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Understanding the impact of different probabilistic failure models
on offshore wind farm performance
- The jack-up vessel long-term chartering context -Author
Adrian Tuiu (s2659360)
Student MSc Supply Chain Management Groningen, June 2018
Master’s Thesis
MSc Supply Chain Management (University of Groningen)
Supervisors
Dr. E. Ursavas (First assessor, University of Groningen) Dr. I. Bakir (Second assessor, University of Groningen)
Mr. A. H. Schrotenboer (Academic advisor, University of Groningen)
Abstract
Offshore wind farms have surged in recent years, due to stronger winds and lower design and operating constraints. However, their turbines are more susceptible to component failures, which leads to higher operations and management (O&M) costs and performance unpredictability. Offshore wind O&M models often make assumptions about the failure probabilities of turbine components over time, in the absence of reliable historical failure data. Such assumptions are common in research on main component failures, which generally require the chartering of a jack-up vessel for repairs. We undertake a Monte Carlo simulation study on different approaches to probabilistic main component failure modeling in a jack-up vessel long-term chartering context. Both a single and a collaborative jack-up vessel chartering scenario indicate large differences in multiple performance measures between different failure modes. Consequently, we contribute to research and practice on offshore wind O&M modeling by highlighting the differing impact of the failure modeling approach chosen on offshore wind farm performance.
2 Acknowledgements
This paper marks the end of my journey at the University of Groningen, the most enriching experience I have had to date on the personal, academic and professional levels. I would like to thank Albert Schrotenboer in particular for his support and advice throughout my adventures with this thesis, as well as Ms. Ursavas and Ms. Bakir for their supervision. I would also like to thank all my friends, who have had to bear with me only talking about offshore windmills for the past four months. Lastly, I am grateful to the university for having allowed students to simultaneously open multiple computers on the same student account; I could not have finished my sensitivity analyses on time without you.
Table of Contents
1 Introduction ... 3
2 Literature Review ... 4
2.1 Wind energy O&M practices and optimization ... 5
2.2 Jack-up vessels in offshore wind O&M ... 6
2.3 Weather modeling ... 7
2.4 Offshore wind failure modeling ... 8
3 Methodology ... 9 3.1 Simulation model ... 10 3.1.1 Model Parameters ... 10 3.1.1.1 Primary inputs ... 11 3.1.1.2 Secondary inputs ... 14 3.1.2 Computing subsystems ... 15 3.2 Failure modeling ... 19 4 Numerical Investigation ... 21 4.1 Base scenario ... 21 4.2 Collaborative chartering ... 26 5 Discussion ... 31 6 Conclusion ... 33 References ... 33
Appendix A – Model Parameters ... 38
Appendix B – Assumptions ... 39
Appendix C – Markov chain weather figures ... 40
Appendix D – Confidence intervals for performance measures ... 41
3 1 Introduction
In light of mounting concerns about climate change, dwindling fossil fuel reserves and ongoing environmental damage, numerous renewable energy development projects have been undertaken in recent times, with wind having emerged as a particularly favorable energy source in this sense. The past decade has noticed a substantial surge in offshore wind-farm projects, owing to steadier and higher wind speeds on average (EWEA, 2012), and less design and operating constraints compared to their onshore equivalents (Burton et al., 2001; Esteban et al., 2011; Kaldellis & Kapsali, 2013). Nonetheless, even though offshore wind-farm projects have experienced considerable growth in recent times, they are faced with multiple specific challenges. For instance, operations and maintenance (O&M) costs comprise up to 30% of their overall lifecycle cost, and can become three times higher than onshore, often owing to inherent accessibility complexities and uncertainties (Blanco, 2009; Musial & Ram, 2010).
A substantial part of the O&M costs in offshore wind pertain to main component failures, particularly in reference to the vessel-associated costs (Dinwoodie et al., 2013), such as repair vessel chartering (Dalgic, Lazakis, Turan, et al., 2015a) or lifting operations for component replacements (Van Bussel & Zaaijer, 2001). O&M activities of main components are generally carried out with the use of jack-up vessels or barges. A budding stream of literature has focused on the evaluation of chartering strategies for these costly vessels (Dalgic et al., 2015a; Stålhane et al., 2017; The Crown Estate, 2014). However, one of the crucial assumptions of such studies relates to the modeling of system and component failure rates, often considered to be constant or to follow certain probability distributions presumed beforehand. Because the failure of a component acts as a trigger for the commencement of a maintenance activity (i.e. deploying the vessel), the failure frequency has a direct impact on the outputs of the model (Martin et al., 2016; Scheu et al., 2017). In addition, empirical work has indicated the high impact of turbine failure rates on wind farm availability (Feng et al., 2010). Consequently, results may be influenced substantially by the failure modeling approach. Additionally, little work has critically assessed the incumbent modeling practices in this sense.
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Scheu et al. (2017) investigated offshore wind farm availability rates given different probabilistic component failure models through a simulation study of offshore wind farm O&M. Their findings highlight significant differences in farm availability rates depending on the failure model chosen, indicating potential inconsistencies among probabilistic approaches to failure modeling of wind turbine components. These limitations are all the more important given the lack of publicly available and/or relevant data on historic wind turbine failure rates (Hameed et al., 2011; S. Sheng, 2015; Scheu et al., 2017). Moreover, even studies benefitting from access to large-scale turbine failure rate data have not succeeded in identifying statistical distributions underlying a wind turbine's lifecycle reliability (Carroll et al., 2016; Faulstich et al., 2011). Hence, we build upon Scheu et al.’s (2017) work, by undertaking a critical assessment of jack-up vessel related O&M performance outputs under differing probabilistic failure models. Our study intends to provide further insights into the latter's contested usefulness.
There are thus several reasons for undertaking such a study. Firstly, there are as of yet few studies on jack-up vessel modeling and the incumbent failure modeling practice is to rely on presumed probability distributions or constant rates, which may be subject to the issues mentioned above and should be thoroughly investigated. For instance, the model proposed in this study would allow a better understanding of O&M costs' sensitivities to the failure modeling approach taken. Secondly, understanding the dynamics of different probabilistic failure models within the envisioned O&M system could contribute to the knowledge on methodological approaches to offshore wind O&M modeling and optimization. Lastly, the outputs of the models assessed could be contrasted with real-world data by practitioners, informing on their usefulness and potentially guiding O&M decision-making and financing strategies.
The remainder of the paper is structured as follows. Section 2 introduces the theoretical background in reference to the various perspectives and methodological approaches to O&M optimization in offshore wind and failure modeling. Section 3 provides an in-depth description of the structure, components and mechanisms of the methodology applied in the study. Section 4 is an application of the developed simulation model to two case studies and presents the results.
Section 5 comprises an interpretation of the results and their implications, as well as the limitations
and opportunities for future research. Section 6 concludes this paper.
2 Literature Review
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as costs or turbine availability, through a broad array of methodologies ranging from mathematical models to simulation, accounting to various degrees for the numerous contingencies involved (Shafiee & Sørensen, 2017). We make a distinction between papers focused on the strategic and tactical offshore wind O&M modeling. Whereas the former caters to a long-term vision of O&M and is the main focus of the current paper, the latter generally entails optimization approaches to operational issues facing WF owners and maintenance providers. For more insights into the latter, we refer to the literature reviews of recent papers in this field, such as in Schrotenboer et al. (2018).
2.1 Wind energy O&M practices and optimization
There are multiple facets and modeling approaches to O&M of wind energy assets. Through a comprehensive review of modeling literature on wind energy maintenance and inspection planning, Shafie and Sørensen (2017) develop a classification of papers based on the examined system configuration, decision making attributes, maintenance strategy, optimization modeling and failure modeling. Referring to their work, this study considers the wind farm level of system modeling from the perspective of an offshore wind farm owner/operator, given the often encountered dilemma of identifying the optimal jack-up vessel chartering strategy, in the context of high associated costs (The Crown Estate, 2014; Dalgic et al., 2015a).
Maintenance strategies for WTs generally involve a set of policies and activities to restore equipment to an intended state. In broad terms, WT maintenance practices can be classified into corrective or preventive. The former refers to repair or replacement activities of WT components after a failure has occurred, whereas the latter implies proactive repair or replacement of components in accordance with a predefined rule (i.e. at specific conditions reported by monitoring systems) (Shafiee & Sørensen, 2017). In this paper we focus primarily on corrective maintenance practices, as they are particularly relevant for main component failures requiring the deployment of a jack-up vessel; high mobilization costs and other impediments make the use of jack-up vessels beyond main component failures potentially less practical than the use of other maintenance vehicles, such as helicopters or crew transfer vessels (Dalgic et al., 2015b; Dalgic et al. 2015c). Repair or replacement activities are thus considered when a main component fails, and referred to hereafter as 'repairs' for simplicity reasons.
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component failures would still require the chartering of a jack-up vessel for replacement, the latter being the focus of this paper.
Optimality criteria often encountered in wind energy O&M models are cost minimization, production loss minimization and availability maximization, several different methods having been proposed in this sense (Shafiee & Sørensen, 2017). Even though there may be a high degree of interrelatedness among these objectives, costs are one of the more important considerations in the context of jack-up vessel O&M activities because of high charter rates, potential scarcity of vessels in high demand periods (i.e. April-October) or on-site uncertainties in regards to weather conditions (Dalgic et al., 2015a). In Section 3 we provide further details and reasoning on our choice of methods and we refer the reader to Shaffiee and Sørensen (2017) for an extensive review of the various analytical methods applied in wind energy O&M optimization, along with their advantages and limitations.
2.2 Jack-up vessels in offshore wind O&M
Smaller maintenance vehicles are not generally suitable for repairs of main WT components due to their weight and size. For the purpose of this study, main components refer to turbine blades, gearbox, generator and transformer, which are commonly located at the top of the WT tower for offshore turbines (The Crown Estate, 2014), and are responsible for a majority of WT failures and overall associated downtime (María et al., 2013). Dalgic et al. (2015a) identify three suitable vehicles for offshore O&M activities required by major failures of these components, namely jack-up vessels, leg-stabilized vessels and heavy-lift vessels. Because leg-stabilized vessels are scarce in the wind energy market (EWEA, 2012) and heavy-lift vessels may be prohibitively expensive (DNV, 2014), jack-up vessels are most commonly employed by WF owners and operators for main component failures. Jack-up vessels have a buoyant hull elevated above the sea's surface, with between 3 and 6 legs which can be stationed on the sea bed, providing a stable platform for performing O&M activities (Dalgic et al., 2015a). They can be equipped with a crane for component lifting and repairs, and the large deck space allows for the storage of multiple spare parts and components (The Crown Estate, 2014).
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Pirrong (1993) notes the three most common types of maritime contracts, namely voyage, time and bareboat charters. Of relevance to the long-term chartering perspective considered in our paper is the bareboat charter, which requires the charterer (i.e. WF owner) to accommodate the daily running costs, voyage costs and cargo expenses related to jack-up vessel WT repairs.
Despite the posited comparative cost advantage of a long-term chartering strategy for larger WFs, the vessel utilization may be particularly low in the event few components end up failing within the modeled period. For instance, Dalgic et al. (2015a) indicate a drop from 87.9% vessel utilization for a hypothetical 300 turbine WF for short-term chartering (i.e. 16 weeks) to 43.2% utilization in a long-term chartering strategy. Moreover, the authors conclude that vessel utilization and overall O&M costs may largely depend on the component failure rate considered. Smaller WFs also appear to be more sensitive to a change in charter length. Understanding the model's sensitivity to different failure distributions potentially represents a valuable step in advancing current modeling practice for jack-up vessel maintenance situations and improving the predictability and risk assessment of WF performance.
2.3 Weather modeling
Weather conditions are an important prerequisite of any offshore O&M model, acting as constraints for multiple activities, such as the deployment of a maintenance vehicle to the site for inspection or repair. For this reason, adequately representing weather conditions plays a marked role on the validity and practical applicability of a model. We undergo a brief review of common practices in weather prediction models and their relevance for generating synthetic weather data, which will guide our choice of weather modeling technique.
A vast amount of research has been dedicated to weather prediction modeling in recent decades, methods primarily varying in accordance with the forecast horizon. Long-term weather forecasting (i.e. up to 1 week ahead) is generally carried out through numerical weather predictions (NWP) (Lorenc, 1986; Soman et al., 2010). Because NWP is based upon complex, multivariate mathematical models and vast amounts of data, they are usually carried out on supercomputers, limiting their applicability for generating synthetic weather data for O&M models (Soman et al., 2010). Medium- to long-range weather forecasting (i.e. up to 1 day ahead) may be undertaken by individual or hybrid methods, for instance by combining NWP with machine learning algorithms, such as neural networks (NN), an approach proposed in Sideratos and Hatziargyriou (2007). Lastly, short- to very short-term forecasting (i.e. within 6 hours) is the most extensively researched horizon, with a variety of statistical and hybrid models suggested. Incidentally, similar approaches are generally employed in the generation of synthetic weather time series. For a more in-depth review and classification of the most common techniques, we refer the reader to Soman et al. (2010) and Chang (2014).
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a variable’s observations on its past values (i.e. lags), accounting for the characteristics specific of the respective time series, in order to generate future predictions. The latter categorizes weather conditions under particular states, after which a transition probability matrix is created, indicating the likelihood of a predicted variable changing its state solely depending on a predefined number of prior states. To exemplify their use, Dalgic et al. (2015b) employ an adapted AR model for weather conditions in their study of logistics planning for offshore WFs and Scheu et al. (2017) propose a Markovian process for simulating wave heights in their paper on failure modes and WF availability, both preserving the weather’s persistence characteristics.
The above two methods experience the same shortcomings when applied to generating synthetic time series as in predictive models. More specifically, as the forecast or synthetic horizon increases, there is a higher risk of omitting real-life characteristics of weather data. For instance, Nfaoui et al. (2004) and Shamshad et al. (2005) evidence that, while synthetic series generated through first- or second-order Markov chains succeed in preserving most features of original weather time series, the autocorrelation function differs significantly due to the inherent characteristics of the method. Additionally, Lei et al. (2009) stress the limitations encountered by AR models beyond short-term forecasts in a review of literature on wind forecasting methods. In sum, while the current approaches to stochastic wind series generation are well documented, there are several limitations that must be acknowledged or circumvented for accurate predictions and modeling.
2.4 Offshore wind failure modeling
We have previously indicated that offshore WFs are exposed to different and often harsher environments than their onshore counterparts, with a direct effect on the turbines' reliability. Reliability in this context refers to an item's ability to perform its required function under given conditions for a given time interval (ECS, 2010). Failure rate is a commonly used measure for reliability, expressed as the number of failures for a given item per unit of time (ECS, 2010). For many applications, the failure rate is not constant over time (Finkelstein, 2008) and new concepts in wind energy often present failure mechanisms that are not completely understood (Echavarria et al., 2008). Furthermore, as mentioned earlier, Carroll et al. (2016) have not observed any clear failure patterns in the historic operational data of 350 WTs, two thirds of which having been operating between three and five years and another third above five years. Given the inherent uncertainties behind WT component failures, assumptions are often made regarding their statistical distributions throughout the turbine's lifecycle (Scheu et al., 2017), however some papers have posited potential underlying mechanisms to component failures as we shall see further.
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development of WT component failure rates through a Weibull distribution, in two optimization studies of offshore wind vessel chartering and use. Secondly, the grey-box approach models the deterioration process underlying the failure, implying that i.e. component deterioration can be represented by a mathematical model accounting for the various stochastic processes involved. Besnard (2013) demonstrates a grey-box approach by modeling a WT blade deterioration process through a continuous time stochastic process (i.e. Markov chain). Lastly, the white-box approach models the physical process of the deterioration, by using certain stress factors (i.e. weather conditions) to estimate component deterioration over time. For example, Ramirez (2010) proposes modeling component failure by making use of fracture physics to explain crack development in WT components over time.
A black-box approach to failure modeling is taken in the present paper, in accordance with the research objective to provide an understanding of the sensitivity of O&M performance outputs to different component failure probability distributions. This is all the more relevant given that the incumbent modeling practice in optimizing offshore wind O&M objectives involving jack-up vessels is to attribute a probability distribution to component failure rates which would resemble a bathtub curve (Dalgic et al., 2015a, 2015b). Moreover, publicly available offshore WT reliability data is often marked by inaccuracy, inconsistency and/or incompleteness (Shafiee & Sørensen, 2017). These issues could potentially owe to offshore wind technology being in its infancy, continually changing turbine designs and/or environmental conditions highly specific to the WF site. The statistical uncertainty underlying component failure rates is hence further enhanced; ideally, distributions would be fitted to a dataset of recorded failures and not presumed (Martin et al., 2016; Scheu et al., 2017).
To sum up, there are multiple perspectives and methodological approaches that can be taken in offshore wind O&M optimization. Still, many of the complexities and uncertainties experienced by WFs can be adequately captured in a simulation model, a method which has been previously applied in the study of offshore wind O&M activities requiring jack-up vessels. Given the increasing size of WFs and emergence of collaborative agreements in jack-up vessel chartering, a long-term chartering strategy may become increasingly relevant. However, many of the existing optimization and simulation models in the field rely on a black-box modeling approach, which is subject to high statistical uncertainty given the unavailability of adequate WT reliability data. It is hence relevant to understand the sensitivity of O&M performance outputs related to jack-up vessels to changes in the probabilistic failure modeling approach.
3 Methodology
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timeframe. Secondly, the possibility to account for numerous relevant dynamic contingencies, such as fuel costs or wave heights, aligns the model with similar environmental complexities to those experienced by WF operators. Lastly, the model's outputs may represent highly applicable practical feedback for WF operators.
Moreover, Ding and Tian (2012) argue that analytical (i.e. mathematical) approaches to modeling O&M strategies for offshore wind farms are hindered by the presence of stochastic elements, weather conditions being one such example (Andrawus, 2008; Byon et al., 2011). Dismissing the spatiotemporal variability specific to these random aspects could lead to an oversimplification of the problem under scrutiny. Additionally, several papers have demonstrated the relevance of simulation modeling for offshore O&M activities, Shafiee and Sørensen (2017) having developed a comprehensive list encompassing most recent work in this sense.
Hence, a Monte Carlo simulation model is built, as it can account for the aforementioned requirements. To begin with, the stochastic nature of several of the model’s variables is accommodated by repeated random sampling from their probability distributions (Law, 2015, p. 393). The random values generated serve as inputs to the model’s functions, resulting in random outcomes. After determining the adequate number of times the model has to be run, averaging the resulting outcomes over the number of runs ideally leads to replicable solutions within a specified confidence interval (Law, 2015, p. 497).
3.1 Simulation model
The model specification in terms of elements and logic builds upon the work of Dalgic et al. (2015a; 2015b) and Scheu et al. (2017), which serve as preliminary validation for programming our simulation model. Validation is an important prerequisite to the appropriateness of the scientific model, as well as of its outputs (Landry et al., 1983; Law, 2015, p. 247). An overview of the simulation model’s components and interactions is presented in Figure 3.1 and the timeline of activities relevant to a component’s failure is illustrated in Figure 3.2, for both single- and collaborative-chartering scenarios. The simulation model is adapted from the aforementioned papers, by integrating Scheu et al.’s (2017) failure modeling framework with Dalgic et al.’s (2015a; 2015b) structure and logic framework. The present model is developed with the software Plant Simulation 13.1 (SIEMENS, 2013).
3.1.1 Model Parameters
We differentiate between primary inputs and secondary inputs. The former are obtained from various external sources and incorporated in the model with minimal adaptations, such as the translation of all cost inputs into euros, at a rate of €1.137/£. The latter are derived from the primary inputs and the model’s logic and are subsequently implemented in the model. Several secondary inputs result from the main computation subsystems and feed into the Performance subsystem, thus we highlight those with particularly high impact on the final outputs. We refer the reader to
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Figure 3.1 - Conceptual model Primary Inputs Vessel Costs Specification Farm/Turbine Size Configuration Distances Failure/Repair Failure rates and distributions Repair times and cost
Weather Wind speeds Wave heights
Outputs Secondary Inputs and Computing Subsystems
Simulated Climate Climate subsystem Repair subsystem Performance subsystem Failure subsystem Downtimes Energy Outputs Farm Availability Vessel Utilization Component MTTR Costs 3.1.1.1 Primary inputs Vessel
The vessel inputs take into account various parameters specific to the long-term chartering or purchasing of a jack-up vessel. We distinguish between cost and operational inputs. While the former are used in the Performance subsystem, the latter indicate various mobilization and operational constraints for the vessel in the Repair subsystem. Operational inputs represent constraints and values of relevance to the vessel’s mobilization and repair activities. For instance, the survivability and operability constraints indicate the wind speeds and wave heights under which the vessel may perform said activities (Dalgic et al., 2015; MPI Offshore, 2013). Additionally, the vessel’s travel and jacking speed indicate the duration of mobilization and repair activities in the simulation model.
Regarding vessel costs, firstly, the fuel cost depends on the fuel consumption and utilization of a vessel, for which a distinction is made between idle and operating days, in accordance with Dalgic
et al., (2015a). Secondly,the staff costs refer to the yearly costs of employment for technicians,
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Figure 3.2 - Timeline of a component failure
Mobilization Weather
Delays Batch Repair Preparation (i.e. resupply) Between wind farms TTF 1 Downtime Failure Occurs Wait for batch TTF 2 Turbine is functional Wait for vessel
Wind farm and turbine
The number of turbines considered in a WF positively relates to the number of component failures, which is relevant for the Failure subsystem. Moreover, the turbines' characteristics, such as power curve, hub height and cut-in/cut-out speeds have an impact on the lost energy output, which is of relevance to the Performance subsystem. The power curve in particular is important, as it provides an estimation of the turbine’s power generation capacity for a given wind speed. In the envisioned collaborative chartering scenario, we also include the distances between wind farms and respectively number of turbines in each farm when computing the final outputs.
Failure and repair
Failure rates, the main focus of this paper, refer to the average yearly rates of failure for main components. Component failures are assumed to follow different statistical distributions over time, serving as inputs to the Failure subsystem. The repair times and costs for the four components of interest (i.e. turbine blades, gearbox, generator and transformer) differ as well and are used in the Repair subsystem. There is no evident consensus in past studies on the values for the aforementioned parameters, for which reason the present paper makes use of the failure rate inputs from Carroll et al. (2017) and repair cost inputs from Carroll et al. (2016), given the comprehensiveness and recentness of their assessment. The repair times are sourced from Dalgic et al. (2015a), because unlike most other sources these repair times do not already take into consideration the weather delays. We refer the reader to Section 3.2 for a more in-depth discussion of the Failure subsystem.
Weather
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offshore wind O&M decisions are often characterized by missing data or present difficult to predict stochastic trends, highlighting the importance of developing accurate weather modeling techniques. Capturing the real-life characteristics of metocean conditions in simulation studies is an added challenge, and a broad array of approaches may be found in offshore wind O&M models to tackling this issue. Nonetheless, as we have noted in Section 2, the incumbent modeling practices are at risk of misrepresenting or omitting important underlying characteristics of metocean time series.
The selected weather dataset feeding the Climate subsystem spans approximately ten years of wind
speed and wave height observations between 18.01.2008 and 01.01.2018 in ten-minute resolution1.
Data points are observed to be missing at random throughout the reference time frame and for varying periods of time. Because our main goal when implementing the weather model (see
Section 3.1.1.2) is to preserve as much of the original characteristics of real-life data as possible
(i.e. correlation of wind speeds and wave heights), an imputation approach is developed with the use of Markov chains. In essence, Markov chains represent stochastic processes under which the probability of a discrete event occurring is contingent upon a predefined number of prior states (Karlin & Taylor, 2012). There is strong evidence on the relevance of Markov chains for missing data imputation, such as through Monte Carlo algorithms (Brooks et al., 2011; Gilks et al., 1996; Li, 1988).
Consequently, a first-order Markov chain is applied in our study for wind speed and wave height data imputation, meaning the probability of wind speed/wave height i becoming wind speed/wave
height j is indicated by 𝑝𝑖𝑗. The value of each variable at the subsequent time step is contingent
only on the current wind speed/wave height state. A Markov transition matrix comprises these probabilities and guides the generation of synthetic weather conditions for the missing data points. The matrix has been developed by determining the number of states each variable can take by examining their histograms, after which the frequency with which a state changes into each other state at a subsequent step in time (i.e. hour) determines the transition probability. We refer to states as wind speed/wave height intervals rounded down to the nearest bin, i.e. 1 meter per second for wind speeds and 0.5 meters for wave heights. An example transition matrix is provided in Figure
3.3 and Appendix C contains the histograms of the two variables.
The missing values (i.e. state changes) are obtained through a process of random sampling from a uniform distribution between 0 and 1 and iterative comparison of this number with the cumulated transition probability to each other state, by advancing along the matrix row respective of the current state. The state at which the cumulated probability exceeds the random number (i.e. the matrix column), indicates the weather state for the subsequent hour. This process occurs when filling in data for every missing hour. The first state of the process is the last known (i.e.
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missing) data point in the time series. Table C.1 in Appendix C illustrates the number of states for the two weather variables, their units and the number of imputed data points.
Figure 3.3 – Example Markov chain transition matrix
3.1.1.2 Secondary inputs
Simulated weather
Based on the metocean dataset spanning several years developed in the Weather inputs, a subdivision of ten non-disjointed yearly datasets is created, so as to retain the correlation between wind speeds and wave heights. Subsequently, at the beginning of each simulation year, a uniform distribution randomly samples integers between 1 and 10, the selected number indicating a particular yearly weather dataset having been chosen for representing weather conditions during the respective simulation year. A similar approach to modeling metocean conditions is described in Dalgic et al. (2015a). The sampling procedure ensures the same order of yearly weather datasets for one simulation replication, implying that the weather conditions are identical for different failure modes. This allows for comparing primarily the influence of failure modes on performance outputs, weather inputs being held constant. Additionally, the original correlation between wind speeds and wave heights is preserved to a large extent when using this method.
Of particular importance is the fact that the same yearly weather dataset may be applied in different simulation years and the chronological order between the chosen datasets is not considered, to reflect the stochasticity inherent to metocean conditions. This owes to inconclusive or contradictory evidence in longitudinal studies on metocean conditions trends, for various time frames (Cox & Swail, 2001; Gulev & Hasse, 1999; Thomas et al., 2008; Young et al., 2011). Thus, the chosen weather datasets span ten consecutive years, yet they are randomized throughout the simulation period (i.e. 25 years) in order to reflect the inherent uncertainty in weather conditions on a yearly basis.
Once the weather conditions have been included in the model, wind speeds at turbine hub level (i.e. 100m observation point) need to be extrapolated to wind speeds at sea level in order to determine whether jacking up/down, mobilization and repair activities for component failures are possible. To this end, the wind power law is employed, a commonly encountered method of extrapolating wind speeds to different altitudes (Byon et al., 2011; Dalgic et al., 2015; Fırtın et al., 2011) which can be seen in Equation 1:
15 𝑣 𝑣 = ( ℎ ℎ ) α (1) where v1 is wind speed at a reference height h1 (i.e. hub level), v2 is wind speed at height h2 (i.e.
sea level), and α is the wind shear exponent, encompassing factors which may impact wind speed,
such as temperature, humidity or the nature of the terrain (Manwell et al., 2009). It is generally assumed that α takes a value of 0.1 in an offshore setting (Burton et al., 2001; Fırtın et al., 2011).
Downtimes
The Repair subsystem records various statistics of interest throughout the simulated period, and the downtime of turbines due to a component’s failure is of particular importance for various performance metrics, such as mean time to repair (MTTR) or lost energy output. Downtimes for each failure are calculated as noted in Equation 2:
𝐷𝑇𝑖 = 𝐹𝑆𝑖 − 𝐹𝐸𝑖 (2)
where 𝐷𝑇𝑖 represents the downtime in hours for turbine i, 𝐹𝑆𝑖 is the start of a failure in simulation hours and 𝐹𝐸𝑖 indicates the end of a failure in simulation hours.
Potential energy output
From the yearly weather datasets serving as inputs for each simulation year, the potential energy output at each hour is calculated in reference to the turbine’s power curve. Subsequently, this serves as input for the lost revenue due to a turbine’s downtime in the Performance subsystem. It is assumed that turbine downtime leads to a loss of energy production, which in turn implies lost revenue. Generally, the calculation of a turbine’s energy output is a function of several elements in addition to wind speeds, such as its capacity factor, air density, or area swept by the blades (Burton et al., 2011). However, not only are those aspects outside the scope of this study, but they also would not substantially contribute to the discussion on failure modes, given that the same hypothetical hourly output would be considered for all failure modes within one simulation replication. The potential hourly energy output is calculated as in Equation 3:
𝐸𝑂ℎ𝑤 = 𝐸𝐶
𝑤 (3)
where 𝐸𝑂ℎ𝑤 represents the potential energy output at simulation hour h for wind speed w, and 𝐸𝐶
𝑤
represents the hypothetical energy output in KWh as a function of the turbine’s power curve for a given wind speed.
3.1.2 Computing subsystems
Failure subsystem
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from each of the probability distributions assessed. TTFs are generated independently of each other for each turbine’s components, as is typical of black-box models. Because the turbine is modeled as a series system, a component’s failure is assumed to cause the turbine’s activity to cease immediately until it is repaired, implying also that no other component may fail in the meantime. For this purpose, the turbine’s state at any given time step is defined by a binary variable, which indicates whether it is failed or functioning. Once this state is changed to ‘failed’ due to a component’s failure, the Repair subsystem is triggered and a repair activity may commence. More details about the failure modeling are provided in Section 3.2.
Repair subsystem
Because it would potentially be less effective to mobilize the vessel for single repairs, it is assumed in this paper that a vessel may only leave the port once a threshold of component failures is met. The number of failures that must occur before the jack-up vessel is mobilized are hereafter referred to as ‘batch size’. Once a batch has failed, a request is made for the jack-up vessel’s mobilization to the wind farm to the first turbine to have failed, if it is available, else the batch is added to the list of scheduled repairs on a first-come-first-serve basis. Before mobilization may proceed, wave heights and wind speeds at sea level must be within the survivability constraints as indicated in the Vessel inputs, for the time frame required for mobilization. The vessel waits in the port until these weather conditions are met. Similarly, jacking and repair activities (i.e. inspection, preparation, replacement) may only commence once the respective weather windows meet the operability constraints. These limitations refer to wave heights and wind speed at sea level for jacking and wind speed at hub level for repairs.
It may thus be the case that there is a favorable window for deploying a vessel to the wind farm, but the wind speed at hub level prohibits repairs. Consequently, the vessel waits on-site until weather allows this activity for the duration of a component’s repair. Lastly, at the end of a repair, the vessel’s return to the port or mobilization to another wind farm is constrained by the same weather conditions. Thus, it may only proceed back or to another wind farm once survivability conditions are met.
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Performance
Multiple performance measures commonly encountered in offshore WF O&M literature are assessed in the present study, in papers such as Byon et al. (2011), Ding and Tian (2012), Dalgic et al. (2015a, 2015b, 2015c) and Scheu et al. (2017). Cost measures are assumed to increase by 5% per year, given inflation. In the scenario with collaborative jack-up vessel chartering, distinctions are made between WFs for the relevant performance measures. The first performance measure is yearly WF availability, defined as the percentage of time a farm’s turbines are functional for each simulation year; alternatively, recorded uptime over total possible uptime. Equation 4 indicates how availability is calculated:
𝐴𝑦 = 1
𝑛𝐻(𝑛𝐻 − ∑ 𝐷𝑇𝑖𝑦
𝑛 𝑖=
) × 100 (4)
Where 𝐴𝑦 is a farm’s availability in year y in percentage points, n is the number of turbines in a
WF, H is the total number of hours in a simulation year and 𝐷𝑇𝑖𝑦 is the downtime per turbine i for
year y in simulation hours.
The second performance measure of interest is the jack-up vessel’s yearly utilization, defined as the percentage of time spent in operation (i.e. not idle/in port). By assessing the utilization, we observe whether and how the failure mode influences the vessel’s usage patterns during the simulated period and provide an estimation of the fuel costs. Utilization is calculated as in Equation 5:
𝑈𝑦 =
𝑀𝑇𝑦+ 𝑀𝐷𝑦+ 𝐽𝑇𝑦 + 𝑅𝑇𝑦+ 𝑅𝐷𝑦
𝐻 (5)
Where 𝑈𝑦 is the vessel’s utilization in year y, H is the total number of hours in a simulation year
and 𝑀𝑇𝑦, 𝑀𝐷𝑦, 𝐽𝑇𝑦, 𝑅𝑇𝑦 and 𝑅𝐷𝑦 are respectively: total mobilization time for year y, total mobilization delay for year y, total jacking time for year y, total repair time for year y, and total repair delay for year i. All the aforementioned measures having as unit simulation hours.
MTTR
MTTR represents the average time in simulation hours required for each component’s repair during one simulation run. It is an indication of how effective the system is in managing component failures and is directly affected by the failure mode chosen. It is calculated as follows:
𝑀𝑇𝑇𝑅𝑘 =𝑁𝐹𝐷𝑇𝑘
𝑘 (6)
Where 𝑀𝑇𝑇𝑅𝑘 is the mean time to repair for component k, 𝐷𝑇𝑘 is the total downtime caused by
component k in simulation hours and 𝑁𝐹𝑘 is the number of failures of component k during one
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Fixed costs
In the calculation of the final O&M cost, various fixed yearly costs are considered in two categories: staff costs (i.e. management, technicians, vessel crew) and vessel-related costs (i.e. insurance, port fees). These costs are assumed to increase by 5% per year in accordance with inflation (Dalgic et al., 2015b). Ultimately, the fixed costs do not bear any weight in the comparison of failure modes, given that they are identical across modes, yet they are included in order to create a more accurate depiction of the final O&M costs.
Fuel costs
Fuel costs represent a sizeable proportion of the overall long-term chartering costs, particularly given that the vessel is assumed to consume fuel even while docked (Dalgic et al., 2015a; 2015b). The yearly cumulated fuel costs are generated as follows:
𝐹𝑦 = 𝐷 × 𝐹𝐶 × (𝑈𝑦× 𝐹𝑂 + (1 − 𝑈𝑦) × 𝐹𝑃) + ∑ 𝐹𝑖
𝑦− 𝑖=
(7)
Where 𝐹𝑦 is the cumulated fuel cost in year y, D is the total number of days in a simulation year,
FC is the cost of fuel per metric ton, 𝑈𝑦 is the vessel’s utilization in year y (see Equation 5 for elements), FO is the fuel consumption per operating day in metric tons and FP is the fuel consumption per day in port in metric tons.
Repair costs
Repair costs cumulate similarly to the fuel costs, on a yearly basis. If a component failed towards the end of a year and was not yet repaired by the beginning of the following year, its repair cost is not included in this tally. See Equation 8 for the repair cost calculation:
𝑅𝐶𝑦 = ∑ 𝑁𝐹𝑖𝑦 4 𝑖= × 𝑅𝐶𝑖 + ∑ 𝑅𝐶𝑖 𝑦− 𝑖= (8) Where 𝑅𝐶𝑦 is the total repair cost for the WF at the end of year y, 𝑁𝐹𝑖𝑦 is the total number of
(repaired) failures per component i in year y and 𝑅𝐶𝑖 is the repair cost per component i, assumed
to be fixed.
Revenue loss
19 𝑅𝐿𝑦 = ∑ ∑ 𝑃𝑂𝑗𝑤 𝐹𝐸𝑖 𝑗=𝐹𝑆𝑖 𝐸𝐶 𝑁𝐹𝑦𝑐 𝑖= + ∑ ∑ 𝑃𝑂𝑗𝑤 𝐸𝑦 𝑗=𝐹𝑆𝑖 𝐸𝐶 𝑁𝐹𝑦𝑓 𝑖= + ∑ ∑ 𝑃𝑂𝑗𝑤 𝐹𝐸𝑖 𝑗=𝑆𝑦 𝐸𝐶 𝑈𝐹𝑦𝑐 𝑖= + ∑ ∑ 𝑃𝑂𝑗𝑤 𝐸𝑦 𝑗=𝑆𝑦 𝐸𝐶 𝑈𝐹𝑦𝑓 𝑖= (9)
Where 𝑅𝐿𝑦 is the total revenue loss due to downtimes in a WF in year y, 𝑁𝐹𝑦𝑐 is the number of
failures occurred in year y that end during the same year, 𝑁𝐹𝑦𝑓 is the number of failures occurred in year y that end in a future year, 𝑈𝐹𝑦𝑐 is the number of unrepaired failures from the previous years
which end in year y, 𝑈𝐹𝑦𝑓 is the number of unrepaired failures from the previous years which end
in future years relative to year y, 𝐹𝑆𝑖 and 𝐹𝐸𝑖 are respectively the starting and ending simulation hour of a failure i, 𝑆𝑦 and 𝐸𝑦 are respectively the starting and ending simulation hours of year y, 𝑃𝑂𝑗𝑤 is the hypothetical power output at hour j for a wind speed w and EC is the electricity price.
3.2 Failure modeling
WT component failures are modeled as discrete events occurring during a simulation, by drawing random numbers from the respective probability distributions represented by each of the analyzed failure modes. It may be the case that average failure rates, as well as their distributions, differ among components in accordance with several contingencies, such as the materials from which a component is built or its exposure to corrosive elements (i.e. wind, sea-water). However, while modeling the effects of loading and corrosion on a single rotor blade can be done realistically, incorporating the numerous contingencies specific to an offshore environment in a component degradation model at the WF level may prove significantly more challenging. Given the limited knowledge on the distributions of component failure rates over time, assumptions are be made in this regard. For instance, Lindqvist and Lundin (2010) assume constant failure rates over time and Dalgic et al. (2015a) use those inputs as average values for a Weibull distribution resembling a bath-tub curve in their study on jack-up vessels.
Whether these assumptions carry practical relevance is to be determined by WF operators. Nonetheless, understanding how the overarching model behaves under substantially different approaches to probabilistic failure modeling may be of relevance to WF operators whose data is not reliable enough for such analyses (i.e. small or recently established WFs). Particularly in the case of collaborative chartering (i.e. by multiple WFs) of a jack-up vessel for the long-term, the numerous farm specific aspects may lead to various challenges in designing an appropriate component degradation model. Reliance on probabilistic models would be a simplifying assumption, yet increase computational feasibility. Additionally, little prior work has effectively examined the collaborative vessel chartering option, another intended contribution of this paper.
Representative average failure rates (i.e. number of failures per component, per turbine, per year) and respective repair times of the four main components considered in our study are presented in
Table 3.1 and the failure modes (i.e. statistical distributions) applied to these average values are
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Marshal & Olkin, 2007) and building up Scheu et al.’s (2017) study. The Weibull distribution in particular is used in many reliability contexts, given its flexibility in taking various shapes in accordance with its parameters. The uniform distribution is also included in order to indicate uncertain times to failure. Finally, the fixed failure interval mode serves as a benchmark for the model’s functionality and to illustrate a worst-case scenario for WF reliability. A more in-depth sensitivity analysis of the impact of changes in other variables of interest (i.e. number of turbines, ‘batch’ repair size) on the model outputs is provided in Appendix E.
Table 3.1
Annual failure rates and repair times Component 𝜆 Repair Time (h)
Gearbox 0.154 144
Blades 0.001 24
Transformer 0.001 144
Generator 0.095 72
The six failure modes considered differ significantly with respect to how they determine failures over time. We undertake a brief discussion of three highly different failure modes. For an in-depth explanation of the relevance, functions and parameters of all modes, we refer the reader to Finkelstein (2008). Equations 10, 11 and 12 and 13 note the probability density function (PDF) f(t), cumulative PDF F(t), survival function R(t) and instantaneous hazard (i.e. failure) rate 𝜆 (t) function respectively, for a Weibull distribution. From Equation 13, one can observe how changes in the shape parameter lead to different failure rate values with a change in t, ceteris paribus.
𝑓(𝑡)=βη (t −𝛾 η ) β− ∗ 𝑒−(t−𝛾η ) β (10) 𝐹(𝑡)=1 − 𝑒−(t−𝛾η ) β (11) 𝑅(𝑡)=𝑒−(t−𝛾η ) β (12) 𝜆(𝑡)=𝑅(𝑡)𝑓(𝑡) = β η ( t −𝛾 η ) β− (13)
Where t is a point in time, β is the shape parameter, η the scale parameter and 𝛾 the location parameter of the Weibull probability distribution.
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an acknowledged challenge (Hameed et al., 2011; Robertson et al., 2013). A Weibull distribution
with shape parameter β = 1 becomes an exponential distribution, with constant failure rate over
time. This is indicative of components whose failure depends to a higher degree on contingencies
other than aging. Lastly, a Weibull distribution with shape parameter β > 1 refers to increasing
failure rates over time, implying for example a negative impact of continuous exposure to maritime conditions on a turbine’s reliability.
Table 3.2
Failure modes for generating TTF
# Distribution functions Parameters and notes
1 Weibull 1 Scale: η = 1/λ Shape: β = 0.5
2 Weibull 2 (Exponential) Scale: η = 1/λ Shape: β = 1 3 Weibull 3 (Rayleigh) Scale: η = 1/λ Shape: β = 2
4 Weibull 4 Scale: η = 1/λ Shape: β = 3.6
5 Uniform Lower bound = 0 Upper bound = 2 * 1/λ
6 Fixed interval TTF are generated sequentially at 1/λ 4 Numerical Investigation
In order to increase the validity of the final results, each experimental setting (i.e. failure mode) is run 100 times for each scenario, accounting to a large extent for the model’s numerous stochastic components. The sensitivity analyses in Appendix E are similarly based upon 100 runs, assessing the impact of changes in batch size, farm size, distance to port, repair times and failure rates on the performance measures of interest. Appendix D presents the confidence intervals for each of the performance measures for the two scenarios to be discussed, calculated in accordance with and as suggested in Robinson (2003, p. 154). The confidence interval is calculated as in Equation 14.
𝐶𝐼 = 𝑋 ± 𝑡𝑛− ,𝛼 ⁄
𝑆
√𝑛 (14)
Where CI is the confidence interval in terms of lower confidence limit (LCL) and upper confidence limit (UCL), 𝑋 is the replication sample mean, 𝑡𝑛− ,𝛼 ⁄ is the critical value of a student
t-distribution with n-1 degrees of freedom and significance 𝛼 2⁄ , S is the standard deviation of the
replication sample and n is the number of replications.
4.1 Base scenario
Under the base scenario, a hypothetical 150 turbine WF is considered to be the long-term charterer of a jack-up vessel. The parameters under which this model is evaluated are presented in Appendix
A. The distance between the port at which the long term chartered jack-up vessel is generally
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weather constraints, these repairs are undertaken and the vessel returns to port for resupply and preparation activities for a subsequent trip.
Figure 4.1 – Farm availability, base scenario (%)
Figure 4.1 illustrates the yearly farm availability in percentage for different failure modes, their
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Figure 4.2 – Jack-up vessel utilization, base scenario (%)
Figure 4.2 depicts the utilization levels of the jack-up vessel on a yearly basis, which is a much
more accurate reflection of the failure rates implied by each failure mode over time. For instance, failure mode 1 suggests decreasing failure rates, which can be noticed in the graph after an initial period of high utilization. Failure mode 2, the exponential distribution, proposes constant failure rates, evidenced by the green line. Failure modes 3 and 4 indicate an increasing trend over time, as would be expected from Weibull distributions with shape parameters larger than 1. The steepness of the curves is also a reflection of the shape parameter’s value. Failure mode 5, the uniform distribution, does not reflect a trend in particular, which is supportive of the reliability uncertainty paradigm. Lastly, the fixed failure intervals mode once more results in sharp peaks with short periods of high utilization followed by swift declines until the next event with concomitant failures. This graph evidences much better the need for accurate failure modeling, given that the vessel’s utilization is a direct determinant of scheduling decisions and various expenditures, such as fuel costs.
Table 4.1 comprises the mean time to repair (MTTR) for each component and failure mode
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take particular note of the gearbox MTTR, as it is the component with the highest average failure rate according to past studies. It can be seen that failure mode 2, with constant failure rates over time, has the lowest MTTR, which may owe to shorter waiting times between failures and higher predictability for the commencement of O&M activities.
Table 4.1
MTTR per component and failure mode, base scenario (h)
Component Weibull 1 Exponential Rayleigh Weibull 4 Uniform Fixed
GearboxMTTR 2713 782 866 920 812 14854
BladesMTTR 2938 617 777 - 716 -
TransformerMTTR 3114 774 1178 - 753 -
GeneratorMTTR 2743 708 800 838 739 14289
Figure 4.3 – Breakdown of Gearbox MTTR, base scenario
For a more thorough investigation of the large differences in MTTR, we undertook a breakdown of the measure in its 10 main elements, as seen in Figure 4.3. The analysis refers solely to the gearbox, for ease of reporting, yet similar results were observed for the other components. It becomes immediately evident that, for all failure modes, the largest percentage of MTTR owes to ‘waiting for a vessel’ to become available, more so for failure mode 1. In reality, with more contingencies causing vessel delays than included in the current model, such as maintenance or dry-docking (Dalgic et al., 2015a), the ‘wait for vessel’ times may be even larger. Figure 4.3 could be the subject of an extensive analysis in itself, yet for simplicity reasons, we only stress once more the relevance of system congestion and dependence on the vessel for timely repairs. It appears to be the case that the vessel’s activities and tasks are not executed rapidly enough for the inflow of failures created by all failure modes.
25 Figure 4.4 – Fuel cost, base scenario (€)
Figure 4.5 – Repair cost, base scenario (€)
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MTTR noticed for failure mode 1 in Table 4.1 also carries a more substantial impact on the lost revenue due to turbine downtime. Relatively large differences can be noticed between the total O&M cost figures in Table 4.2, stressing the relevance of modeling appropriate failure modes in longitudinal cost estimates.
Figure 4.6 – Lost revenue, base scenario (€)
Table 4.2
Total O&M costs, base scenario (mil €)
Weibull 1 Exponential Rayleigh Weibull 4 Uniform Fixed
Total Cost 842.00 823.83 914.05 896.61 801.49 4824.55
4.2 Collaborative chartering
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Nonetheless, we do make a distinction for average availability rates and total costs between the three farms, in order to provide a visualization of each failure mode’s individual impact. The vessel costs (i.e. staff, fixed, fuel) are divided among the three wind farms in accordance with the number of turbines they contain.
Figure 4.7 – Farm availability, collaborative chartering scenario (%)
Figure 4.7 indicates similar availability rates across all farms for all failure modes, with the
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picture of the relevance of failure modeling for estimating the jack-up vessel’s utilization in a collaborative chartering context; with peaks of over 80% for failure modes 2 and 3 and over 90% for failure mode 1, the susceptibility of the farms to prolonged downtimes in case of unexpected catastrophic events is increased. The shapes of the utilization curves also differ to a large extent, which could lead to high scheduling uncertainties in real situations if the failure mode chosen in an O&M model is inadequate. Additionally, these curves reflect the expected shapes of the failure rates over time in accordance with each failure mode.
Figure 4.8 – Jack-up vessel utilization, collaborative chartering scenario (%)
Table 4.3
MTTR per component and failure mode, (h)
Component Weibull 1 Exponential Rayleigh Weibull 4 Uniform Fixed GearboxMTTR 3,666 866 1,027 1,146 887 17,620 BladesMTTR 4,145 544 415 - 412 - TransformerMTTR 4,223 592 391 - 466 - GeneratorMTTR 3,671 790 972 1,101 816 14,012
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Figure 4.9 – Breakdown of Gearbox MTTR, collaborative chartering scenario
Figure 4.10 – Fuel cost, collaborative chartering scenario (€)
The greatest proportion of gearbox MTTR is once more taken by the waiting times for the vessel to become available, to an even larger extent than in the base scenario. It could thus be said that, even when the vessel is readily available in a proximal port to the chartering wind farms for their whole lifespan, it may still be insufficient for catering to component failures in a timely manner.
Figure 4.9 also evidences that the distribution of elements in the MTTR differs vastly between the
different failure modes, failure mode 5 (uniform distribution) proposing the lowest waiting for vessel times, and relatively equal waiting times for other repairs (i.e. within a mobilization trip for one batch of failures) and for a batch to become available (i.e. before vessel mobilization). On the other hand, failure mode 1 estimates that components wait for the vessel to become available for
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the most part, with repair times or weather delays mattering very little in the picture of the overall MTTR. However, the latter could well be the cause of the long waiting for vessel times.
Figure 4.11 – Repair cost, collaborative chartering scenario (€)
The cumulative variable cost estimates, as seen in Figures 4.10, 4.11 and 4.12 exhibit trends corresponding to the base scenario. More specifically, failure modes 2, 3, 4 and 5 suggest stable increases in fuel and repair costs, as well as lost revenues, throughout the farms’ lifetime. On the other hand, failure mode 1 results in larger fuel and repair costs in the early years, yet indicates final costs lower by approximately €30 million and €100 million for the former and respectively the latter measures, in comparison to the other modes. However, these differences are offset by the
lost revenues, failure mode 1 once more overtaking the others by the 25th year of operation in this
respect. As far as total O&M costs go, we observe in Table 4.4 a slight convergence for failure modes 1, 3 and 4, which is all the more insightful given that they represent different failure rates over time. Still, while failure modes 2 and 5 provide relatively similar total cost estimates, they are approximately €100 million lower than for modes 1, 3 and 4. In reference to the distribution of total costs across the three wind farms, it can be said that it is relatively proportional the farm’s size and with larger differences across failure modes as the farm size increases.
Table 4.4
Total O&M costs, collaborative chartering scenario (mil €)
31
Figure 4.12 – Lost revenue, collaborative chartering scenario (€)
5 Discussion
In reference to the base scenario, there is a noticeable impact of the failure mode chosen on the longitudinal progression of certain performance measures. As would be expected, failure modes positing a higher number of failures early on in a turbine’s life result in lower farm availability and higher vessel utilization values in early years and vice versa for those with increasing failure rates. Similarly, variable cost measures reflect to a great extent the failure rate progression of each failure mode over time. In regard to the MTTR, we could see differences of up to 60 hours between most failure modes, and even higher between failure mode 1 and the rest. These differences are indicative of the system’s sensitivity to congestion; more simultaneous failures imply longer queues, higher vessel utilization and susceptibility to weather delays and ultimately higher MTTR. This translates into larger total O&M costs due to lost revenues, resulting in differences of over €50 million between certain failure modes. As such, the importance of accurate failure modeling is highlighted for proper lifetime performance estimations.
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by the large waiting times for the vessel, and this composition significantly differed across failure modes. However, total costs figures were relatively similar for failure modes 1, 3 and 4, which are opposing in nature; the former implies decreasing failure rates, whereas the latter two posit increasing rates. As a consequence, it can be concluded that if total lifetime O&M costs are the main aspect of interest in a similar collaborative chartering analysis, the estimates may be relatively insensitive to the failure modeling approach. Still, the other performance measures are affected to a larger extent and are more susceptible to variability in such models, depending on the failure modeling approach.
There are several contributions put forward from both the scientific and managerial points of view. Firstly, we contribute to offshore wind O&M literature by demonstrating the impact of different probabilistic failure models on various industry-specific performance measures within the scarcely studied, yet highly relevant field of jack-up vessel O&M. Secondly, we develop a numerical analysis of these failure modes within single- and multi-farm long-term chartering contexts, potentially assisting practitioners in O&M decision making processes. Thirdly, we evidence the crucial role of jack-up vessels in MTTR for all components, as well as other performance measures, given that they depend to a large extent on the vessel being available, even in a long-term chartering context. Lastly, the simulation model itself represents a valuable contribution to offshore wind O&M literature and practice, given its scalability and adaptability to a wide array of problems. Within the current framework, several different scenarios can be assessed and more contingencies may be added with ease, facilitating the modeling of future events by wind farm owners. For instance, the outputs of the collaborative chartering scenarios could serve as supporting evidence for the feasibility of such agreements.
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While simulation should by no means aim to fully replicate real-life conditions, it is important that the most important characteristics of the developed model are accurately depicted.
All things considered, there are abounding opportunities for further improvements within the jack-up vessel study framework. For one, the evaluation of grey- or white-box failure models in relation to black-box models would represent a solid addition to the debate on offshore O&M failure modeling. The vessel sharing framework could also be expanded and evaluated for other potential real-life collaborative chartering agreements, given the current model’s modularity and scalability. Additionally, the representation of a condition monitoring system within the present model would create a much more accurate depiction of the future of offshore wind O&M, given the increasing prevalence of such systems in new farms. Lastly, an interesting opportunity for an optimization study lies in identifying the optimal number of repairs for which a vessel should be deployed, as well as their sequence; there are numerous tradeoffs in this context, such as having to choose between extended downtime for larger batches and higher mobilization costs for smaller ones.
6 Conclusion
In this paper, a first attempt was made at understanding the impact of different approaches to probabilistic failure modeling on jack-up vessel-related O&M activities. There have been abounding calls in literature for improving the quality of reliability estimations for offshore wind farms. However, little work has been undertaken towards understanding how exactly different failure modes impact performance outputs in offshore wind modeling. This paper evidences the differing impact of black-box failure modes on main component replacement activities and related performance outputs. Consequently, new insights have been developed in this sense, further stressing the importance of more accurate reliability estimations for predicting future wind farm performance.
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