Operational Expenditure Modelling of the X-Rotor Offshore Wind turbine concept: Sensitivity of Key Modelling Assumptions

The focus of this paper is operational expenditure modelling of the novel X-Rotor offshore wind turbine concept. The X-Rotor presents significant opportunities for operational expenditure reduction. There are, however, numerous uncertainties associated with modelling of those costs. Namely; failure rates for a novel concept are difficult to quantify, and the design of the concept is still being refined. These uncertainties may be addressed via simple sensitivity analyses. Here, three such sensitivity analyses are presented: one focusing on the main bearing failure rate, one on the generator failure rate, and one exploring the provision of redundancy via the operational strategy of secondary rotors. The main bearing failure rate had a particularly significant impact on operations and maintenance costs, accounting for approximately 22% of costs under baseline assumptions. The generator was less impactful as a cost driver, accounting for approximately 10% of costs under baseline assumptions. Lastly, assuming the X-Rotor could operate at 50% capacity upon failure of one of the secondary rotors decreases the operational expenditure by 8% compared to full turbine unavailability.


Introduction
An exemplary X-Rotor concept (XRC) was presented by Leithead et al. [1], a paper in which they outlined the benefits of the concept.In that presentation of an exemplary concept, they outlined possible design configurations and completed preliminary structural and Operations & Maintenance (O&M) analyses.The same concept is the basis for this analysis.The purpose of the novel concept is to reduce the cost of energy for offshore wind farms, through both reduced Capital Expenditure (CAPEX) and Operational Expenditure (OPEX).The concept is a Vertical-Axis Wind Turbine (VAWT), with two pairs of symmetric aerofoil blades angled in an 'X' shape from the ends of a short cross-arm.Contrary to traditional VAWT concepts, there is no Power Take-Off (PTO) system located within this primary turbine.Rather, PTO is provided by two small secondary Horizontal-Axis Wind Turbines (HAWTs) attached to the two lower blades of the primary turbine.See Leithead et al. [1] for more information.Leithead et al. [1] concluded that the XRC could reduce operational costs by up to 55% and capital costs by up to 32%.Since it was a preliminary feasibility study, a full Levelised Cost of Energy (LCoE) was not calculated.The prominent advantages of the concept are summarised by that paper in four points: (i) Cost of energy reduction.CAPEX costs are achieved via (most significantly) no requirement for a gearbox or multi-pole generator for the secondary HAWT drive-trains.OPEX costs are summarised by an increased reliability and decreased reliance on expensive Jack-Up Vessels (JUVs) -however, more OPEX saving opportunities are listed in subsection 2.1.(ii) Floating platform potential.Achieved via a comparatively low centre of gravity, low centre of thrust and reduced weight.(iii) Upscaling potential.Due to the ability to add additional secondary HAWTs.(iv) High density wind farms.Compared to traditional HAWTs, XRC turbines can be installed in higher density groups while maintaining their efficiency.
This work ties into the broader effort to quantify the savings of point (i).More specifically, the OPEX savings.Some work has previously been completed on this point, and is summarised below.

Operations and Maintenance for the X-Rotor
Beyond the initial feasibility studies, there are two studies relevant to OPEX modelling for the XRC.Firstly, McMorland et al. [2] include the XRC in their review of O&M modelling for novel offshore wind turbine concepts.They highlight several important factors which alter XRC OPEX compared to traditional turbines, namely: (i) Reduced drive train complexity.The XRC contains neither a gearbox or multi-pole generator.These are two of the components that contribute most to downtime and Jack-Up Vessel (JUV) use for offshore turbines [3,4].(ii) Lightweight, low nacelles.In Leithead et al.'s feasibility study, 5MW XRC nacelles weigh 10 tonnes (compared to over 200 tonnes for 5MW for traditional turbines [5,6]) and are located 25m above sea level (compared to around 90m for traditional 5MW turbines [5]).[1].This has the potential to radically alter maintenance strategy via improved accessibility and reduced reliance on JUVs.(iii) Modular secondary HAWTs.As an extension of point (ii), the secondary HAWTs can be designed to be modular.This has the potential to radically alter replacement times of components.If spare modules were kept onshore, faulty modules could be quickly removed, replaced and repaired onshore.This would also increase technician safety standards and decrease the need for training.(iv) Redundancy provision.If one of the secondary HAWTs fail, the X-Rotor can be designed such that the remaining functional HAWT can still produce power by a control strategy based on the remaining power converter.This would provide a measure of redundancy unavailable to conventional turbines.
Flannigan et al. [7] followed up this review study with the first detailed study of OPEX modelling for the XRC.In order to account for the uncertainty associated with estimating failure rates for a novel wind turbine concept, they presented a conservative XRC scenario where failure rates were set to higher-than-expected values.They based failure rates and repair times on Carroll et al.'s reliability analysis of offshore wind turbines [8], increasing the figures by 15% where they thought components may increase for the XRC.Where they thought failure rates would be lower for the XRC, they used the same value as Carroll et al.'s [8].
They covered uncertainty in the XRC design by presenting two scenarios: (i) A Primitive 5MW XRC assumed no modularity of secondary HAWTs.This meant that secondary HAWT components (drive train and hub/rotors) required a JUV for replacements.It also assumed no redundancy provision: if one secondary HAWT fails, the whole turbine becomes non-operational (ii) An Established 5MW XRC, assumed modular secondary HAWTs which could be replaced and repaired onshore, and redundancy provision: when one secondary HAWT fails, the turbine operated at 50% capacity.Note that fixed costs; including warehouse, port and other onshore facility costs are not considered in that analysis.These are assumed to be included in a future LCoE analysis.
The study found that the primitive XRC could reduce OPEX by 29% compared to conventional geared HAWTs, but had higher OPEX costs than direct drive WT concepts.However, the established XRC reduced costs by 45% compared to conventional geared HAWTs and by 22% compared to direct-drive concepts.
This study is an extension of the work previously completed by Flannigan et al. [7].The aim is to explore the sensitivity of their results to modelling assumptions by varying the input parameters, and so explore the uncertainty therein.Such sensitivity analyses are useful as inputs to the design process of the XRC.If, for instance, a reduction in the failure rate of a certain component can be achieved by a degree of over-engineering, a cost-benefit analysis would ideally take place weighing OPEX savings on the one hand and CAPEX increases on the other.
Three sensitivity analyses are explored here -namely focusing on: the main bearing failure rate, the generator failure rate, and the capacity of the remaining secondary HAWT when the other one fails.These factors were pinpointed as key areas of uncertainty for the X-Rotor.For the main bearing, OPEX costs are particularly sensitive to the replacement strategy due to the potential for high JUV costs.One way to get around this would be to install an easy removal mechanism -if the OPEX savings from an easy removal mechanism were greater than the cost of implementation, then that removal mechanism would be justified financially.For the generator, OPEX costs are potentially sensitive because they drive removal and replacement of the secondary HAWT modules.If the OPEX cost savings associated with reducing the generator failure rate outweigh the costs of advanced, robust generator and generator bearing design, it would justify that design.The remaining secondary HAWT operation is a key cost driver in that it could have significant effect in power production.

Methodology
This study defines a baseline similar to the 5MW 'Established X-Rotor' defined by Flannigan et al. [7].The same OPEX model is used.Namely, the StrathOW-OM model developed, validated and frequently utilised at Strathclyde University.It hinges on a central operational simulation, consisting of a series of shifts simulated in the time domain.First, several variables are calculated for the lifetime of the farm based on user inputs at an hourly resolution.Namely: time-series of significant wave height and wind speed, the corresponding ideal power production for the farm, and the probability of a subsystem failure in each time-step.The weather conditions are generated using a correlated, Multivariate Auto-Regressive approach (MAR).A Non-Homogeneous Poisson Process (NHPP) is used in conjunction with a Power Law Process (PLP) to model reliability through time, or a Madsen and Stiesdal lifetime failure distribution which incorporates serial defects can be used in the model.The parameters of the failure model are user inputs.For each time step, the conditional reliability is compared to a randomly generated number to determine if a subsytem has failed.Ideal power production is derived from a user specified power curve, and depends on the simulated wind speed time-series.There is a slight alteration to the original code to allow for one of the secondary HAWTs to remain operational on a turbine where the other has failed.There is an additional clause in the XRC simulations block to allow the turbine to run at half capacity.A 5MW XRC is therefore effectively modelled as 2x2.5MW conventional HAWTs producing exactly half the power of a 5MW HAWT.
The combined user inputs (namely climate time-series, vessel specification fleet configuration, wind farm/turbine specification and cost variables) inform three simulations which feed into the central operational simulation (namely the synthetic climate time-series, accessibility and operability analysis and failure analysis).Separate functions are used to simulate minor and major repairs, which can be addressed either by Crew Transfer Vessels (CTV) or Service Operational Vessels (OSVs), and major replacements, which are addressed by Jack-Up Vessel (JUV).Once the shift is simulated, the model records the condition of the wind farm in terms of turbines available and resources utilised.The process is repeated for the specified lifetime of the farm, and the lifetime power production and availability are calculated and stored.This is repeated until there is convergence of availability estimates on cross-simulation values.For more detail about the model, refer to works by Dinwoodie et al.For more detail about changes to the model required for XRC cost modelling, refer again to Flannigan et al. [7].
The only change to model inputs in this paper is the introduction of a main bearing failure rate.For this we refer to Hart et al.'s [9] figure of 0.015 main bearing replacements a year.Note that Hart et al. cite 2 different figures for main bearing replacements: the larger is selected here to stay consistent with the conservative estimates made by Flannigan et al.There is no extant failure data in the literature for minor repair (mr) and major repair (Mr) rates for main bearings.We follow the distinction of Carroll et al [8] for mr and Mr: failures costing less than A C1,000 and between A C1,000 and A C10,000 to repair respectively.We therefore calculate replacement rate ratios to mr/Mr repair rates for the average component from Carroll et al. [8], and assume the same ratios for the main bearing.Beyond this, several input variables for the model are altered to perform sensitivity analyses.Which input variables are altered, and how, is described in the following subsections.
Note that, in order to have figures comparable to Flannigan et al. [7], the O&M costs presented in this paper are made up of: transport costs, staff costs, repair costs and lost production costs.Fixed costs, including insurance and port fees, will be included in a future LCoE analysis.

Main Bearing Failure Rate
The main bearing presents a particular uncertainty within XRC O&M cost modelling for two reasons: (i) As noted by Hart, et al. [9], main bearing failures are either neglected as a category or lumped in with other components in many prominent and often-cited WT reliability analyses -e.g.(Carroll et al. [8]; Wilkinson et al. [10]; Spinato et al. [11]).Reliability figures are therefore only based on one study [9], and only replacement rates are presented there.(ii) XRC main bearings are in the vertical-axis primary turbine.Their operating conditions and the loads they are subject to differ from conventional HAWT turbines, as might their geometry and weight.Their failure behaviour might therefore differ significantly from those available in the literature.
The OPEX (and the attendant uncertainty in the OPEX) associated with main bearings would be significantly reduced if the need for JUVs was removed.However, any reduction in O&M costs would at least partially be negated by an increased CAPEX, as it would require some removal mechanism for the main bearing which would incur a capital cost.An analysis on the sensitivity of O&M costs to main bearing failure rate would therefore be beneficial to the design process of the XRC.
The sensitivity analysis is undertaken by varying the main bearing failure rate from 0% of 0.015 failures/turbine/year [9] to 250% of that figure.O&M costs for the various main bearing failure rate scenarios are compared to the 'established X-rotor' scenario explored by Flannigan et al. [7].Since Flannigan et al. [7] do not include a main bearing failure rate in their OPEX modelling, they provide a useful measure against which the sensitivity of main bearing failures can be explored.Results are presented in units of "additional main bearing lifetime O&M costs per turbine (MA C)".Essentially this subtracts the total O&M cost derived here from the Established XRC defined by Flannigan et al., and divided the difference by the number of turbines in the farm, giving a cost per turbine.This ensures results are presented in a format that is most applicable to decisions on design of the XRC, such as the inclusion of a main bearing exchange mechanism at the design stage.Errors are estimated by calculating the standard deviation of the monte-carlo simulation (MCS) outputs for vessel costs and overall O&M costs, where appropriate.

Secondary HAWT Operation
The second sensitivity study explores the baseline assumption that, when one of the secondary HAWTs fails, the other remains operational at 50% capacity.Flannigan et al. stress that this is a significant factor in lowering the XRCs OPEX, as it significantly reduces lost production costs [7].They highlight that their established XRC model has approximately 1% higher availability than the primitive XRC and direct-drive scenarios.They also note that 50% capacity is a conservative estimate, as the XRC is expected to have a lower reduction in power yield in below-rated operation [7,1].In fact, initial research indicates that this is also a conservative assumption, and that a lower reduction in power yield can be achieved under all operational conditions.
Based on these considerations, three alternative scenarios are considered: (i) The extra-conservative scenario where a failure in one secondary HAWT leads to 100% turbine unavailability.The XRC will likely not adhere to this assumption, but it is worth quantifying the benefit of redundancy provided by the XRC.(ii) The remaining HAWT operates at 60% capacity.It is more likely that the XRC's control strategy will enable improved performance.(iii) The remaining HAWT operates at 70% capacity.Same logic as point (ii), but more optimistic.
Results are initially presented in units of "difference in lifetime per turbine revenue (MA C)".Overall O&M costs are also considered, in units of A C/MWh.

Generator Failure Rate
The generator failure rate used by Flannigan et al. [7] was equivalent to the failure rate for Permenant-Magnet Synchronous Generator (PMSG) for traditional turbines as presented by Carroll et al. [3].Given there are two PTOs per XRC turbine, this assumption constitutes a generator failure rate of 0.936 failures/per/year.This is roughly equivalent to the failure rate of a Doubly-Fed Induction Generator (DFIG), also presented in [3].
There is an opportunity to reduce this estimate for the XRC.The loads on the generators are expected to be much lower than traditional turbines since they have higher rotational speeds and lower torque.Because they are small (and therefore cheap), there is scope for making the generator and its bearings more robust.It would therefore be beneficial to quantify the O&M savings a reduction in the failure rate would entail.
The sensitivity analysis is undertaken by varying the generator failure rate from 100% of the original figures cited in Carroll et al. [3] to 0%.Again, results are presented in units of "additional generator lifetime O&M costs per turbine (MA C)".All values are therefore relative to the O&M costs for the 0% generator failure rate scenario.

Main Bearing Failure Rate
Figure 1 shows the added O&M costs per turbine due to the inclusion of a main bearing failure rate on top of the assumptions of Flannigan et al. [7].If XRC main bearings were to fail as frequently as conventional HAWTs, there is an additional O&M cost of approximately A C1M per turbine over a 20 year lifetime.The reason for the high cost is that main bearings would become the predominant JUV replacement failure mode.Where Flannigan et al. [7] estimate JUV required failures to total 6 over the farm's lifetime for the rest of the components, the number would increase to 42 for the baseline case study explored in this study.This increases their initial OPEX estimate by approximately 22%. Figure 2 explores the relationship between main bearing failure rate and JUV costs.Where repair costs due to main bearing failures are unavoidable regardless of the existence of a removal mechanism and some lost productions costs would remain, most of the vessel costs could be eliminated.Unlike the plot of figure 1, the relationship of figure 2 is not linear.Rather, as more JUV failures occur, the more can be replaced within the same JUV charter.Based on figures 1 and 2, cost savings of between A C519,000 and A C975,000 per 20-year turbine lifetime could be achieved through an inbuilt main bearing removal mechanism if main bearing failure rates were equal to conventional HAWT turbines.Increasing the XRC main bearing failure rate to 150% of conventional HAWT turbines increases potential savings to between A C722,000 and A C1,457,000 per turbine.At 200%, the potential savings reach between A C835,000 and A C1,874,000 per turbine.At 250%, potential savings reach between A C966,000 and A C2,373,000 per turbine.If main bearing failure rates are decreased to 80% of estimates for conventional HAWTs cost savings of between A C855,000 and A C439,000 per turbine could be achieved.At an optimistic 50% reduction in failure rates, potential cost savings are between A C512,000 and A C290,000 per turbine.

Secondary HAWT Operation
Figure 3 shows the effect of different secondary HAWT operational strategies, as laid out in section 2.2, on revenue.The baseline scenario produces a revenue estimate of approximately A C22.22M per turbine over a 20-year lifetime.The 'Full Turbine Unavailability' scenario, which assumes no redundancy provision, decreases this estimate by around A C350,000 -a drop of around 1.5%.However, figure 5 shows a more significant impact on overall OPEX.If expressed in terms in units of A C/MWh, OPEX costs increase by around 8%.
The operational strategies characterised by additional power extraction operation increase the per turbine revenue estimate by around A C96,000 for the 60% capacity scenario and around A C147,000 for the 70% capacity scenario.In relative terms, the 60% and 70% capacity scenarios produce revenue boost of 0.4% and 0.7% respectively when compared to the baseline.Figure 5 shows a 60-70% capacity upon failure of one HAWT results in a reduction in OPEX similar to a 10-20% reduction in main bearing failure rate.

Generator Failure Rate
Figure 4 shows the added OPEX costs per turbine due to the generators.If XRC generators were to fail as frequently as conventional PMSG HAWTs, there is an additional O&M cost of approximately A C0.5M per turbine.While O&M costs are not as sensitive to generator failure rates as they are to main bearing failure rates, the fact that there are two PTOs per turbine ensures it is still a significant factor.The relationship between generator failure rate and generator O&M costs is approximately linear.This means that, as an approximate guide, a reduction in the failure rate of 10% corresponds to a reduction in OPEX of around A C48,500.For completeness, a linear relationship is assumed to continue beyond 100% of the baseline failure rate in figure 5.In reality, generator failure rates are expected to drop compared to conventional turbines.(i) The baseline estimate for the XRC used here has 27% lower O&M cost than the traditional geared HAWTs.This remains true for main bearing failure rates below twice the baseline value.It also remains true regardless of the assumed 50% capacity when one secondary HAWT fails and for generator failure rates that are twice that of conventional turbines.27% is a decrease on Flannigan et al.'s previous estimate of 45% -this shows how significant an impact the main bearing has on O&M costs.It should also be noted that failure rate estimates for the remaining XRC components (not subject to a sensitivity analysis) are still The baseline OPEX estimate reduces by 4% at 70% capacity and by 2.7% at 60% capacity.Lastly, significant savings can be achieved by lowering the failure rate of the generator.However, the generator failure rate needs to fall by around 30% to make up savings similar to an operational strategy that provides 70% capacity upon failure of one HAWT.

Discussion
This study serves as an investigation of the many uncertainties associated with OPEX modelling for a novel wind turbine concept.The sensitivity analysis approach chosen to do so allows the X-Rotor project to identify which key modelling assumptions can be exploited as possible avenues for cost reduction.Failure rates are arguably the largest epistemic uncertainty for the XRC, given (i) the general lack of existing failure data for offshore wind turbines and (ii) the novel topology of the XRC.Two of the components which are believed to be key cost drivers have been investigated here.Similar studies in the future should focus on other key components.Secondary HAWT blades, for example, may forseeably be subject to both decreased bending moments and increased leading edge erosion.
While the sensitivity analysis methodology presents a method to explore the uncertainty of OPEX estimates due to input factors, it does not make any effort to quantify these uncertainties.Future work would also benefit from an attempt to quanitify uncertainties in component failure rates.Perhaps the most suitable candidate methodology to do so is expert elicitation.Jenkins et al. [12] and Zitrou et al. [13] provide examples of the application of expert elicitation methods to O&M modelling in the wind industry.
Since the XRC design is currently being refined, some insights from the results presented here will feed in to that process.The main bearing has a high impact on OPEX costs for the XRC.The key decision to be made here is whether to include a built-in mechanism for easy removal and replacement of the main bearing in the turbine design.This decision is both (i) complicated by uncertainties surrounding main bearing failure rate and (ii) potentially costly, as potential OPEX savings are of an order of magnitude of 100's of thousands to millions of euros per turbine.Section 3.1 quantified potential savings for different failure rate figures.However, significant uncertainty remains in the modelling of main bearing repairs.Whether the remaining secondary HAWT is operational after one fails has a significant impact on OPEX.Whether it has improved performance is also an important factor.The impact of generator failure rate is significantly less than the main bearing failure rate.Nonetheless, there are still OPEX savings to be had here.Specifically, a 10% reduction in failure rate corresponds to an approximate A C48,500 saving in O&M costs.
Finally, OPEX modelling is one half of the problem -the other is CAPEX modelling.This work therefore feeds into the broader goal of cost of energy modelling for the XRC.The design decisions and uncertainties represented here have more value when they are used for a costbenefit analysis balancing CAPEX and OPEX costs.This is ultimately the next step for the presented work.

Conclusion
This study presents a series of sensitivity analyses exploring key factors for operational expenditure estimates of the X-Rotor concept.It builds on the work of Flannigan et al. [7], using the same operational cost model to obtain results.Baseline model inputs were the same as their 'Established X-Rotor' cost-modelling scenario, with the exception that a main bearing failure rate was introduced.Introducing a conservative failure rate for the main bearing has a significant impact on operational expenditure estimates, increasing the previous estimate by 22%.
The main bearing failure rate is the first subject of three sensitivity analyses.Results show that operational expenditure estimates for the X-Rotor are particularly sensitive to the main bearing failure rate.However, most costs associated with main bearing failures might be avoided by including a rapid removal mechanism and removing the need for jack-up vessels.Main bearing failure rates need to reach around 150% that of conventional turbines before the the X-Rotor has a higher operational expenditure than the modelled traditional geared HAWT concept.It should be noted, however, that there is additional, unexplored uncertainty in repair time and cost inputs for the main bearing.
The second sensitivity analysis focuses on the operational strategy of the X-Rotor when one of the secondary horizontal-axis wind turbines fails.Assuming full-turbine unavailability upon failure of one secondary rotor (as opposed to 50% turbine unavailability) has a significant impact on operational expenditure estimates.In relative terms, it represents an 8% deviation on the baseline estimate.Assuming that secondary rotors have improved performance when one of them fails leads to a reduction in the baseline estimate of between 2.7% and 4%.The assumption of increased performance leads to an extra A C96,000-147,000 per turbine revenue.
The final analysis explored the sensitivity of the generator failure rate.Results showed an approximately linear relationship between the generator failure rate and operational expenditure estimates.As a rough estimate, every 10% reduction in generator failure rate entails a A C 48,500 reduction in operational expenditure.Whether over-engineering of the generator would be worthwhile would depend on the corresponding capital costs.A cost benefit-analysis could be partly facilitated by the results presented in this study.

Figure 1 .
Figure 1.Additional O&M costs per turbine attributable to the main bearing, with respect to the 'Established X-Rotor' scenario defined by Flannigan et al. [7]., after 50 simulations.The error bars represent the standard deviation of the simulation outputs.

Figure 2 .
Figure 2. Additional JUV costs attributable to the main bearing; 50 monte carlo simulations.The error bars represent the standard deviation of the simulation outputs.

Figure 5
places the sensitivity analyses in the context of overall O&M costs.The purposes of this plot are twofold:

Figure 3 .
Figure 3. Mean change in revenue per turbine due to different operational strategies when one secondary HAWT fails; 50 monte-carlo simulations.The error bars represent the standard deviation of the simulation outputs.

Figure 4 .
Figure 4. Added OPEX per turbine attributable to the XRC generators; 50 monte carlo simulations.The error bars represent the standard deviation of the simulation outputs.

Figure 5 .
Figure 5. Plot exploring O&M cost estimated for the XRC under various modelling assumptions (blue lines) with a and geared HAWT concept (green) included for comparison.