine. Gamma processes are defined by shape and scale parameters. In our study, shape parameter k changes depending on wind category and is equal to a constant α multiplied by average wind speed of present wind category 𝑣̅̅̅, while scale parameter θ is constant all the time. Constants in parameter 𝑝 values for gamma processes were chosen so that the combination of those would result in average deterioration increment approximately equal to 2. However, our choice of constant was not justified and since there is an infinite amount of different α and θ values that could produce an average increment level of 2, sensitivity analysis has to be performed.

In all of the analyses that were performed earlier, α was set to be equal to 0.25 and θ was set to be equal to 0.75. Such choice of constants produces relatively stable deterioration increments that are rarely higher than 10% of failure level. For this sensitivity analysis, we want to investigate the effects of deterioration increments being less stable and maximum increment values being larger. To achieve that, we will increase the value of θ by 100 and 200% and then choose appropriate value for α so that average deterioration increment stays at 2. This results in α value of 0.125 when θ is equal to 1.5 and α value of 0.09 when θ is equal to 2.25. Figures 23 and 24 show how optimal preventive maintenance threshold and mean cost per unit time change at various scale parameter values. Only scale parameter was plotted because knowing one parameter, another one can be determined from equation 𝛼𝑣̅𝜃 = ∆𝑑

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Figure 23. Optimal PM threshold versus scale parameter

Figure 24. MCUT versus scale parameter

5.11.2. Maximum wind that allows for maintenance

In Section 7.2. we looked at maximum wind category that allows to safely operate crew transfer vessels. Since these vessels are limited by wave height more than wind speed, we used Beaufort wind force scale to convert wind speed into wave height and it showed that maximum wind category that still allows to safely operate CTVs is category 4. However, Beaufort wind force scale assumes well developed sea and wind conditions, which means that it is more likely that overestimation of wave height occurs. Furthermore, there are many factors that determine wave height and relying solely on wind might be inaccurate. Additionally, we took a value for maximum wave height in which CTV can be operated from specification sheet, but vessels can improve in the future or other means of transport could become superior in terms of cost and performance. It would therefore be useful to determine how changing maximum wind speed that allows for maintenance VMAX affects results of our study. We will only consider higher maximum wind categories than used previously for the reasons that were already explained in this section.

Figures 25 and 26 show how optimal PM threshold and mean cost per unit time change at increasing maximum wind speeds that allow for maintenance. As it can be seen in Figure 25, optimal PM threshold increases steeply with every additional wind category that allows for maintenance. As explained in section 7.9.1., these curves do not follow a pattern of marginally straight increasing lines and experience steeper increases at some points and less steep at others partly because PM threshold levels are increased by five, which reduces accuracy compared to one where PM threshold values

30 35 40 45 50 55 60 0.75 1.5 2.25 O pti m al P M thre sho ld Axis Title CS MS1 Summer MS1 Winter MS2 MS3 Summer MS3 Winter 600 700 800 900 1000 1100 0.75 1.5 2.25 MC U T θ CS MS1 MS2 MS3

Incorporating wind in maintenance planning decisions for offshore wind turbines