My title https://doi.org/10.14311/APP.2022.36.0090 Acta Polytechnica CTU Proceedings 36:90–98, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague INFLUENCE OF THE STRUCTURAL INTEGRITY MANAGEMENT ON THE LEVELIZED COST OF ENERGY OF OFFSHORE WIND: A PARAMETRIC SENSITIVITY ANALYSIS Marko Kinnea, ∗, Muhammad Farhana, Ronald Schneidera, Sebastian Thönsa, b a Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany b Lund University, Faculty of Engineering, Division of Structural Engineering, Department of Building & Environmental Technology, Faculty of Engineering, Box 118, 221 00 Lund, Sweden ∗ corresponding author: marko.kinne@bam.de Abstract. The levelized cost of energy (LCoE) is an important measure to quantify the macro-economic efficiency of an offshore wind farm and to enable a quantitative comparison with other types of energy production. The costs of the structural integrity management - which is required to ensure an adequate lifetime reliability of the turbine support structures - are part of the operational expenditures of an offshore wind farm. An optimization of the structural integrity management may reduce the operational expenditures and consequently the LCoE. However, the effect of the structural integrity management on the LCoE is hardly known. To investigate this effect, this paper presents a sensitivity analysis of the LCoE of a generic offshore wind farm. The probabilistic models of the parameters influencing the LCoE are based on a literature study including an explicit model for the structural integrity management. The analysis reveals that LCoE may potentially be reduced if an optimization of the structural integrity management enables a service life extension. Keywords: Levelized cost of energy, sensitivity analysis, structural integrity management. 1. Introduction In the context of the energy transition in Germany and the European Union, the relevance of renewable energy is steadily increasing in contrast to conven- tional energy sources such as coal-fired power plants. Besides hydropower and solar energy, offshore and onshore wind energy is becoming a major part of re- newables energies and is likely to be expanded in the future. Over the past 20 years, the total number of wind turbines increases from 9400 to 29600 in Germany, whereof 1500 wind turbines with a total capacity of 7.7 GW are currently installed offshore [1, 2]. According to the EU strategy presented by the EU Commission in 2020, €800 billion will be invested in offshore re- newable energy over the next 30 years to increase the capacity of offshore wind energy from 12 GW to 60 GW by 2030 with an aim to reach a total capacity of 300 GW by 2050 [3]. In addition to the investments in the expansion of renewable energy, however, the efficiency of renewable energy sources measured in terms of the levelized cost of energy (LCoE) must also be considered to ensure that these energy sources are competitive. As an example, in 2018 the LCoE of offshore wind energy in Germany was still higher than the LCoE of other main energy carrier such as brown coal [4]. Besides the reduction of the investment costs and the increase of the power production, wind farm operators optimize structural integrity management (SIM) procedures to reduce the LCoE. Such optimiza- tions are constrained by different rules and standards (e.g. requirements set out in Germany by the Bunde- samt für Seeschifffahrt und Hydrographie (BSH) or in United Kingdom by the Department for Business, Energy & Industrial Strategy and the Marine Manage- ment Organisation). The challenge is to optimize the operation of an offshore wind farm including the SIM in compliance with the governing rules and standards. In the existing literature, the overall costs related to the SIM are low in contrast to other costs such as the investment costs and the costs related to the turbine integrity management [5, 6]. Based on this information, the question is whether it is worthwhile to optimize the SIM for the support structures in an offshore wind farm to reduce the LCoE. In this paper, a sensitivity analysis is performed to quantify the influence of the SIM on the LCoE of a generic offshore wind farm and to investigate the op- portunity of upgrading/optimizing the SIM to reduce the LCoE (i.e., an optimization of the inspection and maintenance strategy as well as monitoring systems). To investigate the influence of the SIM on the LCoE, the operational expenditures are divided in a part related to the structures and a part related to the tur- bines. The LCoE is calculated on the basis of current scientific literature, in which the operational expendi- tures related to the support structures in an offshore 90 https://doi.org/10.14311/APP.2022.36.0090 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 36/2022 Levelized cost of energy of offshore wind Figure 1. Illustration of a global sensitivity analysis, adapted from [5]. wind farm are determined based on the requirements defined by the BSH. To determine the effect of the SIM and other influencing parameters, the first order sensitivity index (Sobol index) is calculated based on a parametric model of the LCoE. 2. Levelized Cost of Energy The LCoE quantifies the average net costs for gener- ating electricity with a certain type power plant. It is defined as the ratio between (a) the sum of the costs consisting of the capital expenditures (CAPEX) and accumulated operational expenditures (OPEX) and (b) the sum of the annual energy production (AEP) over the service life L (Equation 1) [6]. LCoE = CAP EX + L∑ t=1 OP EX (1 + i)t L∑ t=1 AEP (1 + i)t (1) The CAPEX contain the investment costs of an offshore wind farm, while the OPEX include the costs related to the operating of the support structures and turbines including the costs for monitoring, inspection and maintenance. OPEX and AEP are discounted based on the discount rate i. The AEP of an offshore wind farm is computed as the product of the nomi- nal (turbine) capacity nomcap, the nominal capacity availability factor nomcapava, the turbine availability turbavaf ac, the number of wind turbines nwt and the feed in tariff f eedin ((Equation 2) [7]. AEP = nwt · nomcap · 365.25 · 24 · nomcapava · tubravaf ac · f eedin (2) The capital expenditures are calculated in function of the number of wind turbines nwt in a particular wind farm and the investment costs per wind turbine turbinvest (Equation 4) CAP EX = nwt · turbinvest (3) The operational expenditures depend on the number of wind turbines nwt and the operational costs per wind turbine turboperation (Equation ??). OP EX = nwt · turboperation (4) 3. Sensitivity Analysis A sensitivity analysis provides information on how input parameters X and their uncertainties influence the output Y of a deterministic model. A distinction is made between local and global sensitivity analyses [5]. A local sensitivity analysis studies the influence of variability of the input parameters on the model output around a point x0. Generally, the influence of small changes in input parameters on the model output is investigated. A global sensitivity analysis determines the influence of the input parameters by varying them over their entire domain. The basic procedure of a global sensitivity analysis is illustrated in Figure 1. The input parameters may have the same or different marginal probabilistic distributions. The variance of the model output Y depends on the variance of the input parameters and the relations implemented in the deterministic model. In a global sensitivity analysis, the share vi of the variance of model output y that is caused by the input parameter xi is determined. A sensitivity analysis can pursue different goals [8, 9]: • Robustness: Understanding the model’s robustness with regard to the input parameters • Ranking: Rank input factors according to their importance • Screening: Identifying input factors with minor importance, which can be omitted • Mapping: Identifying the areas of input parameters, which lead to extreme model outputs • Decision support: Quantify the effect of decision variables on the model output. In this contribution, the sensitivity analysis is per- formed to rank the parameters influencing the LCoE according to their importance. To this end, the variance-based sensitivity analysis is applied which defines an input parameter’s importance in terms of its contribution to the variance of the model output V ar[Y ] = V ar[g(X)]. In this approach, the influence of the uncertainty in an input parameter Xi on the variance V ar[Y ] is quantified by a first order measure Vi (Equation 5) [9] Vi = V arXi {EX−i [ g (X) |Xi]} (5) 91 M. Kinne, M. Farhan, R. Schneider, S. Thöns Acta Polytechnica CTU Proceedings Wind turbine CAP EXstruc/k€/MW CAP EXturbine/k€/MW Reference 4-A-14 677 2021 [10] 4-D-14 861 2131 [10] 8-A-14 689 1997 [10] 8-D-14 722 2180 [10] 6.1-MW Fixed-Bottom Offshore Wind Turbine 723 2823 [11] Generic Offshore Wind Turbine 1065 2891 [12] Table 1. CAPEX of different offshore wind turbines divided into a structural and a turbine part. in which EX−i [ g (X) |Xi] is the expected value of Y = g(X) with respect to all input variables except Xi, which is fixed. Vi is zero, if Xi has no effect on Y and the expected values is constant with regards to Xi. If Xi is the only random variable with an effect to the model output, Vi is equal to the full variance of the model output V ar[Y ]. The first order measure Vi can be estimated using a Monte Carlo Simulation, which results in nM CS samples of the model output [9]. For every input parameter Xi, the sample pairs (Xi, Y ) are ordered according to the value of Xi. The samples are divided into blocks of size nb and the mean value µYi of each block is an estimate of EX−i [ g (X) |Xi]. The variance of the block means µYi is an estimate of Vi. A more efficient way for determining the first order measure Vi is the Sobol sequence [13]. Based on Vi, the first order sensitivity index Si can be computed as follows [14] (Equation 6). Si = Vi V ar[g(X)] = V arXi {EX−i [ g (X) |Xi]} V ar[g(X)] (6) 4. Numerical study To study the influence of the structural integrity man- agement on the LCoE, the capital and operational expenditures are divided into a part related to the structure and a part related the turbine (Equation 7 and 8). CAP EX = nwt · (CAP EXstruc + CAP EXturbine) (7) OP EX = nwt · (OP EXstruc + OP EXturbine) (8) The capital expenditures CAP EXstruc and CAP EXturbine for one offshore wind turbine are ob- tained from the data listed in Table 1. The values provided in Table 1 are normalized by the nominal turbine capacity. Based on the data listed in Table 1, a range of [677, 1065]/k€/MW is assumed for the capital expenditures related to the structure CAP EXstruc, while the capital expenditures related to the turbine CAP EXturbine exhibit a range of [1997, 2891]/k€/MW. The operational expenditures related to the struc- ture are derived based on a study documented in [15]. The characteristics as well as the environmental and operational conditions of the wind farm considered in [15] are summarized in Table 2. Based on this wind farm, the operational expenditures are estimated for an inspection and monitoring strategy with three dif- ferent settings (optimistic, average, pessimistic) [15]. The inspection and monitoring strategy is in accor- dance with the requirements defined by the BSH as summarized in Table 3. According to the requirements set out by the BSH, general visual inspection (GVI) of the primary and sec- ondary steelwork of the support structures in the wind farm above water is performed every year to provide a general overview on any obvious mechanical damage, fatigue or corrosion. Typically, such an inspection is performed by inspectors from a crew transfer ves- sel. In addition, 25% of the support structure are inspected using close visual inspection (CVI) and de- tailed visual inspection (DVI). The aim of CVI is to identify fatigue or corrosion and determine whether non-destructive testing (NDT) would be necessary to investigate the welded connections. In contrast to GVI, such an inspection is carried out closer to the support structure. According to [15], the objective of DVI is to determine the extent of detected damage. For this purpose. methods of non-destructive testing (NDT) may also be used. Below water, the number of support structures con- sidered for GVI is reduced to 25% every year, while the aim of obtaining a general overall overview on the condition of the support structures remains the same. However, the difference is that a remotely operated vehicle is used to perform the inspection. CVI below water is performed to identify corrosion or fatigue damage and to determine whether NDT would be nec- essary to inspect the structural components [15]. For this type of inspection, good environmental conditions and visibility as well as marine growth cleaning are required. DVI is used to determine the extent of de- tected damage using NDT methods [15]. The number of support structures inspected by CVI and DVI per 92 vol. 36/2022 Levelized cost of energy of offshore wind Characteristic Unit Value Number of OWTs − 100 Turbine capacity MW 5 WF area km2 50 Average distance to port Km 50 Average water depth m 30 Foundation type − Monopile Number of offshore substations − 1 Average wind speed m/s 10 (at hub height) Tidal conditions s 0.5 (HAT to LAT) 50-year wave M 6.5 Current m/s 1 Number of export cables − 1 Table 2. Wind farm characteristics and environmental and operational conditions [15]. Activity SHMS in 10% of WTs Inspection Frequencyduring Service Life Above Water GVI of primary and secondary steelwork 100% every year 25 CVI of primary and secondary steelwork 25% every year 6.25 DVI of primary and secondary steelwork 25% every year 6.25 Seabed scour survey 100% the 2 first yearsand then 25% every year 7.75 Subsea marine growth survey 25% every year 6.25 Cathodic protection potential survey 100% the 2 first years and then 25% every year 7.75 CVI of the grouted connection 25% every year 6.25 Below Water GVI of primary and secondary steelwork 25% every year 6.25 CVI of primary and secondary steelwork 25% every year 6.25 DVI of primary and secondary steelwork 25% every year 6.25 Table 3. Inspection strategy [GVI: general visual inspection; CVI: close visual inspection; DVI: detailed visual inspection] [15]. Boundary conditions optimistic average pessimistic OP EXstruc 1.2% 1.6% 1.9% OP EXturbine 98.8% 98.4% 98.1% Table 4. Relative contribution of OP EXturbine and OP EXstruc to the OP EX. 93 M. Kinne, M. Farhan, R. Schneider, S. Thöns Acta Polytechnica CTU Proceedings Figure 2. Illustration of the distribution types for a given value range defined in terms of the min. and max. value. year below water is the same as the number of support structures inspected by CVI and DVI above water. A seabed scour survey, a subsea marine growth survey and an inspection of the cathodic protection are performed for 100% of the support structures in the first two years. Thereafter, this inspect effort is reduced to 25% of the support structures in each year. The objective of the marine growth survey is to determine the coverage, thickness and type of marine growth on the support structures and sacrificial anodes to guide decisions on removing the marine growth. In a scour survey, the seabed around the support structures is inspected to monitor changes in the topology (local and global). An inspection of the cathodic protection determines if there is adequate global cathodic protection of the submerged part of the support structures. According to the requirements defined by the BSH, continuous sensor-based monitoring systems (struc- tural health monitoring systems and conditional mon- itoring systems) have to be installed on 10% of the wind turbines. The operational expenditures related to the struc- tures OP EXstruc and turbines OP EXturbine relative to the OPEX are given in Table 1. These values are determined in [15] based on the inspection and moni- toring scenario described above in conjunction with optimistic, average and pessimistic estimates of the associated costs. From Table 4 it can be seen that the OP EXstruc ranges between 1.2% to 1.9% of the overall OPEX. The accumulated discounted operational expenditures L∑ t=1 OP EXstruc + OP EXturbine (1 + i)t of an offshore wind farm correspond to approximately 25% of the total costs consisting of capital and operational expen- ditures [21]. To estimate the ranges of the abso- lute values (min./max. values) of OP EXturbine and OP EXstruc, a simple Monte Carlo simulation is per- formed. In this analysis, the CAPEX is modelled as a uniform distributed random variable. Furthermore, the service life and the discount rate are also modelled as uniform distributed random variables. In combi- nation with the knowledge on the relative values of OP EXturbine and OP EXstruc (modelled as uniform distributed random variables) (Table 4), the ranges of the absolute values of OP EXturbine and OP EXstruc can be estimated. From this analysis it was found that the operational expenditures OP EXturbine exhibit a range of [64, 135]/k€/MW/year, while the operational expenditures OP EXstruc are [0.8, 2.6]/k€/MW/year. In the current case study, it is assumed that the service life L of the wind farms may be extended from 20 years up to 30 years [20]. The nominal capacity availability factor nomcap ava describes the ratio between the average power output of a wind turbine (usually one year) to its maximum output and exhibits a range of [0.4, 0.5] [16]. This factor is affected by a variety of influencing factors and conditions including the windspeed. The turbine availability factor tubrava f ac specifies the expected average availability over the service life. Considering only downtime the turbine itself. The factor accounts for the loss of energy associated with amount of time, when the turbine is not available to 94 vol. 36/2022 Levelized cost of energy of offshore wind Variable Unit Uniformdistribution Normal distribution Ref. Lower bound Upper bound Mean value Standard deviation (99.7%) Standard deviation (90%) Number of wind turbines nwt 100 100 100 0 0 Nominal capacity nomcap [MW] 6 6 6 0 0 Nominal capacity availability factor nomcap ava 0.4 0.5 0.45 0.02 0.03 [16] Turbine availability factor turbava f ac 0.857 0.996 0.93 0.025 0.04 [17] Feed in tariff f eedin [€/kWh] 0.14 0.16 0.15 0.003 0.006 [18] Turbine invest: structure CAP EXstruc [k€/MW] 667 1065 871 70 118 Table 1 Turbine invest: turbine CAP EXturbine [k€/MW] 1997 2891 2444 162 271 Table 1 operational expenditures: structure CAP EXstruc [k€/MW/year] 0.8 2.6 1.7 0.3 0.54 [5, 17] operational expenditures: turbine part CAP EXturbine [k€/MW/year] 64 135 99.5 12.2 21.6 [5, 17] Discount rate i 0.06 0.08 0.07 0.003 0.007 [19] Service life T [year] 20 30 25 1.8 3 [20] Table 5. Parameters of the probabilistic models applied in the sensitivity study. produce energy, e.g. due to failure or maintenance. The availability of the turbine per year is in the range of [0.857, 0.996] [17]. The feed in tariff f eedin describes the state fixed re- muneration for electricity to subsidize certain types of electricity production, e.g. electricity generated by off- shore wind. It is in the range of [0.14, 0.16]/€/kWh for offshore wind [18]. The discount rate i is in the range of [0.06, 0.0825]/year for offshore wind in Germany [19]. Often, only the minimal and maximal value of the parameters are available in the literature, but not the distribution type. First, it is assumed that the parame- ters influencing the LCoE are normal distributed. The calculation of the sensitivity indexes is performed for two different standard deviations of the input param- eters. It is assumed that the input parameter ranges account for 99.7% and 90% of the values, whereby both ranges are symmetric to the mean value. In addition, the sensitivity indexes are also calculated 95 M. Kinne, M. Farhan, R. Schneider, S. Thöns Acta Polytechnica CTU Proceedings Figure 3. First order sensitivity indices of the parameters influencing the LCoE. Parameter First order sensitivity index normal distributed parameter range: 90% normal distributed parameter range: 99.7% normal distributed parameter range: 90% and nomcap ava as Weibull distributed uniform distributed Nominal capacity availability factor 0.25 0.25 0.54 0.25 Turbine availability factor 0.11 0.12 0.08 0.12 Feed in tariff 0.09 0.09 0.06 0.09 capital expenditures: structure 0.04 0.05 0.03 0.05 capital expenditures: turbine 0.2 0.2 0.13 0.2 operational expenditures: structure 0.01 0.01 0.01 0.01 operational expenditures: turbine 0.16 0.17 0.11 0.16 Discount rate 0.11 0.11 0.07 0.11 Service life 0.09 0.08 0.05 0.08 Table 6. First order sensitivity indices of the different input parameters. for uniform distributed input parameters (Figure 2). Moreover, in an additional calculation, the nominal capacity availability factor is modelled as a Weibull distributed random variable to reflect the large influ- ence of the wind speed [22]. The parameters of the Weibull distribution are determined by assuming that 5% of the values are smaller than 0.4 (the lower value of the parameter range) and 5% are larger than 0.5 (the upper value of the parameter range). This results in a scale parameter of 0.47 and a shape parameter of 18.23. max. value In the current case study, realizations 96 vol. 36/2022 Levelized cost of energy of offshore wind of the turbine availability factor tubrava f ac which are larger than one are set to be equal to one. Note that, in the current example, the probability that the nominal capacity availability factor nomcap ava is smaller than zero or larger than one is zero regardless of whether it is modelled as a Weibull or normal distributed random variable. In the calculation of the sensitivity indices, several simplifications are made. First, the input parame- ters are modelled as independent random variables. However, in reality dependence among some of the parameters exist, e.g. between the turbine availability factor and the costs due to maintenance / repair or in- vestment costs. Another simplification is made in that the LCoE is determined without considering failure of the support structures, which are typically associated with large costs. This simplification is reflected in the model of the OP EXstruc, which describes only the inspection and monitoring costs without taking into account any failure costs. Further simplifications are made in the probabilistic modelling of the input parameters. As an example, the feed in tariff f eedin and the discount rate i are modelled as time-invariant random variables even though they typically vary with time. The influence of the adopted simplifications has to be investigated in future research. The parameters of the probabilistic models applied the sensitive analysis of the LCoE are provided in Table 5. According to Figure 3 and Table 6, the indices de- pend on the distribution types. When modelling all the input parameters with the same distribution type (normal or uniform distributed), almost the same sen- sitivity indices are obtained. When modelling the nominal capacity availability factor as a Weibull dis- tributed random variable, its influence increases, while the influence of the remaining parameters decreases. However, the trend in the relative importance of the parameters remains approximately the same. It can be seen that the nominal capacity availability factor has the highest (first-order) sensitivity index, followed by the capital and operational expenditures related to the turbines. The discount rate, the turbine availability factor, and the feed in tariff have sensi- tivity indices in the same order of magnitude. The operational expenditures related to the support struc- tures have always the smallest sensitivity index. The sensitivity index of the capital expenditures related to the support structure is smaller than the sensitivity index of the service life. 5. Summary and concluding remarks In this contribution, a sensitivity analysis is performed to quantify the influence of the structural integrity management (SIM) on the levelized cost of energy (LCoE) of an offshore wind farm. The LCoE of a wind turbine/ farm describe the average net present cost, which arise from the conversion from wind to electri- cal power. To quantify the influence of the structural integrity management, the operational expenditures are divided into a part related to the structures and a part related to the turbines. The input parame- ters and their uncertainties are derived based on a literature study and characterize the actual situation/ data. The sensitivity analysis is performed for differ- ent probabilistic models of the influencing parameters. To quantify the relative influence of the parameters, their first order sensitivity index is calculated. Based on the computed sensitivity index of the oper- ational expenditures related to the support structures, it can be concluded that an optimization of the struc- tural integrity management (SIM) aiming to reduce the operating costs may have negligible influence on the LCoE. A similar result has been obtained in a case study considering the effect of D-Strings on the LCoE of offshore wind turbine blades [23]. However, a significant influence of a service life ex- tension on the LCoE is found. It can thus be concluded that the structural integrity management should be directed towards a service life extension. 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