Wind Farm O&M: The Case of Jack-up Vessels
(Final version)
A
UTHORR. Greijdanus (S2570246/140631476)
Student MSc Operations Management (Dual Award) Groningen, January 2016
M
ASTER THESIS(
DUAL AWARD)
MSc Technology & Operations Management (University of Groningen) MSc Operations & Supply Chain Management (Newcastle University)
S
UPERVISORSDr. Fazi (First supervisor, University of Groningen) Dr. Dong (First supervisor, Newcastle University)
Dr. Veldman (Academic advisor, University of Groningen)
A
BSTRACTOffshore wind energy is becoming a viable alternative to finite energy sources. However, the cost of offshore wind must be further reduced to make offshore wind energy competitive. This requires innovation in multiple areas. One such area is Operations & Maintenance (O&M) which accounts for 30% of the cost of offshore wind. Of the O&M cost, 50% can be directly contributed to the jack-up vessel, which is characterized by high costs and low utilization. It is proposed that jack-up vessel sharing between operators can simultaneously solve the problems of high costs and low utilization. In this thesis, the concept of resource sharing between operators has been evaluated by means of a quantitative modelling approach. Stochastic processes, such as weather patterns and component failure rates, have been incorporated in a Monte Carlo simulation. The results provide insights in how operators can benefit from resource sharing. It is concluded that cost benefits up to 66% can be achieved compared to a leasing policy. However, operators must develop cost allocation schemes to equally distribute these benefits.
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CKNOWLEDGEMENTSThis thesis, which marks the end of my academic years, would not have been if it were not for Dr. Jasper Veldman, who I would like to thank for bringing me into the research project ‘Sustainable
service logistics for offshore wind farms’, as well as providing feedback. I would also like to thank Dr.
Stefano Fazi and Dr. Jingxin Dong for their supervision and feedback during the past months. And, Jeroen Stellingwerf for proofreading. Also, Filips de Jager for arranging industry contacts and broadening my understanding of practice. Furthermore, I would like to thank my fellow students for being there with me in the trenches. Finally, my appreciation to the “non-living”, i.e. the university coffee machines for their vital services and my trusty computer for crashing only once during my many hours of simulation.
T
ABLE OFC
ONTENTS1.
INTRODUCTION ... 2
2.
THEORETICAL BACKGROUND ... 3
2.1 Developing maintenance policies ... 3
2.2 Planning maintenance operations ... 5
2.3 Building a maintenance support organization ... 6
2.4 Resource sharing ... 6
2.5 Conceptual framework ... 7
3.
METHODOLOGY ... 8
3.1 Research method ... 8
3.2 Simulation techniques ... 9
3.3 The research model ... 9
4.
THE MODEL ... 11
4.1 Problem description ... 11 4.2 Conceptual model ... 12 4.3 Scientific model ... 145.
RESULTS ... 22
5.1 Validation ... 24 5.2 Search experimentation ... 25 5.3 Case study ... 276.
DISCUSSION ... 29
7.
CONCLUSION ... 31
REFERENCES ... 32
APPENDIX A: LIST OF INPUT DATA ... 36
APPENDIX B: LIST OF ASSUMPTIONS ... 37
APPENDIX C: WEATHER DISTRIBUTION FITTING ... 38
APPENDIX D: MOBILISATION PROTOCOL ... 40
APPENDIX E: VESSEL SHARING SYSTEM CHART ... 41
1.
I
NTRODUCTIONIn today’s society the demand for renewable energy is increasing (REN21, 2015). Due to pressure from the scientific community and concerned citizens, many governments are acknowledging their role in combating climate change. In the Netherlands, the energy agreement for sustainable growth gives voice to the willingness of businesses and the government to make the economy sustainable (SER, 2013). Globally, changes in governmental policies have six-folded investments in renewable energy during the last decade (UNEP, 2015). This increase has led to many innovations in the energy sector, particularly in the field of wind energy (Wangler, 2013). These innovations are making wind energy a viable alternative to finite energy sources such as fossil fuel, furthering interest in wind energy. However, there are indications that there are limits to the growing potential of wind energy. One limitation is that offshore wind farms suffer from relatively higher failure rates. As a result, their operational availability is in the range of 60-70%, opposed to 95-99% for onshore wind farms (Shafiee, 2015a). Consequently, offshore wind energy costs is €200/Megawatt-hour (MWh) but must be reduced to €140/MWh to become competitive (Global Offshore, 2012). Considering the average lifecycle of a wind farm is 20 years, many of the investments made in the past decade may prove to be unprofitable due to higher than expected operating costs.
A possible area to increase the availability of offshore wind farms, and preserve the profitability of offshore wind energy is rethinking Operations & Maintenance (O&M), which accounts for 20-30% of the lifecycle cost of a wind farm (El-Thalji, 2012). According to Shafiee (2015b) four strategic O&M issues are being considered. Firstly, rethinking the design of an offshore wind farm to lengthen time-between-failures. Secondly, developing maintenance policies to reduce downtime. Thirdly, optimising the location and capacity of the maintenance support organization. Finally, outsourcing maintenance operations to external service providers since maintenance resources (e.g. cable-layer vessels, jack-up vessels) account for 73% of the total O&M cost, while their utilization rates are low (Krohn, Morthorst, & Awerbunch, 2009).
Dalgic, Lazakis, Turan & Judah (2015) investigated the optimal jack-up leasing strategy. In their concluding remarks, they suggest jack-up purchasing for larger wind farms, and regional collaboration between wind farm operators, as directions for future research. In this thesis, the concept of resource
sharing between operators is evaluated. The jack-up vessel is chosen as the subject of this research due to
its high cost of maintenance and low utilization rate. A jack-up vessel is a self-elevating vessel that is capable of raising its hull from the ocean’s surface to provide a stable platform for heavy lifting and large component replacement (The Crown Estate, 2014). By sharing a jack-up vessel between multiple offshore wind farms, the individual cost of maintenance decreases. Such a strategy would simultaneously tackle the issues of high O&M costs and low vessel utilization, while contributing to reducing the cost of offshore wind energy.
However, a resource sharing strategy comes with its own set of challenges. Firstly, operators have limited access to the shared vessel, which could result in repair delays and negatively affect the performance measures (i.e. downtime, availability and costs). Secondly, each wind farm must conduct their own mobilisation and demobilisation activities (e.g. welding of components). It may be beneficial to perform these activities at the same harbour. Therefore, this thesis will both explore the sharing of the jack-up vessel as well as the onshore harbour resources. The contribution of this piece of research is, to the best of the author’s knowledge, the first study on resource sharing in the wind farm literature. The main research question is: what is the effect of resource sharing on the performance measures of offshore wind farms?
In order to address the research question, a quantitative modelling approach has been taken. A model has been developed to simulate a wind farm maintenance systems under both leasing and resource sharing policies. The model has been developed using data provided by industrial stakeholders. The challenge was combining data on weather conditions, such as wind speeds, with failure rates and operational parameters in a correct manner that reflects real-world operations.
2. T
HEORETICALB
ACKGROUNDO&M is potentially a significant contributor to making offshore wind farms viable. This question has first been addressed by Krokoszinski (2003) where the concept of Overall Equipment Effectiveness (OEE) was applied to wind farm operations. From this analysis, it became clear that O&M could be a significant contributor to making offshore wind farms viable. In practice, the O&M cost of a typical wind farm project accounts for 20-30% of the lifecycle cost (El-Thalji, 2012). These costs can be separated into three categories: preventive maintenance, corrective maintenance and operations (Walford, 2006). ‘Preventive maintenance’ is a type of maintenance where maintenance is performed before a failure occurs. For wind farms, this largely depends on the recommendations of the turbine supplier resulting in scheduling maintenance twice a year (Byon, Perez, Ding, & Ntaimo, 2011). ‘Corrective maintenance’ is restoring a system after a failure has occurred. A high amount of corrective maintenance must be anticipated due to the complexity of wind turbines. In fact, for onshore turbines, a ‘run to failure’ strategy is often applied because of the existing high technical availability, and ease of access when failure does occur (Barberá et al., 2013). Finally, ‘operations’ consists of day-to-day activities such as monitoring and controlling turbine operations. This is typically supported by a Supervisory Control and Data Acquisition (SCADA) system that allows central control as well as record data to analyse and improve future O&M activities.
Despite operators having access to such data, O&M strategies for wind farms are still in their infancy. While O&M is a minor issue for onshore wind farms, it is a major concern for offshore wind farms. Wind farms located >15km offshore have a 25% inaccessibility factor due to high wind speeds and wave heights (Van Bussel, 1999). Only helicopters are unaffected by high waves but are still grounded at wind speeds >20m/s (Van Bussel & Bierbooms, 2003). Whether a vessel or helicopter is used to access offshore locations, the cost of transit and access are still high compared to onshore locations (Besnard, Fischer, & Tjernberg, 2013). The lower availability combined with higher O&M costs have made offshore wind farms a subject of interest for the scientific community. Much of the earlier work were exploratory studies, focused on understanding existing phenomenon and defining concepts (Hendriks et al., 2000; Krokoszinski, 2003; Van Bussel & Bierbooms, 2003). While these papers established the groundwork, it is in the nature of Operations Research to develop and test new solutions for practical problems. According to Besnard et al. (2011), current research on offshore wind farms O&M can be separated into three interconnected issues: developing suitable maintenance policies, maintenance planning and building a maintenance support organization. The remainder of this section reviews the literature on these relevant O&M issues, examines the concept of resource sharing and presents a conceptual framework that is derived from the literature.
2.1 Developing maintenance policies
In order to develop new theoretical insights and solve the practical needs of wind farm operators, researchers started to develop quantitative models in the mid-2000’s. One of the earliest models was developed by Vittal & Teboul (2005) who illustrated the effects of a stochastic operating environment on a corrective maintenance policy. Research on preventive maintenance would follow, and is split between Time-Based Maintenance (TBM) and Condition-Based Maintenance (CBM). Figure 1 presents an overview of the most modelled turbine components. These components are summarized below:
Figure 1. Turbine components which have been modelled in several papers. Numbers refer to individual studies.
TBM optimisation. In practice, preventive maintenance is triggered by the passage of time, also
known as Time-Based Maintenance (TBM). TBM is based on the recommendation of the turbine supplier. This approach to TBM is applied in the Operations & Maintenance Cost Estimator (OMCE) (Rademakers, Braam, Obdam, & Pieterman, 2009). According to Ding & Tian (2012), not enough models have been developed to optimise TBM. Ding & Tian (2012) optimised TBM by minimizing maintenance cost as a function of the age threshold. In their model cost savings up to almost 50% could be achieved compared to corrective maintenance. For this, they assumed all components follow a Weibull distribution with increasing failure rates (i.e. wear-out pattern). This indicates failures are more likely to occur later in life, suggesting there is an optimal age to perform TBM. However, Andrawus, Watson & Kishk (2007) attempted to optimise TBM based on actual failure data. They analysed failure data of four components using Maximum Likelihood Estimation on the Weibull distribution to determine the shape (𝑘) and scale (λ) parameters. They found that only the main shaft displayed a wear-out pattern (𝑘 > 1). However, the main bearing, gearbox and generator displayed random failure patterns (𝑘 ≈ 1). Hence, age is not a major contributor to component failure, and TBM optimisation is unlikely to be an effective policy. The authors concluded that Condition-Based Maintenance (CBM) could be a more suitable policy due to the random failure pattern.
CBM application. CBM is another type of preventive maintenance where a measurable parameter
signals potential failure (𝑃) before a functional failure (𝐹) occurs (Tsang, 1995). For wind farms the so-called ‘P-F curve’ can be developed based on temperature, vibrations and acoustics produced by the turbine (Ding & Tian, 2012). McMilann & Ault (2007) developed their model using condition data extracted from a SCADA system to determine the deteriorated state. Byon et al. (2011) and Perez, Ntaimo & Ding (2015) used hidden Markov models to reflect inaccurate data availability. These papers demonstrate CBM can outperform TBM. However, all papers assume condition data to be readily available. Yet the real-time application of condition monitoring remains a large challenge for wind farms (Ding & Tian, 2012). The P-F interval should be sufficiently large to provide time to prevent failure. Kusiak & Li (2011) were able to predict potential failure with an acceptable accuracy only 60 minutes before functional failure occurred.
CBM application for offshore wind farms is in its inception, and TBM optimisation has thus far proven
2.2 Planning maintenance operations
The occurrence of unexpected failure can have a severe impact on the turbine downtime resulting in high revenue losses (Besnard et al., 2013). For large components this is particularly challenging as this requires chartering a jack-up vessel. Figure 2 provides an overview of the processes involved in Jack-up operations. These processes are stochastic in nature and can have a significant impact on the downtime. According to a report of The Crown Estate (2014), delays to heavy lift jack-up vessels can arise from:
Chartering: finding a suitable jack-up, negotiating a contract and waiting for the vessel to arrive.
Spare part delivery: long lead time on spare parts since large spare parts are not kept in stock.
Mobilisation: sea fastening (i.e. welding) to prevent spare parts from moving during transit.
Transit time: sea transit to (and from) the wind farm.
Turbine preparation: time taken to undertake site survey and prepare turbine for lifting operation.
Replacement: replacement of large component involving lifting operations.
Demobilisation: removal of the welding and other modifications made during mobilisation.
Figure 2. Overview of jack-up related processes and potential delays (The Crown Estate, 2014)
During these processes, the weather conditions must be considered when planning maintenance. Rough weather can severely limit the accessibility of offshore wind farms, potentially delaying the before mentioned activities until conditions improve (Besnard et al., 2013). In most offshore maintenance operation models the weather conditions play a key role. Weather conditions are generally simplified into two factors: wind speed (𝑚/𝑠) and wave height (𝑚). Each vessel has its own maximum wind and wave threshold. For instance, in the OMCE the crew transfer vessel is assumed to operate up to a wind speed of 12 𝑚/𝑠 and a wave height of maximum 2.0 𝑚. The ‘weather window’ is the time period in which these conditions continuously exist (Rademakers, Braam, Zaaijer, & Van Bussel, 2003).
Due to the weather conditions, Opportunistic Maintenance (OM) is considered the core maintenance tactic for offshore wind farms (El-Thalji, 2012). The opportunistic planning model of Besnard et al. (2011) is an example of OM. In this model, preventive maintenance is expedited to coincide with corrective maintenance in order to minimise the downtime. This tactic is suitable for small components that do not require large weather windows. However, large components require large weather windows. During the autumn and winter, the weather conditions can become so harsh that there are hardly any large weather windows (Van Bussel & Bierbooms, 2003).
2.3 Building a maintenance support organization
Building a maintenance support organization consists out of a number of strategic decisions regarding the location of maintenance facilities, maintenance fleet size and spare part management (Besnard et al., 2013). An asset management approach is applied by considering the total cost involved in these decisions (El-Thalji & Liyanage, 2010). Maintenance support organizations have received reasonable attention in the offshore wind farm literature (Shafiee, 2015b). A number of models exist to minimise the total cost as a function of the model’s decision variables. In these models a trade-off is made, typically between the cost of delay and the cost of maintenance. Besnard et al. (2013) presented a model to optimise small repair maintenance support. Decisions were made regarding the work shift times, the location of the maintenance facilities, the number of maintenance crews and whether to acquire a helicopter. The cost of maintenance was the product of these decisions. The cost of delay was reflected by the energy yield losses (€/MWh) that occurred due to the downtime. A similar study was conducted by Pieterman, Braam, Obdam, Rademarkers & van der Zee (2011) using the OMCE. In this study, the sensitivity of the total cost with regards to the number of crew transfer vessels and the location of the mother vessel was analysed. The trade-off was made on the basis of the total cost of maintenance and the cost of delay.
With regards to the jack-up vessel, such studies have not been conducted because it is presumed that the high Capital Expenditure (CAPEX) of owning a jack-up vessel cannot compensate for the reduction in the cost of delay. Instead, Dalgic, Lazakis, Turan, et al. (2015) investigated the optimum jack-up vessel
leasing strategy. The number of turbines, the charter type and the charter period served as decision
variables. They found that for 100 turbines a short-term ‘time charter’ for a period of 3 weeks is optimal. However, for a 300 turbine wind farm, a long-term ‘bareboat’ charter of 25 years is optimal. During a bareboat charter, the Operational Expenditure (OPEX) is carried by the wind farm operator, including technician salaries. Despite the OPEX, a 30% cost reduction could be achieved by the 300 turbine wind farm compared to the 100 turbine wind farm, primarily due to of the substantially lower charter rate for bareboat chartering. In practice, the jack-up charter rate can account for over 50% of the yearly O&M costs (Van Bussel & Zaaijer, 2001). The authors, therefore, propose that jack-up purchasing can be cost-effective for larger wind farms when there are sufficient turbines to warrant the CAPEX. Furthermore, they suggest investigating the cost benefits of regional collaboration between smaller wind farms as a direction for future research. The aim of this thesis is to address this question through the concept of resource sharing.
2.4 Resource sharing
Resource sharing is a relatively unexplored concept. The handful of papers written on resource sharing typically draws from the related literature on resource pooling. Resource pooling is a method by which demand, that arises from multiple sources, is fulfilled from a single large server instead of multiple smaller servers (Yu, Benjaafar, & Gerchak, 2015). Examples can be found in manufacturing and healthcare literature, where costly resources are pooled into centralized departments (e.g. maintenance shop, radiology department). This is beneficial when demand is random, and would otherwise require departments to invest in additional resources to meet peak demand. By pooling existing resources, peak demand from a single source can be absorbed. In addition, combining demand from multiple sources improves the utilization rate within the centralized department, potentially allowing for resource reduction. There are two key differences between resource pooling and resource sharing. Firstly, the former concerns the pooling of resources within a single firm, while the latter involve the sharing of resources among multiple independent firms. Secondly, the independent firms are often geographically dispersed, and
transit time becomes a relevant variable (Sahba & Balciog̃lu, 2011).
Aside from random demand, there is another requirement for resource sharing; the firms sharing their resources must have homogeneous characteristics (Karsten, Slikker, & Houtum, 2011; Yu et al., 2015). This includes; similar size, lead times and delay costs. According to the authors, if such characteristics are heterogeneous, the sensitivity to a delay will differ among firms leading to a discrepancy in the long run (i.e. some firms benefiting more from resource sharing than other firms).
2.5 Conceptual framework
Based on the literature, the following framework is suggested to organize and approach the problem (figure 3). This framework provides an overview of the key concepts and knowledge on the problem. Within this framework, the performance measures are the dependent variables.
According to the literature, resource sharing can have a positive effect on performance. However, due to the geographically dispersed demand sources (i.e. wind farms), and the mobility of the server (i.e. jack-up), it is expected that the effect of resource sharing on the performance will be mediated through
logistics delay time (i.e. waiting, chartering, mobilisation and transit time). By sharing resources, operators
are no longer dependent on leasing from the spot market, which will eliminate the chartering time and reduce the total logistics delay time. However, additional waiting time will be incurred when vessels are occupied at one wind farm while demand arises from another. Furthermore, by sharing vessels the sea transit time to each individual wind farm will increase. Hence, resource sharing can negatively affect the waiting and transit times. The degree to which this occurs will likely depend on the number of wind farms and distance between wind farms. It is expected that under some configurations, resource sharing will negatively affect the total logistical delay time and thus performance.
Moreover, weather conditions have an impact on performance independently of the introduction of resource sharing. Weather factors are known to have a negative effect on logistics and maintenance delay times, and will adversely affect the system and must be taken into account.
Finally, the effect of a batch repair threshold is considered for the comparison with the leasing policy. Therefore, the batch threshold should be optimised for a fair comparison between the leasing and the resource sharing policies.
Figure 3. The general conceptual framework of the problem
The framework in figure 3 will be applied to answer the main research question:
What is the effect of resource sharing on the performance measures of offshore wind farms?
In addition to the main research question, the following sub-questions have been formulated:
Under what configurations does resource sharing provide the largest cost benefit?
What is the additional benefit or vessel + harbour sharing compared to vessel sharing?
3. M
ETHODOLOGYAs touched upon in the introduction, a quantitative modelling approach is applied to evaluate resource sharing in this thesis. This section further discusses this research methodology and is split into three parts. The first part provides the classification for the research method and justifies the chosen method. The second part discusses appropriate techniques for the research method. Finally, in the third part, the research model is addressed.
3.1 Research method
Meredith et al. (1989) define quantitative model based research as a rational knowledge generation approach. It is based on the assumption that reality can be simplified in objective models that either explains existing behaviour or provide insights in how to behave. The latter is known as normative research. In this line of research, the focus is on developing policies and strategies to find an optimal solution for a defined problem (Bertrand & Fransoo, 2002). This line of research is typically axiomatic in nature, meaning the optimal results hold true within the objective model. However, one should be careful to extrapolate feedback from the model into a scientific claim. According to Betrand & Fransoo (2002), this is a common flaw in modelling. To overcome this problem, this thesis has followed the research model of Sagasti & Mitroff (1973). This model is further addressed in section 3.3.
According to Meredith et al. (1989) axiomatic normative research typically conducted by means of analytical equations. This approach is desired because it generally leads to higher quality scientific results (Bertrand & Fransoo, 2002). However, when a described problem is too complex, it will result in a mathematical model that is too complex to be solved (Law & Kelton, 2007). Within the quantitative modelling approach there is an alternative method: simulation research (see figure 4). Law & Kelton (2007, p. 5) define simulation research as “numerically exercising the model for the inputs in question to see how
they affect the output measures of performance”. The benefit of simulation research over analytical research
is that a simulation model is capable of expressing the variability, interconnectedness and complexity of a described problem, whereas an analytical model forces oversimplification (Robinson, 2003).
Figure 4. Ways to study a problem situation (Law & Kelton, 2007)
Justification. With respect to wind farm modelling, the use of simulation research is justified on the
Classification. Based on the theory discussed in the previous section, the model can be classified as
a dynamic, stochastic, discrete and terminating system (Law & Kelton, 2007). Dynamic, for many of the variables in the model will evolve over time (e.g. weather), opposed to static where time is not relevant.
Stochastic, since the model incorporates random (i.e. probabilistic) components (e.g. failures), opposed to
deterministic where the outcome is identical each time the model is solved. Therefore, the model must be ‘run’ multiple times to determine the distribution of the dependent variables (i.e. performance measurements). Changes in policy must be compared on the basis of these outcome distributions (Meredith et al., 1989). The model is discrete in the sense that the state of the system changes as a result of certain events that can occur randomly in time. An example from wind farm literature being Byon et al. (2011) who applied event-based simulation for their wind farm degradation model. The alternative is continuous simulation as seen in Ding & Tian (2012). Here the state of a system is continuously measured over time. It should be noted that ‘continuous’ does not mean the data is continuously measured. Instead, the size of the duration steps is sufficiently small to simulate a continuous process. Finally, the model is a terminating
system since a wind farm simulation has a defined start (i.e. commissioning) and ending (i.e. end of use).
3.2 Simulation techniques
Based on the classification, an appropriate technique to test the hypotheses is the Monte Carlo
method. This method repeatedly samples from the probability distributions of the dynamic and stochastic
components within the model. Based on the random variates they produce, computations are run through the model yielding random outcomes. The distribution of the outcome provides insight in the likelihood of a favourable outcome. By means of experimentation, it is possible to optimise the outcome and develop new insights (Thomopoulos, 2013).
Spreadsheet simulation. For many simulation problems, separate software products have been
developed such as plant Simulation and ProModel. However, Monte Carlo simulation can also be conducted in a spreadsheet program such as Microsoft Excel (Thomopoulos, 2013). In operations research, the use of spreadsheet calculation is recognized as a valid modelling tool (Brandenburg, Govindan, Sarkis, & Seuring, 2014). Excel is particularly useful for developing solutions to novel problems. However, there is one issue with Excel for the purpose of simulation research. According to McCullough (2008), the built-in random number generator of Microsoft Excel is flawed and insufficient for scientific research. Therefore random numbers will be generated by means of the linear congruent method. This method is presently the common method to generate random numbers on a computer (Thomopoulos, 2013).
Distribution fitting. The first step towards building a scientific simulation model in Excel involves
fitting probability distributions to the sample data of each component. This involves collecting the data and selecting an appropriate continuous distribution (e.g. Normal, Exponential, Lognormal, Gamma, beta, Weibull). Once the data has been fitted, the parameters of each component can be entered into the model. Thereafter, all components must be connected correctly as to simulate the problem description (Robinson, 2003). This is done based on the conceptual model. Once the model is completed it can be ‘run’ by generating random variables on a scale from 0 to 1. By means of the Inverse Transform method the random variable can be inversed into a random variate.
3.3 The research model
the model is not valid, the theoretical solution will not be meaningful in reality. In axiomatic normative research, it is often wrongfully assumed that the scientific model reflects reality because the conceptual model does. The feedback (in the narrow sense) shortcut (i.e. 2 → 3 → 4 → 2) is taken to make scientific claims about reality (Bertrand & Fransoo, 2002).
Figure 5. Quantitative research model based on the work of Sagasti & Mitroff (1973)
The following quantitative modelling approach can be derived from research model:
1. Conceptualization. Sagasti & Mitroff (1973) argue that a conceptual model is more art than science
and can only be checked by its stakeholders. The primary concern is gaining acceptance for the simplifications and assumptions made during conceptualization. There are no strict criteria for evaluating a conceptual model. Instead, the conceptual model should be evaluated in terms of the
scientific model that is derived from it.
2. Modelling. The scientific model is the formal representation of the mental image and reality. The
scientific model is derived by the modelling process. Parallel to the modelling process is the verification process which ensures the model is true to the conceptual model. Verification can be performed by the researcher alone (Robinson, 2003). During the modelling process, the researcher defines the variables in operational terms.
3. Validation. Once a scientific model has been built, the process of validation can start. Validation
considers the degree to which the model corresponds with reality and fits the purpose for which it was build (Bertrand & Fransoo, 2002). According to Robinson (2003), 100% accuracy is not the aim, nor can it ever be achieved. Due to the newness of the policies under evaluation, a statistical output comparison with reality is not possible. Only when the model is judged to be accurate, can scientific claims be made on the basis of the theoretical solutions provided by the scientific model (Landry, Malouin, & Oral, 1983).
4. Simulation. Once sufficient accuracy has been established the scientific model can be applied to the
simulation process. This often is a straightforward process in which the model ‘runs’ and generates output. The optimum theoretical solution can be approached by means of search experimentation (Robinson, 2003). Finally, to judge the quality and efficiency of the solution mechanism (e.g. algorithm, policy) the researcher can experiment with the model inputs (i.e. sensitivity analysis).
5. Implementation. Axiomatic research typically ends with a discussion based on the theoretical results
4. T
HE MODELThis section is structured according to the quantitative research model introduced in the previous section (see figure 5). Section 4.1 addresses the problem description. Section 4.2 discusses the conceptual model, which was conceptualized from the problem description. Based on the conceptual model, a scientific model was developed (section 4.3).
4.1 Problem description
In this thesis, the problem is considered to be a trade-off between the cost of (jack-up) maintenance and cost of (repair) delay. The individual cost of maintenance will decrease as the number of wind farm operators increases. However, the likelihood of operators simultaneously placing demand upon the system increases as well. Resulting in a longer queue and higher delay costs. It is expected that an optimal trade-off exists on the total cost curve. The objective of the model is to evaluate the effects of resource sharing on the total O&M cost by experimenting with various wind farm configurations (i.e. number of wind farms, distance between wind farms). Three policies have been evaluated:
Policy 1: Vessel leasing (VSL)
Policy 2: Vessel sharing (VSS)
Policy 3: Vessel + harbour sharing (VHS)
Under policy 1, the wind farms operate in isolation and it is assumed that the jack-up vessel is leased on the spot market. Hence, the vessels are not shared nor owned by the operators. A vessel would mobilise at Harbour A (𝐻𝐴), transit to Wind Farm A (𝑊𝐹𝐴), perform maintenance and transit back to 𝐻𝐴 for demobilisation (i.e. 𝐻𝐴→ 𝑊𝐹𝐴 → 𝐻𝐴). At Wind Farm B (𝑊𝐹𝐵) similar events would occur independently of 𝑊𝐹𝐴 (see figure 6). This policy is reflective of the real-world practice.
Under policy 2, the operators collaborate by purchasing a jack-up vessel and sharing the vessel between their wind farms. It is expected that VSS can outperform VSL. However, when VSS is applied, the transit time will increase since the vessel must transit between harbours (after demobilizing at 𝐻𝐴 and before the consecutive mobilisation at 𝐻𝐵). In figure 6 this is visualized with two dotted arrows between the harbours to indicate the additional transits. This increases the total number of transits (i.e. 𝐻𝐴→ 𝑊𝐹𝐴→ 𝐻𝐴→ 𝐻𝐵→ 𝑊𝐹𝐵→ 𝐻𝐵→ 𝐻𝐴), which negatively affects the transit time.
Under policy 3, operators share their onshore harbour resources, in addition to the shared jack-up vessel. This allows operators to conduct demobilisation and mobilisation processes at the same harbour, which reduces the mobilisation time. In addition, the number of transits decreases (i.e. 𝐻𝐴→ 𝑊𝐹𝐴 → 𝐻𝐵 → 𝑊𝐹𝐵→ 𝐻𝐴), which positively affects the transit time. In figure 6 this is visualized with four dashed arrows.
4.2 Conceptual model
Robinson (2003, p. 65) defines a conceptual model as “a non-software specific description of the
simulation model that is to be developed, describing the content, inputs, outputs, decision variables, assumptions and simplifications of the model”. Figure 7 provides the conceptual model of the offshore wind farm maintenance operations system. The system is drawn as a cyclical model between four subsystems:
wind farm operations, jack-up mobilisation, sea transit and wind farm maintenance.
Content. The wind farm operations subsystem can be seen as the ‘catalyst’ of the system. This
subsystem logs the availability of the turbines on each wind farm and computes their energy yield. The subsystem also models component failure using failure data. As a series system, failure of one component causes the entire turbine to fail. Once a failure occurs, the component’s failure time is sent to the Jack-up
mobilisation subsystem on the basis of a First-Come-First-Served (FCFS) principle. This subsystem applies
a protocol to determine whether to chart a new up on the spot market, mobilise a charted/owned jack-up or utilize an already mobilized jack-jack-up. The subsystem is simplified by assuming spare parts and repair crews are always available. Once the vessel is mobilized, the departure time is sent to the sea transit
subsystem. This system will determine the transit time based on the location of the jack-up and the
destination, as well as the jack-up’s operating speed. In addition, the subsystem will check with the weather
pattern subsystem if the weather window at that time allows for the transit to occur. If not, then the transit
will be delayed until the weather is favourable. Once the transit is completed, the arrival time is sent to the
wind farm maintenance subsystem. This subsystem will determine the duration of the repair based on the
repair time data. Once more the weather pattern subsystem is checked to see if the weather window allows for the jack-up to operate. If not, then the repair will be delayed until the weather is favourable. Once the repair is completed, the repair time is sent back to the wind farm operations subsystem. This subsystem will calculate the next time when failure for this component occurs, and the cycle repeats.
Figure 7. Conceptual model of the offshore maintenance operations system
Inputs. Input data (i.e. the known information) is split into five categories. Vessel data consists of
Decision variables. The decision whether and when to apply the resource sharing policies developed
in this thesis depends on unknown information. These decision variables can be optimised by running the model multiple times and comparing the effect on the KPI’s (outputs). The following decision variables can be distinguished with regards to resource sharing:
Vessel sharing applied (binary)
Harbour sharing applied (binary)
Number of wind farms (interval)
Number of turbines on each wind farm (interval)
Distance between wind farms (interval)
When vessel sharing is applied it is assumed a jack-up vessel has been purchased. Harbour sharing can only be applied when vessel sharing is applied. The number of wind farms determines the individual cost of maintenance for each operator that is collaborating in jack-up sharing. However, the utilization rate of the jack-up will increase as demand for component replacement arises from more wind farms. Similarly, when the number of turbines increases, the demand from each wind farm increases. Hence, the delay time will increase as the number of wind farms and turbines increase. The durations of these delays are, in part, affected by the distance between wind farms. It is expected that wind farms in closer proximity are more likely to benefit from jack-up sharing.
Outputs. The output measures are broken down in five measurable indicators that are relevant to
the objective of the model. These indicators are often cited within wind farm O&M literature (Byon et al., 2011; Ding & Tian, 2012; McMilan & Ault, 2007; Rademakers et al., 2003). The first indicator is Mean Downtime (MDT), which measures the maintainability of the turbines. Indicators such as ‘number of failures’ and ‘Mean-Time-Between-Failures’ (MTBF) are, by themselves, not considered relevant indicators because the inherent reliability of the components is not the subject of this thesis. Eq. (1) provides mathematical expression of the MDT. 𝐸 denotes the total number of events in the study period.
𝑀𝐷𝑇 =1
𝐸∗ ∑(𝑅𝑒𝑝𝑎𝑖𝑟 𝑡𝑖𝑚𝑒𝑒− 𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑡𝑖𝑚𝑒𝑒)
𝐸
𝑒=1
(1)
The second performance measure is the wind farm availability (𝐴𝑊𝐹), this is the percentage of the time period considered in years (𝑇) a wind farm, as a whole, is available to generate wind energy (Eq. (2)).
𝐴𝑊𝐹𝑇 =
𝑀𝑇𝐵𝐹𝑇
𝑀𝑇𝐵𝐹𝑇+ 𝑀𝐷𝑇𝑇∗ 100%
(2)
The third performance measure is the vessel utilization rate (𝑈𝑅𝑉). This is the percentage of the time period considered that the vessel is being utilized (Eq. (3)).
𝑈𝑅𝑉= 1 𝑇∗ ∑(𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒𝑒− 𝐷𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑡𝑖𝑚𝑒𝑒) 𝐸 𝑒=1 ∗ 100%
(3)
The fourth performance measure is the cost of maintenance (𝐶𝑀). This is the total cost of jack-up leasing (i.e. day rate and chartering cost) and capital and operational expenditure (i.e. CAPEX and OPEX) of owning a jack-up vessel (Eq. (4)). 𝑆𝐶 denotes the actual number of separate charters. 𝐷 denotes the period in which a depreciation expense is allocated in years. Linear depreciation is assumed.
The final performance measure is the cost of delay, expressed as the sum of production losses. Eq. (5) provides mathematical expression. 𝑀𝑊ℎ and 𝐹𝑇ℎ are the megawatts generated per turbine and the
number of failed turbines at hour ℎ, respectively. 𝐻 denotes the total number of hours in the study period.
𝐶𝐷 = ∑(𝑀𝑊ℎ∗ 𝐹𝑇ℎ∗ 𝐸𝑛𝑒𝑟𝑦 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑀𝑊ℎ)
𝐻
ℎ=1
(5)
Assumptions & simplifications. Although the model includes various subsystems, which combined
form a comprehensive picture of a maintenance operations system, a number of simplifications had to be made due to time constraints. The model does not include preventive maintenance. This is considered acceptable because in reality TBM and CBM are often not applied for large components. Secondly, spare parts and maintenance crew management are not considered in the model by assuming both have unlimited availability and no costs. Although spare parts delivery could delay the system, it would occur irrespective of the application of resource sharing. Hence, the impact on the performance is identical for all policies under evaluation. Furthermore, vessels are assumed to travel at a predefined average speed with no variation during transit. Finally, only the replacement of large components is modelled. In reality, most failures are either repairs or replacements of small components. However, this simplification is admissible because repairs and small replacements are performed using work boats, which are not the subject of this thesis. A complete list of the made assumptions can be found in Appendix B.
4.3 Scientific model
After conceptualization, the modelling phase can start. The result of this phase is the scientific model. This section describes the modelling techniques applied in the scientific model. First the weather pattern subsystem is described because the output of this subsystem serves as input for the other subsystems. Thereafter the wind farm operations subsystem is described since this system initiates and enforces the continuous cycle that is the main system. The remaining subsystems are described in logical order: jack-up mobilisation, sea transit and wind farm maintenance (see figure 7).
4.3.1 Modelling the weather pattern subsystem
Weather patterns are difficult to model. The large fluctuations in wind speed are highly dependent on multiple ground and atmospheric conditions (Gavriluta et al., 2012). Similarly, wave heights depend on the ocean floor and wind conditions. Aside from necessitating complex modelling approaches, a large amount of accurate data is required. It is for such reasons that many wind farm O&M models omit a weather subsystem or use deterministic parameters (Besnard et al., 2013). When the wind is only simulated to determine the energy yield, then simple wind power generation models are sufficient (Vallee, Lobry, & Deblecker, 2007). For each time interval these models sample from a fitted probability function. However, this does not result in a realistic weather pattern over time intervals. Therefore, this method is insufficient for the purpose of this thesis. Wind speed and wave height pattern must be modelled with sufficient accuracy to calculate the ‘weather windows’, i.e. the intervals in which weather conditions are expected to be suitable for transit or maintenance (Van Bussel & Bierbooms, 2003). This is input for the Sea Transit and Wind farm maintenance subsystem, where rough weather can delay operations. The remainder of this section described how weather patterns are modelled based on real weather data1.
Wind speed modelling. The wind speed distribution is estimated based on data from the period
01.01.2004 till 31.12.2014. The data was measured at a height of 80 meters, which is approximately the height of a turbine hub. This data is used for the transit and repair weather window calculations. For illustration purposes, data from the years 2009 and 2010 have been plotted as time series in figure 8. Both years follow a similar pattern. Although there is no visible trend (i.e. consistently increasing or decreasing), there is a seasonal component (see also Appendix C, figure C1). As expected, during autumn and winter the likelihood of extreme wind speeds increases, which limits the access to offshore wind farms. Aside from
seasonality, there is a cyclical pattern in the time series (i.e. the wind speed at time X is related to the wind speed at time X-1). This particular characteristic of the wind speed makes it impossible to randomly sample from the data. In order to correctly model the wind speed, it must therefore first be broken down in its components.
Figure 8. Empirical wind speed time series (at turbine hub level)
Firstly, the monthly seasonal factor (𝑆𝑡) is calculated and removed from the data by means of seasonal indices. This is common practice in time series forecasting, as seen in inventory literature (Chopra & Meindl, 2007). A seasonal index is calculated by dividing the average of a particular season by the average of the entire time series. The time series is deseasonalized by dividing each data point by its respective seasonal index, which removes the seasonal factor from the data. Thereafter the deseasonalized data is fitted to a normal distribution, as seen in simple wind power generation models. The normal and Weibull distributions are popular models to characterize the stochastic behaviour of wind speed (Jin, Tian, Huerta, & Piechota, 2012). The normal distribution is fitted using the Maximum Likelihood Estimation (MLE) method (Fisher, 1922). The MLE is a common method by which the optimal fit between sample data and population distribution can be calculated (Andrawus, 2008). The approximation with the normal distribution is provided in figure C2 and C3, giving a wind speed distribution of 𝜇 = 13.7 𝑚 𝑠⁄ with 𝜎 = 4.2. To simulate the wind speed, two random uniform variates (𝑢1, 𝑢2) are generated as seen in Eq. (6). At each point in time (𝑡), a random deseasonalized wind speed (𝑤𝑠𝑡𝑑) is generated from the normal distribution using the Sine-Cosine Method of Box & Muller (1958) as shown in Eq. (7). Figure C4 demonstrates that this method accurately generates random variables.
𝑢~𝑈(0,1) = (𝑢1, 𝑢2)
(6)
𝑤𝑠𝑡𝑑= 𝜇 − {√−2 ln(𝑢
1) cos[2𝜋(𝑢2)]} 𝜎
(7)
Once 𝑤𝑠𝑡𝑑 is generated, the corresponding time period (𝑡) is checked and the seasonal component (𝑆𝑡) is added to the variable. This simulates the process by which wind speeds in winter and autumn are much higher than in the summer and spring. Note that had the data not been deseasonalized, then the data could have been fitted to a Weibull distribution. However, randomly sampling from the Weibull distribution would result in incorrect output (e.g. wind speed peaks from the winter occurring in the summer).
𝑤𝑠𝑡𝑠= 𝛼(𝑤𝑠𝑡−1𝑠 ) + (1 − 𝛼)(𝑤𝑠𝑡𝑑𝑆𝑡)
(8)
The alpha is determined by comparing the simulation model with the empirical data on the basis of the monthly average 𝑤𝑠𝑡𝑠 and the maintenance window. When 𝛼 = 0.1, the output matches the empirical data (i.e. the duration of the weather windows of each season is realistic). Figure C5 and C6 provide visual confirmation, and figure C7 presents examples of a simulated wind speed time series. The wind speed is generated at hub level. To extrapolate the wind speed at a different height level, the power law of Justus and Mikhail (1976) is applied. The power law has been recognized as a useful method to translate wind speed data to different height levels in many papers (Byon et al., 2011; Dalgic, Lazakis, Dinwoodie, et al., 2015). Eq. (9) provides the mathematical formulation of the power law.
𝑤𝑠2/𝑤𝑠1= (ℎ2/ℎ1)0.1
(9)
Here 𝑤𝑠2 denotes the wind speed at the hub level (ℎ2). For sea trips in the sea transit subsystem, as well as the wave height model, the wind speed at sea level (ℎ1) must be extrapolated. Solving Eq. (9) with respect to ℎ1 results in Eq. (10). In the model, Eq. (10) is applied to calculate wind speeds at sea level (𝑤𝑠1).
𝑤𝑠1= ℎ10.1𝑤𝑠2/ℎ20.1
(10)
Wave height modelling. To determine whether an offshore wind farm can be accessed by sea, the
significant wave height is taken as a second indicator. The American National Weather Services (2014, p. 2) defined significant wave height as “the average of the one-third highest wave heights observed at sea”. Waves are created when the wind blows over water and transfers its energy into the water. The wave height depends on the wind speed, duration of the wind and the fetch (i.e. the length of the water over which wind is blown). Historical data1 on significant wave height is applied to model wave heights. Accurately modelling
waves will require data on all these independent variables. However, a correlation analysis between wind speed (𝑤𝑠𝑡𝑠) and wave height (𝑤ℎ𝑡𝑠) produced a very high Pearson Correlation of 𝑟 = 0.71 (𝑝 < 0.01), see figure C8 for more details. In this computational study, the correlation is assumed to be 𝑟 = 1, so wave height could be developed solely on the basis of the wind speed.
In order to correctly model wave height, it is important that the correlation between wind speed and wave height remains. It is not possible to sample from a fitted wave height distribution since there would be no correlation between the random wind speed and random wave height. Instead, the wave height must be modelled based on its direct relationship with the wind speed, represented by the factor beta (𝛽). Only the seasonal factor (𝑆𝑡ℎ) is extrapolated from the wave height data, thereafter the data is disregarded. The seasonal component is added to the procedure to calculate wave height (𝑤ℎ𝑡𝑠), as shown in Eq. (11).
𝑤ℎ𝑡𝑠= (𝑤𝑠𝑡𝑑/ 𝛽)𝑆𝑡ℎ
(11)
The beta is optimised by means of the Minimum Mean Squared Error (MMSE) method with the use of Excel Solver. The Mean Squared Error (MSE) denotes the average of the squares of the differences between an estimator and the estimated value. In this case, the empirical wave data is estimated by means of Eq. (11). When 𝛽 = 3.4, the MSE is minimized. In figure C9 the outcome of Eq. (11), with 𝛽 = 3.4, is compared with the empirical data. Although the empirical data has steeper peaks and valleys, the model is sufficiently accurate with respect to the access criteria of the jack-up vessel.
4.3.2 Modelling the wind farm operations subsystem
is broadly considered to be the most extensive tool for analysing costs and downtime and has received a validation statement from Germanischer Lloyd (Dalgic, Lazakis, Dinwoodie, et al., 2015).
System failure modelling. In wind farm reliability systems there are hundreds of turbines, each
with hundreds of components. Many components survive the 20 years lifecycle of the wind farm, and those that do fail are not known to do so according to a known probability distribution. In the OMCE model, the failure rate of components is therefore assumed to be constant. In this thesis the same assumption is made. The exponential distribution is the only distribution that is characterized as having a constant failure rate (λ). The use of the exponential failure density function is common practice in power system reliability modelling. Several studies have been carried out with the aim of generating generic information on the failure rates of turbine components (Lange, Wilkinson, & Delft, 2010; Spinato, 2008). The failure rates applied in this thesis are generic estimates based on the collective data of ReliaWind2 and WindStats3.
In order to simulate the time to failure, one random uniform variate (𝑢) is generated as seen in Eq. (12). Hereafter, a random Time-To-Failure in years (𝑇𝑇𝐹𝑦) is generated with the inverse of the exponential function as shown in Eq. (13). The ability to generate 𝑇𝑇𝐹𝑦 is central to the functions of the wind farm operations subsystem: initiating the system, generating new events (i.e. component failures) and calculating the energy yield.
𝑢~𝑈(0,1) = (𝑢)
(12)
𝑇𝑇𝐹𝑦= − ln(𝑢)/λ
(13)
Initiating the system. The system is initiated by determining the system start date, system end date
and the list of unique components. The list of unique components is the product of the number of wind farms, the number of turbines per wind farm and the number of components in each turbine (see figure 1). For each unique component, the first failure time is generated as seen in Eq. (14).
𝐹𝑖𝑟𝑠𝑡 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 = 𝑆𝑦𝑠𝑡𝑒𝑚 𝑠𝑡𝑎𝑟𝑡 𝑑𝑎𝑡𝑒 + 𝑇𝑇𝐹𝑦× 365
(14)
The subsystem ranks the list of component failure times in ascending order (First-Come-First-Served). Failure times > system end date are removed from the list as they would needlessly demand computational power. The remaining failure times compose the basis of the event list. The earliest failure time on the list marks the first component failure (event 1). The failure time of event 1 is sent to the Jack-up mobilisation subsystem, this action initiates the main system.
Generating new events. As seen in figure 7, the main system computes the following output times
for each event: 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 → 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 → 𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 → 𝑟𝑒𝑝𝑎𝑖𝑟 𝑡𝑖𝑚𝑒. The time between failure and repair is the Downtime (DT). The DT is affected by the performance of the remaining subsystems discussed in the next sections. The repair time is fed back into the wind farm operations subsystem, completing the cycle. For each unique component that completes the cycle, a new failure time is generated with Eq. (15). This enables a two-state model of component availability depicted in figure 9.
𝑆𝑢𝑏𝑠𝑒𝑞𝑢𝑒𝑛𝑡 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 = 𝑅𝑒𝑝𝑎𝑖𝑟 𝑡𝑖𝑚𝑒 + 𝑇𝑇𝐹𝑦× 365
(15)
2 ReliaWind is an EU consortium with the goal to improve the next generation of wind turbines
Figure 9. A two-state model of turbine availability
Each time a new failure time is generated, the event list is rearranged in accordance with the FCFS principle. This allows for components with high failure rates to fail n number of times before components with a low failure rates fail for the first time. By rearranging the event list in FCFS order after each change in the system, it is possible to operate an event-based simulation in Excel. The system stops generating new events when the failure time > system end date, this action terminates the system. Until then, generated failure times are sent to the jack-up mobilisation subsystem (see 4.3.3).
Energy yield. The final function of the operations subsystem is calculating the energy yield. By
logging the failure and repair times of each turbine, the number of Available Turbines (𝐴𝑇𝑡) and Failed
Turbines (𝐹𝑇𝑡) at time 𝑡, can be computed. 𝐹𝑇𝑡 is applied in the cost of delay, as seen in see Eq. (5). 𝐴𝑇𝑡is
applied to calculate the energy yield by computing the product of 𝐴𝑇𝑡and the power output in megawatt at
time 𝑡 (𝑀𝑊𝑡). 𝑀𝑊𝑡is determined by checking the wind speed (𝑤𝑠𝑡𝑠), generated in section 4.3.1, in the power curve (see figure 10). A turbine with 4.0 Megawatt (MW) power output is considered. The cut-in speed (i.e. the parameter when the wind is strong enough to start power generation) is 4 m/s, and the cut-out speed (i.e. the parameter when the wind is too strong and the turbine is disconnected) is 25 m/s.
Figure 10. Power curve of a 4.0 MW turbine
4.3.3 Modelling the jack-up mobilisation subsystem
Upon receiving the failure time of an event, the Jack-up mobilisation subsystem starts preparing the transit and maintenance of the failed component. The function of this subsystem is to calculate the
departure time of the jack-up vessel. Vessel mobilisation is rarely modelled in wind farm O&M literature.
Mobilisation protocol. Most subsystems consist out of straightforward computations with the
parameters and event times as input. However, the Jack-up mobilisation subsystem includes the decisions variables from section 4.2 and can be visualized as a yes/no flowchart (see Appendix D). The protocol starts when a new failure time is received from the wind farm operations subsystem. A workboat is sent to the failed turbine for inspection to determine the required repair action. If a jack-up is required then the protocol continues to run. If not, then the calculation is aborted as only large component replacements are considered in this thesis.
When vessel sharing is not applied, the protocol will chart, mobilise and utilize vessels from the spot market. When chartering a vessel, a self-imposed delay can be incurred due to the batch repair threshold and seasonal inaccessibility. Whether an additional vessel is charted depends on two factors: the length of the queue, and/or whether it is expected that a repair can be performed within the remaining chart time of an already charted vessel.
In case vessel sharing is applied, then the protocol will mobilise and utilize the owned vessel. It is not possible to lease vessels when vessel sharing is applied. When there are no more components available on the vessel, a return to harbour is required before the vessel can perform its next replacement. The return time is provided by the sea transit subsystem, discussed in the section 4.3.4. Upon returning the harbour the vessel will be mobilized with the components required for the next repairs.
If harbour sharing is applied in addition to vessel sharing, then it is possible to demobilise and mobilise at the same harbour. If not, then an additional transit is needed to demobilise at the harbour of the previous event before transiting to the harbour of the next event for mobilisation. In case no return to harbour is needed, then a mobilized vessel can immediately be utilized. However, waiting time can be incurred if the vessel is currently preoccupied with another repair. All things considered, the protocol can compute the following outcomes:
Chart new jack-up on the spot market
Chart new jack-up on the spot market with self-imposed delay
Mobilize charted/owned jack-up
Mobilize charted/owned jack-up with demobilisation delay
Utilize mobilized jack-up
Utilize mobilized jack-up with waiting time delay
Each outcome has a different calculation for the departure time. Appendix D provides the calculation for each outcome. The departure time is sent to the sea transit subsystem (see 4.3.4).
Chartering time modelling. In this context, chartering time is defined as the time between searching
for a vessel on the spot market and the charted vessel arriving at the harbour. Due to an insufficient number of available jack-up vessels, there is significant uncertainty in the chartering time (Dalgic, Lazakis, Dinwoodie, et al., 2015). This is modelled by means of a triangular distribution, otherwise known as the ‘lack of knowledge’ distribution. This type of distribution is applied when there is no empirical data to estimate the parameters, often expert opinion is obtained to gain estimates for the minimum (𝐶𝑇𝐿𝐿), maximum (𝐶𝑇𝑈𝐿) and most likely (𝐶𝑇𝑚) value (Thomopoulos, 2013). In this thesis the estimates are based on expert opinions using a two rounds Delphi survey (Hsu & Sandford, 2007). In order to simulate the chartering time in hours (𝐶𝑇ℎ), one random uniform variate (𝑢) is generated as seen in Eq. (12). Hereafter, a 𝐶𝑇ℎ is generated from the triangular distribution as shown in Eq. (16).
𝐶𝑇ℎ= 𝐶𝑇𝐿𝐿+ √𝑢(𝐶𝑇𝑈𝐿− 𝐶𝑇𝐿𝐿)(𝐶𝑇𝑚− 𝐶𝑇𝐿𝐿) 𝑓𝑜𝑟 0 < 𝑢 < (𝐶𝑇𝑚− 𝐶𝑇𝐿𝐿)/(𝐶𝑇𝑈𝐿− 𝐶𝑇𝐿𝐿)
𝐶𝑇ℎ= 𝐶𝑇𝑈𝐿− √1 − 𝑢(𝐶𝑇𝑈𝐿− 𝐶𝑇𝐿𝐿)(𝐶𝑇𝑈𝐿− 𝐶𝑇𝑚) 𝑓𝑜𝑟 (𝐶𝑇𝑚− 𝐶𝑇𝐿𝐿)/(𝐶𝑇𝑈𝐿− 𝐶𝑇𝐿𝐿) < 𝑢 < 0
(16)
4.3.4 Modelling the sea transit subsystem
and return time of the vessel. Existing wind farm O&M models model the sea transit as a fixed distance between the wind farm and the harbour (Besnard et al., 2013; Dalgic, Lazakis, Dinwoodie, et al., 2015; Rademakers et al., 2009). As the first of its kind, the maintenance operations system in this thesis considers multiple wind farms and harbours. This allows for the resource to move between locations and simulate the ‘sharing’ of vessels. As such it is possible for a vessel to travel from harbour A to harbour B before the transit to an offshore wind farm, or from wind farm A to wind farm B during a maintenance campaign.
Variable distance calculation. To calculate the variable distance between the departure and arrival
locations of a sea transit, the latitude (𝐿𝑎𝑡) and longitude (𝐿𝑜𝑛) coordinates of each location are employed. It is assumed that vessels can travel the Great-Circle Distance in nautical miles (𝐺𝐶𝐷𝑀), which is the shortest distance between two locations measured along the surface of the earth’s sphere. This distance can be computed using Haversine’s equation (Sinnott, 1984). To measure the distance in nautical miles, a radius (𝑅) of 3440,065 must be inserted in Eq. (17). For each transit to, and from, a location the 𝐺𝐶𝐷𝑀 is calculated based on the current location of the vessel, and its destination. The 𝐺𝐶𝐷𝑀 is divided by the Operating Speed in nautical miles (𝑂𝑆𝑀) of the vessel to compute the Transit Duration in hours (𝑇𝐷ℎ) as seen in Eq. (18). The 𝑇𝐷ℎ is input for the weather delay calculation.
𝑎 = (sin(𝐿𝑎𝑡2𝑡− 𝐿𝑎𝑡1))2+ cos(𝐿𝑎𝑡1) × cos(𝐿𝑎𝑡2) × (sin( 𝐿𝑜𝑛2− 𝐿𝑜𝑛1)/2))2 𝑏 = 2 × tan−1(√𝑎, √(1 − 𝑎)) 𝐺𝐶𝐷𝑀= 𝑅 × 𝑏
(17)
𝑇𝐷ℎ= 𝐺𝐶𝐷𝑀 𝑂𝑆𝑀(18)
Figure 11 illustrates how the application of Haversine’s equation impacts the distances between wind farms. In this example, the furthest distance between wind farms is 604 NM but the distance between other wind farms is shorter. Notably, between the wind farms that are placed between the 50 and 60 𝐿𝑎𝑡 coordinates (e.g. 𝑊𝐹𝐶 to 𝑊𝐹𝐸).
Weather delay calculation. The simulated wind speed and wave height patterns from section 4.3.1.
can now be applied to determine the weather windows. This is achieved by checking the jack-up access criteria4. For each hour in the weather pattern time series, the model determines if access is possible. For
each hour, the cumulative value of ‘hours till rough weather’ is calculated, as visualized in figure 12. This value represents the weather window at any given point in time. At departure time, or repair time (in the case of a return transit), the sea transit subsystem checks the weather window. If the weather window >=
travel duration, then the vessel can depart. Otherwise, the subsystem will look for the next weather window
that is larger or equal to the travel duration. The number of hours until a sufficiently large weather window is noted as the Weather Delay in hours (𝑊𝐷ℎ). For example, in figure 12 the weather window is 6 hours on the 1st of January at 14:00. Consequently, 6 hours later at 20:00 there is rough weather with a wind speed
above the 12 m/s. If a transit is required to take place with a duration >6 hours, then this transit must be delayed until 21:00 (i.e. 𝑊𝐷ℎ= 7) when the wind speed drops below the 12 m/s for the next 11 hours.
4 Jack up wind speed and wave height survivability data is obtained from J-UB (2015)
Figure 12. Transit weather window
The arrival time is calculated by inserting the 𝑇𝐷ℎ and 𝑊𝐷ℎ in eq. (19). In a similar fashion the, return time can be calculated as seen in Eq. (20). The application of the return time has been discussed in the previous section. In the next section, the application of the arrival time is discussed.
𝐴𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 = 𝐷𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 + 𝑇𝐷ℎ+ 𝑊𝐷ℎ
(19)
𝑅𝑒𝑡𝑢𝑟𝑛 𝑡𝑖𝑚𝑒 = 𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 + 𝑇𝐷ℎ+ 𝑊𝐷ℎ
(20)
4.3.5 Modelling the wind farm maintenance subsystem
The wind farm maintenance subsystem is triggered when a vessel’s arrival time is entered. The function of this subsystem is to calculate the repair time of the component. For each type of component the inspection time, preparation time, replacement time and finalisation time is given as a fixed value (see Appendix A). Once a component failure occurs a work boat is sent out to inspect the turbine and determine the cause of failure. The application of the inspection time is discussed in 4.3.3. After it is determined that a jack-up vessel is required, another workboat is sent out to prepare the turbine for component replacement. Replacement of the component cannot start until the preparation is completed. Therefore, the replacement start time is the maximum of the preparation time and the arrival time of the vessel.
Replacement delay calculation. Installation involves the heavy lifting for which a jack-up is
required, and may only be performed during safe working conditions. Therefore replacement start times after 18:00h are delayed until 7:00h. Furthermore, the replacement can be delayed due to rough weather. This is calculated in the same manner as transit delay in section 4.3.4. The Replacement Delay in hours (𝑅𝐷ℎ) are the hours of rough weather before a replacement can commence. The replacement time can be calculated by inserting the before mentioned variables in Eq. (21).
𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 = 𝑚𝑎𝑥 (𝑝𝑟𝑒𝑝. 𝑡𝑖𝑚𝑒, 𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒) + 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 + 𝑅𝐷ℎ
(21)
Repair time calculation. Once a replacement is completed the jack-up vessel can depart for its next
assignment or return to harbour, as in Eq. (20). The workboat will stay behind to perform the final repair stage. Here the installation is finalised, the quality of the repair assessed and the turbine re-commissioned for use, assuming an ‘as good as new’ condition. The repair time is calculated as in Eq. (22). The repair time is sent back to the Wind Farm Operations subsystem, completing a cycle of the main system (see figure 7). The model will continue to calculate cycles until the system end date is reached. Afterwards, the system will calculate the performance measures from section 4.2. The results of the model are presented in the next section.
