Reducing cost uncertainty in the drivetrain design decision with a focus on the operational phase

In order to identify holistically better drivetrain concepts for onshore application, their operational behaviour needs to be considered at an early design phase. In this paper, a validated approach for estimating drivetrain concept-specific risk of unplanned maintenance based on open access data is presented. Uncertain influencing factors are described with distribution functions. This way, the poor data availability in the early design phase can be used to give an indication about the concept’s 10 choice influence on the unplanned operational turbine behaviour. In order to get representative comparisons, Monte Carlo method is applied. This makes it possible to model the life of a fictional wind turbine based on the derived distributions. Technical availability and drivetrain influenced unplanned maintenance effort are defined as evaluation criteria. The latter is constituted by labour, material, and equipment expenses. By calculating the range of fluctuation of the evaluation criteria mean values, this approach offers an indication about the inherent risk in the operational phase induced by the drivetrain concept 15 choice. This approach shows that open access data or expert estimations are sufficient for comparing different drivetrain concepts over the operational phase in an early design stage. The approach is applied on the five most common state-of-theart drivetrain concepts. The comparison shows that the drivetrain concept without a gearbox and with a permanent magnet synchronous generator performs the best in terms of absolute unplanned maintenance effort over the lifetime as well as on the inherent risk. For future research, the influence of the maintenance strategy as well as site and park specific impacts on the 20 unplanned concept behaviour should be included. For adapting this method to new concepts, a physically based approach could be developed which would make it possible to estimate probability distributions for the uncertain factors. Nevertheless, this approach will help to identify holistically better drivetrain concepts by being able to estimate the inherent risks in the operational phase. Freia Harzendorf, Ralf Schelenz, Georg Jacobs https://doi.org/10.5194/wes-2020-37 Preprint. Discussion started: 10 February 2020 c © Author(s) 2020. CC BY 4.0 License.

It is assumed that the entire drivetrain consists of repairable assemblies, which means each assembly can sustain more than one failure and is 'as good as new' after repair or replacement. In reality, repair never reaches the reliability of a new component. Still, this assumption makes it possible to model the life of a fictional wind turbine based on the derived 115 distributions.
A statistical approach, Monte Carlo method, is utilized for deriving representative results as it makes it possible to calculate a multitude of fictional turbine lives. It has the ability to conduct a high number of random experiments based on uncertain influencing variables. Basis for this method is the law of large numbers. It says that, by performing a large number of experiments, the mean of the results will get close to the expected value. This approach is suitable for the present problem as 120 it is constituted by different uncertain factors that can be described by continuous distribution functions. Furthermore, this method offers the possibility to not just get insights on the expected value but also about the results occurrence probability.
Inverse-Transform sampling method is used for generating random numbers with a defined distribution. This way, a sufficient (2) Estimating the drivetrain influenced unplanned maintenance effort (OME [€]) is a bit more complex cf. Formula (2). It is constituted by labour, material and equipment expenses. Labour expenses ( ) is influenced by the uncertain factor duration of repair or replacement as well as the number of technicians ( ) which is failure severity dependent (s) and the wage of a technician ( ). While material expenses ( ) is determined taking the severity of the failure and component specific 135 investment cost into account (m). Furthermore, the component specific weights (we) combined with a crane function (c) account for equipment expenses ( ). Having included component specific mass and cost makes this approach scalable in rated power and rotor diameter. https://doi.org/10.5194/wes-2020-37 Preprint. Discussion started: 10 February 2020 c Author(s) 2020. CC BY 4.0 License.

Model implementation
The following Section gives insights on how the model idea is implemented. Some general assumptions are presented in the 140 beginning before the model procedure is introduced. Failure rate, downtime, failure severity, duration of repair and replacement are modelled as uncertain factors. Collected data about these factors is allocated to the different components and their design.
Design unspecific information is assorted to the component in general. This unspecific information is later considered for all component designs. This allows to make the most out of the available data while not favouring one design or distorting the result. Figure 2 shows an overview of the models structure and the underlying assumptions. Model input are the component 145 design, rated power, and the rotor diameter. One model iteration represents the operational behaviour of a drivetrain from installation until end of its design lifetime.
For every operational year component failure occurrence and failure time are calculated. It is assumed that the components failure behaviour follows a Weibull distribution. This is a common assumption for technical systems. Weibull distribution makes it possible to reveal the main nature of the failure being premature, random, or due to wear out. Weibull parameters for 150 the failure behaviour of the different components are determined based on mean times to failure. Mean time to failure as the reciprocal of failure rates is derived from available failure rates from literature (for sources see Table in Figure 2). Maximum likelihood method is applied for deriving Weibull parameters for mean time to failure. It is assumed that failure rates for the different component designs already consider subsequent faults due to the chosen system. Therefore, components can be modelled independently from each other. 155 In case of a failure, its severity needs to be determined. Referring to Carroll et al., failure severity categorizes failures due to their impact on material cost (Carroll et al., 2014b). It is distinguished between minor repair, major repair, and major replacement. The first row in Table 1 gives the definition of the failure severity types. Failure severity is considered with a uniformly distributed random number and a percentual distribution determined from (Carroll et al., 2015a). Unfortunately, this distribution is deduced from an offshore database. 160 Failure severity affects downtime. Downtime due to minor repair is modelled with a constant value. For major repair and replacement, downtime is assumed to follow a normal distribution. Distribution parameters are derived from literature (compare Table in Figure 2). The accumulated downtime over the drivetrains design lifetime allows now an estimate about the 165 effect of the unplanned drivetrain failures on technical availability (AV).

Uncertain factor Model implementation Source
Failure rate Weibull distribution/Triangulation (Fischer and Wenske, 2015;Fischer et al., 2015;Ozturk et al., 2018;Shafiee and Dinmohammadi, 2014;Ribrant Johan, 2006 Referring to Formula (2) the estimation of O&M effort (OME) is constituted by material, labour, and crane expenses (compare 170 Table 1). Minor repair is repair which leads to material cost up to 1,000 €. In this model material expenses are neglected for minor repair due to their small amount. Major repair is implemented as a random number between 1,000 -10,000 €. According https://doi.org/10.5194/wes-2020-37 Preprint. Discussion started: 10 February 2020 c Author(s) 2020. CC BY 4.0 License.
to Carroll major replacement is a replacement which leads to material cost over 10,000 €. In the model, it is assumed that the entire component needs to be exchanged if this failure type occurs. Material expenses are therefore modelled as the investment cost of the failed component. Component and design specific investment is calculated based on rated power and rotor diameter 175 using the NREL Cost and Scaling Model (Fingersh et al., 2006).

Model validation
The verification and validation are done by comparing modelled values with published data combined with a general reasonability check. In the beginning, the failure behaviour is in the focus. The following components in the following designs 195 are in the scope: moment, trunnion, 3-point and 4-point suspension system, two and three-stage gearbox, permanently magnet synchronous generator (PMSG), electrically excited synchronous generator (EESG) and doubly fed in duction generator (DFIG) as well as partiall and fully rated converter. Initial null hypothesis is that all components failure behaviour can be described by a Weibull distribution. Due to the small sample size, an Anderson-Darling goodness of fit test is conducted. This test is applicable to samples with a minimum size of four. Null hypothesis for a Weibull distribution is not rejected for the two 200 stage gearbox and the three stage gearbox with a three point suspension system, all generator types and the partially rated converter with a five percent significance level. Though they are modelled by a Weibull distribution. The three-stage gearbox with a four-point suspension system follows a log-normal distribution again confirmed by an Anderson-Darling goodness of fit test. For all main bearing arrangement designs as well as the fully rated converter, this test is either not applicable or the null hypothesis is rejected. Therefore, a triangulation is applied. An Anderson-Darling goodness of fit test supports the 205 assumption that components downtime can be described by a normal distribution. Unfortunately, no design specific modelling for downtime is possible due to a lack of data.

210
There are a few publications available in literature where the failure behaviour of different wind turbine drivetrain subassemblies has been empirically evaluated and described by a Weibull distribution. Figure 3 shows the shape factor of the Weibull distribution for different components failure behaviour from literature and modelled. A first look reveals a wide spread in the shape factor in literature not indicating an ambiguous failure behaviour. It needs to be considered that the Weibull shape  Figure 5 gives an overview about the calculated mean drivetrain influenced unplanned maintenance effort over the entire turbines lifetime for 1,000,000 iterations split into the labour, material and crane expenses share. The direct drive concepts (B & C) score best. Mainly due to the reason, that they lack a gearbox. Main source for expenses for the direct drive concepts is 245 the generator. Here the EESG performs worst. Failure rate wise PMSG and EESG seem to be on the same level, this is derived from the same labour expenses level and the Weibull parameters. Still material expenses are higher for the EESG as it is modelled more expensive in the NREL CSM. It is furthermore, heavier than the PMSG resulting in higher crane expenses.
Despite of its higher failure rates, the DFIG results in the lowest unplanned operational effort. Looking into the behaviour of the component converter it is visible, that the converter has a minor influence on the overall expenses. Reason is the low 250 amount of needed replacements which usually lead to high expenses. This is in line with literature which says that converter failures can often be solved remotely or with low effort. No direct influence for the main bearing arrangement on the unplanned operational expenses is calculated. This can be explained by the mean time to failure used for the triangulation which is in the scale of 10 6 years. Looking at the gearbox it is apparent, that this is the componentent responsible for most of the unplanned operational expenditure of the drivetrain. Due to less high rotating components, the two-stage gearbox is more reliable than 255 both three stage versions. Furthermore, the exchange of a two-stage gearbox is less expensive as the gearbox is lighter and has lower investment cost. A distinction between three stage gearbox with a three point and a four-point suspension is discernible.
Due to the non-torque loads entering the gearbox with a three-point suspension system, it is less reliable and leads to higher unplanned operational effort.  case scenario in the early lifetime. Concept E can result in expenses over 300 times the mean yearly value. For better vividness, the plot is cut at a range of fluctuation of 100. It needs to be kept in mind that the failure behaviour for gearboxes is derived from a lot more data points than the behaviour of the other components. This can lead to a higher deviation as more possible applications are covered. A solely technical cause is questionable.

Conclusion
In order to identify holistically better drivetrain concepts for onshore application, its operational behaviour needs to be taken into account in an early design phase. In this paper, a validated approach for estimating drivetrain concept specific risk of unplanned maintenance effort and technical availability based on open access data is presented. By describing uncertain 285 influencing factors with distributions, the poor data availability in literature and in the early design phase can be used to get an indication about the concepts choice influence on the unplanned operational turbine behaviour. This approach furthermore allows to include information about the concept's behaviour from different applications and different sources. If data availability is low, a triangulation can be applied. By using triangulation incremental innovation and completely new concept ideas can be evaluated as well. In order to get representative comparisons Monte Carlo method is applied. This way a multitude 290 of drivetrain lifetimes can be modelled following the distributions behaviour. The most relevant influencing factors are considered by modelling failure rate, downtime, failure severity and duration of repair and replacement as uncertain factors.
Technical availability and drivetrain influenced unplanned maintenance effort are defined as evaluation criteria. The latter is constituted by labour, material and equipment expenses. By calculating the range of fluctuation of the results, this approach offers an indication about the inherent risk in the drivetrain influenced unplanned maintenance effort which is a central 295 criterium. Scalability is given, as material and equipment expenses are scaled with turbine rotor diameter and rated power.
This approach shows that openly accessible data or expert estimations are sufficient for comparing different drivetrain concepts over the operational phase in an early design stage. It shows, that most of the component designs failure behaviour can be described by distributions, mainly Weibull distributions. A component design distinction of state-of-the-art concepts is possible this way. 300 The application of this approach on five state-of-the-art drivetrain concepts for a 3 MW, 120 m rotor diameter turbine shows that direct drive concepts lead to the lowest drivetrain influenced unplanned maintenance effort over the lifetime. Despite of https://doi.org/10.5194/wes-2020-37 Preprint. Discussion started: 10 February 2020 c Author(s) 2020. CC BY 4.0 License.