Impact of wind turbine nominal power limitation over wind turbine blade remaining useful life and its economic consequences

Abstract

The present paper investigates the effects of wind turbine nominal power limitation on the remaining useful life of turbine blades. It also looks at the economic impact of this limitation. In this context, the paper provides wind turbine owners and operators with an overview of how to potentially extend the remaining useful life of wind turbine blades and lays out the economic benefits that can be achieved via the modulation of nominal power. In investigating wind turbine blade damage, prior studies focused mainly on predictive models based on the 10 minutes SCADA data wind speed history, without however, trying to protract the remaining useful life of the blades. Only a handful of papers have explored the possibility of increasing the remaining useful life by adjusting the start-up and shutdown procedures with poor results. It would appear that wind turbine blade fatigue damage mainly increases when the wind turbine is in a power production regime, and the mechanical stresses associated with this regime are a function of the nominal power of the wind turbine. The present work therefore investigates the impacts of nominal power changes on both the remaining useful life of wind turbine blades and the economic value of the wind turbine in a bid to identify an optimal control mode. The wind turbine blade damage evaluation is based on 10 minutes SCADA data and the FAST simulation tool with the ultimate goal of providing wind turbine operators with an easy application. The damage evaluation is then applied considering different nominal power levels for the same wind turbine model in order to see the resulting impact on the remaining useful life. This project therefore takes a pioneering approach by proposing a remaining useful life optimization tool to wind turbine operators, in effect, a decision-making tool regarding which exploitation strategy to adopt.

Keywords

Wind turbines damage estimation rainflow counting composite materials predictive maintenance remaining useful life

Introduction

To support the ever-growing global demand for energy, the wind energy sector’s share of electricity production is expected to go from its current 5% to 45% by 2050 (DNV GL Energy Transition Outlook, 2020). The levelized cost of energy (LCOE) stands as a key driver enabling this surge of production. To achieve the anticipated 30% reduction in the cost of wind turbine (WT) energy production from 2020 to 2050, improving operation and maintenance (O&M) strategies should be the main focus to ensure a decline in the LCOE. Wind turbine blades (WTB) constitute a crucial component when dealing with WT fatigue. This is because the WTB failure rate is among the highest compared to other components (0.13/year), ranking almost at the same level as the transformer, gearbox or tower (Li et al., 2022; Zhu et al., 2018). Secondly, there are substantial costs associated with repairing or replacing WTB (International Energy Agency, 2013; Mishnaevsky, 2019).

Contemporary research endeavors are focused on predictive maintenance strategies for WTB aimed at optimizing their O&M costs, with the final objective of evaluating the potential for expanding the remaining useful life (RUL) of WT. The main goal of predictive maintenance is to prevent expensive corrective actions and repair fees associated with reactive maintenance via smart planning. Two main categories of predictive maintenance have been established (Eder & Chen, 2020). The first one is founded on data-driven approaches. One such predictive maintenance models involves an exponential representation of the damage behavior of WTB (Liu et al., 2023). Another approach uses a Bayesian dynamic network, discretizing WTB damage into multiple levels of severity. In this model, the progression from one damage step to the next is described by a probability distribution. The primary advantage of data-driven models is their ability to provide damage assessments with minimal computational requirements (Eder & Chen, 2020; Liu et al., 2023). Nevertheless, such models are limited by the fact that they require hard-to-obtain parameters that are crucial for ensuring a reliable assessment of the RUL.

Next comes the second predictive maintenance category, which relies on physical models, such as the FASTIGUE (Eder and Chen, 2020). Several physical models for computing the WTB’s RUL already exist, with those using the Miner’s rule being the most commonly employed due to their straightforward operational simplicity (Bergami and Gaunaa, 2014; Germanischer Lloyd, 2010; I. E. Commission et al., 2019; Jang et al., 2015; Jiang et al., 2015; Liu et al., 2023; Marín et al., 2009; Meng et al., 2019; Ragan and Manuel, 2007; Ravikumar et al., 2020; Sanchez et al., 2016; Tibaldi et al., 2016; Vera-Tudela and Kühn, 2017; Yisu et al., 2022). Other approaches are available but they are less commonly used due to their inherent limitations. For instance, physical damage models based on Paris-Erdogan’s elastic crack propagation law require the presence of a pre-existing crack to be applicable (Eder and Chen, 2020; Ravikumar et al., 2020; Valeti and Pakzad, 2019). Physical models perform well at providing accurate evaluations of damage behavior. However their application to the entire lifespan of a WT (typically 20–30 years) can be exceedingly time-consuming. Furthermore, with them, a wind speed (WS) sampling frequency of 1 Hz is required to obtain a dependable computation of WTB damage. This because of WTB are highly sensitivity to WS fluctuations at this frequency (Bashirzadeh Tabrizi et al., 2019; Jang et al., 2015; Meng et al., 2019). Consequently, given the tremendous volume of data generated by 1 Hz WS SCADA measurements and the time-consuming nature of fatigue assessment via physical damage models, carrying out a comprehensive evaluation of WTB damage over an extended period (Jang et al., 2015) is impractical. Another issue in this context is the uncommon use of 1 Hz frequency SCADA data by wind farm operators. This is mainly attributable to the recommendation in the IEC standard 61400-12-1 (IEC-61400-12, 2017) for the use of 10 minutes aggregated signals (minimum, maximum, standard deviation, average) in evaluating the energetic performance of WT (I. E. Commission et al., 2019). Consequently, the industry standard is to operate with 10 minutes SCADA data, even though data with higher frequencies may be needed to assess WTB fatigue. Therefore, to cover the widest range of wind farms, it is imperative to develop a WTB fatigue damage estimator that can run effectively with standard 10 minutes SCADA data.

As an increasing number of WT are approaching their theoretical life expectancy of 25 years (Bureau Veritas, n.d.), the question of extending the WTB RUL has become a growing concern among wind farm operators. This objective aims to boost total energy production while running the same WT and then enhancing the profitability of facilities. However, notwithstanding the existence of multiple approaches for predicting WTB damage behavior, there has been only limited attempts to explore the potential to extend the WTB RUL via the optimization of the WT operation. As of the publication date of this paper, only a few articles have worked on the extension of WTB RUL via the optimization of shutdown procedures with a limited impact on the overall WTB damage (Jiang et al., 2013, 2015; Jiang and Xing, 2022; Luan and Moan, 2021). The present study therefore details a new approach to protract the WTB RUL by optimizing the operation of the WT.

The primary objective here is to investigate the overall fatigue damage behavior of WTB and the possibility of RUL extension considering 10 minutes SCADA data and various nominal power settings, $P_{n o m i n a l}$ , applied to a 5 MW WT from the NREL library. The model introduced in this study initially calculates the WTB damage resulting from WS fluctuations within each 10 minutes SCADA data interval. To this end, a turbulence model employing the Kaimal spectrum and turbulence intensity (TI; Kaimal et al., n.d.; Jonkman and Buhl, 2006) is used to generate a numerical and stochastic 1 Hz WS signal for each 10 minutes SCADA data segment. Subsequently, considering the generated 1 Hz WS signal and the selected nominal power level of the WT, the WTB damage is computed using the widely used Miner’s rule for each of the 10 minutes SCADA data segments over the investigated timeframe. Finally, by summing the evaluated damage for each 10 minutes SCADA period, an overarching assessment of the WTB fatigue damage is computed.

This study is structured into four main sections. The first section introduces the numerical tools and the available data, along with an explanation of the underlying assumptions employed in developing the model herein. The second section focuses on the methodology used in estimating WTB damage, utilizing 10 minutes SCADA data, numerically simulated 1 Hz WS signals, and the selected nominal power for the 5 MW WT model chosen in this research. The third section presents a detailed analysis and discussion of the results, with a particular emphasis on the impact of different nominal power settings on the overall WTB fatigue damage. Finally, the study concludes with a comprehensive overview of the contributions made by this research and presents suggestions for potential future leads to further enhance the findings presented by the studied approach.

Resources and hypothesis

Resources

For the purposes of this study, real 10-minute aggregated signals extracted from SCADA data, specifically a 10-minute mean WS history, obtained from a wind farm comprising several 5 MW wind turbines, covering the period of February 2017 to May 2020, were utilized. To calculate the aerodynamic loads on the blades, aeroelastic models from FAST and Matlab^® were utilized and subjected to load cases as specified in the IEC 61400-1 standard (I. E. Commission et al., 2019). A comprehensive numerical model of the WTB is essential for an accurate evaluation of its root stress. Unfortunately, due to confidentiality reasons, the specific design details of the WT model employed by the studied wind farm remain undisclosed.

The decision was thus made to utilize the 5 MW WT numerical model proposed by the open-access NREL library (Dykes and Rinker, 2018; Jonkman et al., 2009), as it provides a numerical model that is detailed enough for use in fatigue assessment. As this numerical model differs from the one actually installed at the investigated wind farm, it was anticipated that the calculated fatigue damage experienced by the numerical WT would differ from that of the real WT. Nonetheless, the ranking of WT based on the level of WTB damage was expected to remain unchanged. Consequently, in this paper, although the calculated WTB fatigue damage is relative rather than absolute, it still enables a comparative analysis of damage among WT within a same wind park.

Environmental effects on wind turbine damage

WTB fatigue is influenced by several environmental factors, including temperature fluctuations, which can impact material fatigue strength (Hawileh et al., 2015; Ziane et al., 2016), as well as the effects of rain erosion on the fatigue damage to WTB coatings (Hu et al., 2021), the force of gravity (Barnes et al., 2015), etc. Nevertheless, WTB fatigue damage is mainly affected by two major bending moments, namely, edgewise and flapwise bending (I. E. Commission et al., 2019; IEC-61400-12, 2017; Lars et al., 2017; Manwell et al., 2009). In certain locations, such as the blade root (Jiang et al., 2015; Jiang and Xing, 2022), depending on the specific position around this root, the fatigue behavior of the root section can be predominantly influenced by either edgewise or flapwise bending (Jiang et al., 2015; Lars et al., 2017; Manwell et al., 2009). Flapwise bending is mainly induced by the WS and wind shear (Lars et al., 2017). According to the IEC-61400-1 standard (I. E. Commission et al., 2019), when carrying out a fatigue analysis for a certain mean WS must correspond a TI according to the wind class for which the WT is designed (A, B, or C, with A being the most turbulent; see Figure 1). As for the wind shear, it is considered using the power law with a power law exponent $α = 0.2$ , as proposed by default in (DNV GL Energy Transition Outlook, 2020; I. E. Commission et al., 2019) in the following equation:

V (z) = V_{h u b} {(z / z_{h u b})}^{α}

(1)

Figure 1.

Graph showing the evolution of the TI according to the mean WS as described by the standard IEC-61400-1.

with $V (z)$ being the WS at the height $z$ above the ground, $V_{h u b}$ the WS at the WT hub and $z_{h u b}$ the height of the hub. Then, the edgewise bending is submitted to the WS, as well as to gravity (Lars et al., 2017; Manwell et al., 2009). Finally, the wind turbine blades are also submitted to radial forces induced by the centrifugal force and gravity (Joncas, 2010; Lars et al., 2017; Manwell et al., 2009). The main factors influencing the flapwise and edgewise bending and the radial forces are summarized in Figure 2. To recap, to describe the WTB fatigue behavior in the present project, the mean WS in conjunction with the TI and the wind shear will be considered as the gravity effects and the centrifugal force, respectively.

Figure 2.

Schema presenting the main causes of flapwise bending, edgewise bending, and radial force.

Hypothesis

This study exclusively examines damage at the blade root location, which is anticipated to be the most sensitive section of the WTB to fatigue damage (Lars et al., 2017; Manwell et al., 2009; Zárate-Miñano et al., 2013). Regardless of the wind WT model, the root section is considered to be circular (Eder and Chen, 2020; Joncas, 2010; Lars et al., 2017; Manwell et al., 2009; Marín et al., 2009; Meng et al., 2019), simplifying the damage analysis to a basic shape. Additionally, the skin thickness and the root diameter of the WTB are solely influenced by the overall WTB length (Bortolotti et al., n.d.4; Joncas, 2010). This characteristic facilitates the configuration of a conceivable WTB root design based on basic information from the numerical WTB model.

The WTB root is mainly submitted to flapwise and edgewise bending. The variations in stress induced by flapwise and edgewise bending lead to the initiation and propagation of damage. In the context of a WTB pitch with an angle α = 0°, edgewise bending corresponds to the in-rotor plane direction, while flapwise bending is associated with the out-rotor plane direction. However, based on estimations carried out with a 5 MW WTB from the NREL library and the FAST simulation tool, it appears that flapwise bending is more sensitive to WS fluctuations. Hence, the primary focus of this study is on stress resulting from WS fluctuations.

The WS fluctuations are obtained from a simulated 1 Hz WS signal, stochastically generated using the TurbSim module from FAST, which operates in the Kaimal spectrum (Bashirzadeh Tabrizi et al., 2019; Jonkman and Buhl, 2006). This spectrum is a widely used tool in the literature for simulating turbulent wind flows, particularly in the context of onshore sites (Hong and Li, 2018; Yi et al., 2021). It was designed to represent the wind flows over a flat and homogeneous onshore site within the atmospheric boundary layer, making it a recommended choice according to the IEC 61400 standard (I. E. Commission et al., 2019).

The damage resulting from these WS fluctuations is an accumulative phenomenon. It is thus assumed that the overall WTB damage $D_{t o t}$ at time ( $t \in R_{+}$ ) is defined as the sum of various damages ( $D_{i}$ ), outlined as:

D_{t o t} (t) = D_{O p e r a t i o n} (t) + D_{P a r k e d} (t) + D_{S D} (t) + D_{E S D} (t) + D_{S U} (t) + D_{E v e n t s} (t) + D_{t_{0}}

(2)

In this context, the components contributing to WTB damage are defined as follows: $D_{O p e r a t i o n}$ represents the damage incurred during the operation of the wind turbine (WT), $D_{P a r k e d}$ (t) pertains to damage when the WT is at a standstill, and $D_{S D}$ and $D_{E S D}$ correspond to the damage during standard WT shutdown and emergency shutdown, respectively. $D_{S U}$ represents the damage caused by WT start-up, and $D_{E v e n t s}$ signifies damage induced by extreme environmental conditions, such as wind velocities exceeding $V_{c u t - o u t}$ (in our study, set at 25 m.s⁻¹), which may occur during a severe storm affecting the wind farm for example.

However, this study does not consider $D_{E v e n t s}$ since the latter involves intricate mechanisms, such as resonance problems or sudden material failures, which differ from fatigue-related damage (Li et al., 2020). Additionally, even though $D_{t_{0}}$ can significantly impact the WTB strength (Lagdani 2022; Marín et al., 2009; Rainflow, 2023), it is not within the scope of this study. Typically, $D_{t_{0}}$ is attributed to manufacturing defects or wind turbine installation issues, which are challenging to assess and are unrelated to fatigue mechanisms. Since this study focuses primarily on fatigue-induced damage, $D_{E S D}$ is also excluded because available SCADA data does not distinguish between emergency and standard shutdowns. Furthermore, both $D_{S D}$ and $D_{S U}$ will not be factored in the fatigue damage assessment due to their relatively low damage contribution versus the overall fatigue damage. It should be recalled that the primary focus of this study is to evaluate the resulting effects of the nominal power limitation modification on wind turbine’s fatigue damage. So, $D_{P a r k e d}$ will not be taken into consideration because during a standstill regime, the fatigue damage does not depend on the nominal power value, for obvious reasons. However, $D_{O p e r a t i o n}$ will be considered in the analysis as it is influenced by the nominal power of the wind turbine (as explained in the next part). Finally, in this study, only $D_{O p e r a t i o n}$ is investigated, reducing the expression of $D_{t o t}$ as follows:

D_{t o t} (t) = D_{O p e r a t i o n} (t)

(3)

Evaluation of WTB damage

Our SCADA data provides access only to mean wind speeds measurement, $V_{m e a n}$ , and TI averaged over 10 minutes, while wind turbine blades have natural frequencies of around 1 Hz in the edgewise and flapwise moments. Therefore, it is essential to calculate blade damage considering the 10-minute SCADA data and the influence of a wind signal sampled at a frequency of 1 Hz within each 10-minute period provided by the SCADA data. The concept proposed here consists in creating a database containing an assessment of blade damage caused by wind sampled at a frequency of 1 Hz over a 10-minute period, called here $V_{H F}$ , for each wind condition the wind turbine may encounter (in terms of $V_{m e a n}$ , and TI). Subsequently, when reading the SCADA data containing $m$ 10-minute periods, the resulting damage for each 10-minute period, denoted as $d_{10 m i n, t}$ , will be selected from this damage database based on the mean wind speed $V_{m e a n, t}$ and the turbulence intensity $T I_{t}$ specified at time period $t$ . Finally, the total damage to the wind turbine blade $D_{t o t}$ will be the sum of the damages found for each 10-minute period recorded in the SCADA data (see Figure 3), as follows:

D_{t o t} = \sum_{t = 1}^{m} d_{10 m i n, t}

(4)

Figure 3.

Flowchart showing the global process enabling the evaluation of $D_{t o t}$ .

Simulation of high-frequency wind $V_{H F}$

As explained earlier, to build the 10-minute damage database, all wind conditions to which the wind turbine may be exposed need to be simulated. To this end, the TurbSim module of FAST is employed to generate stochastic wind profiles sampled at 1 Hz from 10-minute periods (see Figure 4). These wind profiles are generated for $V_{m e a n}$ ranging from the cut-in wind speed ( $V_{c u t - i n} = 3$ m.s⁻¹) to the cut-out wind speed ( $V_{c u t - o u t} = 25$ m.s⁻¹), with a step of 1 m.s⁻¹ and a wind shear coefficient $α$ as chosen in Part 2. TI is arbitrarily selected, such as that of the turbulence class A, B, and C as described in the IEC 61400-1 standard (I. E. Commission et al., 2019; see Figure 1). Consequently, a high-frequency wind signal over 10 minutes, $V_{H F}$ , is obtained as a function of $V_{m e a n}$ and TI.

Figure 4.

$V_{H F}$ simulated stochastically for $V_{m e a n} = 10$ m.s⁻¹ and a turbulence class C.

Creation of the WTB damage database over 10-minute periods considering $V_{H F}$

As explained in Part 2, WTB damage results from three loading conditions: flapwise bending ( $M_{f l a p}$ [N.m]), edgewise bending ( $M_{e d g e}$ [N.m]) and a radial force ( $F_{r a d}$ [N]). It was decided to simulate loads over a 10-minute period for a constant WS ranging from $V_{c u t - i n}$ to $V_{c u t - o u t}$ with a step of $0.1$ m.s⁻¹ (see Figure 5). Simulations were conducted using FAST and the numerical model of the 5 MW wind turbine, with 3 different nominal powers, 5 MW, limited to 4.5 MW and 4 MW. The nominal power was modified in the “DISCON” file, which describes the behavior of the WT. During our simulations, it was observed that each of these loads can be decomposed into two simple signals (see Figure 6): firstly, a constant signal corresponding to the effect of WS on $M_{e d g e}$ and $M_{f l a p}$ and the rotor rotation speed on $F_{r a d}$ ; secondly, a periodic signal whose period depends on the rotor rotation speed for all three loads and whose oscillation amplitude depends on the wind shear coefficient $α$ for $M_{e d g e}$ and $M_{f l a p}$ and on the rotor rotation speed and blade weight for $F_{r a d}$ .

Figure 5.

Graph of loadings according to the time at $V_{m e a n} = 11$ m.s⁻¹ for a 10-minute period and a nominal power of 5 MW.

Figure 6.

Graph showing the decomposition of the radial force for a 5 MW WT at a constant $WS = 11$ m.s⁻¹ for a 10-minute period and a nominal power of 5 MW.

Due to its inertia, the rotor rotation speed is assumed to be constant over a 10-minute period and is therefore dependent on $V_{m e a n}$ . This assumption removes from consideration the impact of high-frequency wind variations $V_{H F}$ on the periodic component of the $M_{e d g e}$ and $M_{f l a p}$ signals and the entire signal $F_{r a d}$ . However, the constant component of the $M_{e d g e}$ and $M_{f l a p}$ signals depends on $V_{H F}$ due to the natural frequency of the blades, approximately 1 Hz in flapwise and edgewise bending. The following idea is to take into account $V_{H F}$ to reconstruct the signal of moments $M_{e d g e}$ and $M_{f l a p}$ by adding the periodic component of these moments $M_{e d g e, A C}$ and $M_{f l a p, A C}$ (which depends on $V_{m e a n}$ ), to the mean component $M_{e d g e, D C}$ and $M_{f l a p, D C}$ directly influenced by $V_{H F}$ , as follows:

M_{e d g e} (V_{H F}) = M_{e d g e, A C} + M_{e d g e, D C} (V_{H F})

(5)

M_{f l a p} (V_{H F}) = M_{f l a p, A C} + M_{f l a p, D C} (V_{H F})

(6)

The average values of $M_{e d g e, D C}$ and $M_{f l a p, D C}$ are recorded for each tested constant wind speed, allowing to plot their behavior as a function of the wind speed (see Figure 7). By utilizing the curves of $M_{e d g e, A C}$ and $M_{f l a p, D C}$ as functions of the wind speed, it becomes possible to convert the previously obtained high-frequency WS, $V_{H F}$ , into the moment signals $M_{e d g e, DCHF} (V_{H F})$ and $M_{f l a p, DCHF} (V_{H F})$ . These moment signals can then be inserted into equations (3) and (4) in place of $M_{e d g e, D C} (V_{H F})$ and $M_{f l a p, D C} (V_{H F})$ to obtain $M_{e d g e} (V_{H F})$ and $M_{f l a p} (V_{H F})$ over 10 minutes and at a frequency of 1 Hz for given parameters $V_{m e a n}$ and TI (see Figures 8 and 9). The revised equations (3) and (4) are:

M_{e d g e} (V_{H F}) = M_{e d g e, A C} + M_{e d g e, DCHF} (V_{H F})

(7)

M_{f l a p} (V_{H F}) = M_{f l a p, A C} + M_{f l a p, DCHF} (V_{H F})

(8)

Figure 7.

Graph showing $M_{e d g e, D C}$ and $M_{f l a p, D C}$ according to the WS of a 5 MW WT under different nominal powers.

Figure 8.

Graph showing $M_{f l a p}$ , $M_{f l a p, A C}$ , and $M_{f l a p, D C}$ for $V_{m e a n} = 10$ m.s⁻¹ and a turbulence class C.

Figure 9.

Graph showing $M_{e d g e}$ , $M_{e d g e, A C}$ , and $M_{e d g e, D C}$ for $V_{m e a n} = 10$ m.s⁻¹ and a turbulence class C.

The signals $M_{e d g e, A C}$ and $M_{f l a p, A C}$ , along with the entire radial force signal, were recorded for constant wind speeds ranging from $V_{c u t - i n}$ to $V_{c u t - o u t}$ with a step of 1 m.s⁻¹. The method used to record bending moments and the radial force is summarized in Figure 8.

Once the profile of moments $M_{e d g e}$ and $M_{f l a p}$ is obtained, it needs to be converted into a stress signal. The expressions for the maximum stresses in the flapwise and edgewise directions ( $σ_{f l a p}$ and $σ_{e d g e}$ [Pa]) are as follows:

σ_{f l a p} = \frac{M_{f l a p} c}{I} + F_{r a d}

(9)

σ_{e d g e} = \frac{M_{e d g e} c}{I} + F_{r a d}

(10)

Here, $c$ represents the radius of the blade section at its root [m] (Joncas, 2010; Lars et al., 2017). $I$ is the moment of inertia [m⁴] of the blade section at its root. However, to obtain $I$ , it is necessary to know the thickness of the wind turbine’s skin at its root, denoted as $t_{r o o t}$ [m]. However, $t_{r o o t}$ is unknown for the blade model used here. To obtain a reliable estimate, an empirical formula describing its thickness as a function of the rotor radius $R$ was chosen (Joncas, 2010):

t_{r o o t} \approx 0.08 \sqrt{\frac{R}{40}}

(11)

Given that the wind turbine blade is made of composite materials (glass/epoxy) (Li et al., 2020; Marín et al., 2009), it is advisable to assess damage based on the history of deformations rather than the strain history (DNV GL Energy Transition Outlook, 2020; Li et al., 2020). Thus, the strain history in the flapwise direction, $S_{f l a p}$ , and the edgewise direction, $S_{e d g e}$ , is obtained from the stress history $σ_{f l a p}$ and $σ_{e d g e}$ using the Hooke’s law. Since the resulting signal is complex, the Rainflow Counting (RFC) method (Rainflow, 2024) is applied to extract deformation cycles in terms of mean value $S_{i, M}$ and amplitude $S_{i, A}$ as follows:

[S_{i, A}, n_{i}] = RFC (u (t), S_{i, M}, S_{u})

(12)

where $S_{u}$ is the maximum strain to failure of the weakest ply in the composite, $u (t)$ is the analyzed strain history, and $n_{i}$ is the number of strain cycles for the $i$ -th cycle. Once the cycles $n_{i}$ are characterized, it is the number of cycles to failure $N_{i}$ that needs to be computed. The DNV certification guide (DNV GL Energy Transition Outlook, 2020) proposes an approach based on the Goodman diagram and strain, as follows:

N_{i} = {[\frac{R_{k, t} + | R_{k, c} | - | 2 γ_{M a} S_{k, M} - R_{k, t} + | R_{k, c} | |}{2 (γ_{M b} / C_{1 b}) S_{k, A}}]}^{m}

(13)

with:

γ_{M b} / C_{1 b} = γ_{M 0} C_{2 b} C_{3 b} C_{4 b} C_{5 b}

(14)

The different parameters used here are presented in the nomenclature.

Once $n_{i}$ and $N_{i}$ are calculated, the Miner’s rule can be applied, as recommended by the IEC 61400-1 standard (DNV GL Energy Transition Outlook, 2020; I. E. Commission et al., 2019), to assess the wind turbine blade damage resulting from a simulated 10-minute wind speed signal at a frequency of 1 Hz, $d_{10 m i n}$ :

d_{10 m i n} = \sum^{\frac{n_{i}}{N_{i}}}

(15)

To summarize the $d_{10 m i n}$ estimation process, a stochastic wind speed signal $V_{H F}$ is generated via TurbSim based on the provided $V_{m e a n}$ and TI parameters. Then, the $V_{H F}$ signal is successively converted into stress and deformation signals in the flapwise and edgewise directions after analyzing the wind turbine behavior using FAST for different $V_{m e a n}$ values. Subsequently, the RFC is applied to the strain signal to characterize the cycles. Once this is done, the Miner’s rule is utilized to evaluate the $d_{10 m i n}$ . Then $d_{10 m i n}$ is recorded in a database. Because $V_{H F}$ is generated stochastically, it was arbitrarily chosen to repeat the process 100 times to cover the entire range of possible damage values for each simulated $V_{m e a n}$ and TI (see Figure 11). Thus, for each simulated $V_{m e a n}$ and TI, the $d_{10 m i n}$ damage is recorded as a Cumulative Distribution Function (CDF) consisting of 100 possible damage values, sorted from smallest to largest. The process is schematically represented in Figure 12.

Figure 10.

Flowchart explaining the process leading to the recording of the WTB loads for different WS and nominal powers.

Figure 11.

Graph showing 100 stochastic $V_{H F}$ generated for $V_{m e a n} = 10$ m.s⁻¹ and a turbulence class C.

Figure 12.

Flowchart explaining the process leading to the obtention of the CDF database of the WTB damage $d_{10 m i n}$ .

Results and discussion

Thanks to the above methodology, it was possible to assess the evolution of wind turbine blade damage over long periods taking into account the $V_{m e a n}$ provided in the SCADA data as well as the influence of $V_{H F}$ and the weight of the blade. The evaluations of this damage over 1 year in the flapwise and edgewise directions are presented in Figures 13 to 18. The results are summarized in the following Table 1:

Figure 13.

Evaluation of the WTB damage $D_{t o t}$ in the flapwise direction over a 1-year period with a turbulence class A for different nominal powers applied to a 5 MW WT numeric model.

Figure 14.

Evaluation of the WTB damage $D_{t o t}$ in the flapwise direction over a 1-year period with a turbulence class B for different nominal powers applied to a 5 MW WT numeric model.

Figure 15.

Evaluation of the WTB damage $D_{t o t}$ in the flapwise direction over a 1-year period with a turbulence class C for different nominal powers applied to a 5 MW WT numeric model.

Figure 16.

Evaluation of the WTB damage $D_{t o t}$ in the edgewise direction over a 1-year period with a turbulence class A for different nominal powers applied to a 5 MW WT numeric model.

Figure 17.

Evaluation of the WTB damage $D_{t o t}$ in the edgewise direction over a 1-year period with a turbulence class B for different nominal powers applied to a 5 MW WT numeric model.

Figure 18.

Evaluation of the WTB damage $D_{t o t}$ in the edgewise direction over a 1-year period with a turbulence class C for different nominal powers applied to a 5 MW WT numeric model.

Table 1.

Table presenting the evaluation of $D_{t o t}$ in flapwise and edgewise directions for different configurations in terms of nominal power and turbulence class.

Direction of $D_{t o t}$	Turbulence class	$P_{n o m i n a l}$			Overall $D_{t o t}$ reduction between 5 MW and 4 MW
Direction of $D_{t o t}$	Turbulence class	5 MW	4.5 MW	4 MW	Overall $D_{t o t}$ reduction between 5 MW and 4 MW
$D_{t o t, f l a p}$	A	$5.0 \times 10^{- 2}$	$3.4 \times 10^{- 2}$	$2.0 \times 10^{- 2}$	$60.0 %$
	B	$2.6 \times 10^{- 2}$	$1.8 \times 10^{- 2}$	$1.0 \times 10^{- 2}$	$61.5 %$
	C	$1.2 \times 10^{- 2}$	$7.9 \times 10^{- 3}$	$4.7 \times 10^{- 3}$	$60.8 %$
$D_{t o t, e d g e}$	A	$4.2 \times 10^{- 3}$	$3.6 \times 10^{- 3}$	$3.1 \times 10^{- 3}$	$26.2 %$
	B	$4.3 \times 10^{- 3}$	$3.7 \times 10^{- 3}$	$3.1 \times 10^{- 3}$	$27.9 %$
	C	$4.3 \times 10^{- 3}$	$3.7 \times 10^{- 3}$	$3.2 \times 10^{- 3}$	$25.6 %$

Firstly, it is notable that the total damage in the flapwise direction, $D_{t o t, f l a p}$ , is highly sensitive to a decrease in $P_{n o m i n a l}$ , regardless of the turbulence class, with a reduction in $D_{t o t, f l a p}$ of up to $60 %$ when reducing $P_{n o m i n a l}$ from 5 MW to 4 MW. Concerning the total damage in the edgewise direction, $D_{t o t, e d g e}$ , there is also a significant sensitivity to $P_{n o m i n a l}$ , with the damage decreasing by approximately $26 %$ for the same range of nominal power. These differences stem from the modification of the bending moment curves as a function of wind speed depending on the chosen $P_{n o m i n a l}$ (see Figure 7). By analyzing these curves, it can be observed that beyond the nominal wind speed $V_{n o m i n a l}$ (the wind speed at which nominal power is reached), the bending moments decrease with $P_{n o m i n a l}$ . This subsequently impacts the simulations of $M_{e d g e} (V_{H F})$ and $M_{f l a p} (V_{H F})$ , and thus the resulting $d_{10 m i n}$ damage.

Next, as expected, $D_{t o t, f l a p}$ is also highly sensitive to the wind turbulence class. Thus, for $P_{n o m i n a l} =$ 5 MW, $D_{t o t, f l a p}$ decreases by $76.0 %$ between a class A and a class C wind. This is the result of the influence of TI on the $M_{f l a p} (V_{H F})$ signal. In contrast, the turbulence class seems to have almost no impact on $D_{t o t, e d g e}$ . This is due to the predominance of $M_{e d g e, A C}$ , which is not influenced by TI, in the expression of $M_{e d g e} (V_{H F})$ (see Figure 9).

Finally, a last point to note is that as the turbulence class decreases in intensity and $P_{n o m i n a l}$ decreases, $D_{t o t, f l a p}$ approaches $D_{t o t, e d g e}$ . This yields the following Table 2:

Table 2.

Table presenting $D_{t o t, e g d e}$ in terms of percentage of $D_{t o t, f l a p}$ considering the turbulence class and $P_{n o m i n a l}$ .

	Turbulence class	$P_{n o m i n a l}$
	Turbulence class	5 MW	4.5 MW	4 MW
$D_{t o t, e g d e}$ as a percentage of $D_{t o t, f l a p}$ in the same conditions	A	$8.4 %$	$10.6 %$	$15.5 %$
	B	$16.5 %$	$20.6 %$	$31.0 %$
	C	$35.8 %$	$46.8 %$	$68.1 %$

Table 3.

Table presenting the global energy production over a 1-year period for different values of $P_{n o m i n a l}$ .

$P_{n o m i n a l}$	5 MW	4.5 MW	4 MW
Global energy produced (MWh) over a 1-year period	$1.48 \times 10^{4}$	$1.43 \times 10^{4}$	$1.36 \times 10^{4}$
Global energy produced as compared to that obtained with $P_{n o m i n a l} =$ 5 MW	$100 %$	$96.6 %$	$91.9 %$

Therefore, we can conjecture that if $P_{n o m i n a l}$ and/or TI become too low, then $D_{t o t, e g d e}$ will exceed $D_{t o t, f l a p}$ , and consequently become the limiting factor in the WTB’s RUL. This result further justifies the need to study $D_{t o t}$ in both the flapwise and edgewise directions to ensure a reliable estimation of the RUL.

To assess whether increasing the RUL of the wind turbine blade by reducing $P_{n o m i n a l}$ is financially beneficial, it is necessary to analyze the impact such a process has on the electricity production of the turbine. The theoretical electricity production was therefore evaluated based on the $V_{m e a n}$ provided in the SCADA data used for the estimation of $D_{t o t}$ and the power curves obtained for the different variations of the WT’s nominal power (see Figures 19 and 20). It is worth noting that the electrical power provided by the turbine primarily depends on $V_{m e a n}$ , which implies that the overall energy output is not influenced by TI. The results are presented in the table below:

Figure 19.

Evaluation of the energy production according to the chosen nominal power for 1-year period.

Figure 20.

Power curves of the numeric 5 MW WT for different nominal powers.

Figure 21.

Weibull distribution of $V_{m e a n}$ stored in the SCADA data for a 1-year period.

According to these results, decreasing $P_{n o m i n a l}$ from 5 MW to 4 MW leads to a decrease in $D_{t o t, e d g e}$ of $26 %$ and $D_{t o t, f l a p}$ of $60 %$ , regardless of the wind turbulence class, at the cost of an $8.1 %$ decrease in total electricity production in our case study. Therefore, we end up with a significant increase in the RUL of the WTB compared to the annual loss of electricity production for the tested configurations. This could lead to an increase in the amount of energy produced over the entire operational lifespan of the WT, resulting in an improved return on investment.

It is noteworthy that the $8.1 %$ decrease in energy production over 1 year when reducing $P_{n o m i n a l}$ from 5 MW to 4 MW is due to the distribution of $V_{m e a n}$ in our WS history. Indeed, by calculating the Weibull distribution of the latter, it is evident that most of the time, $V_{m e a n} < V_{n o m i n a l}$ , indicating that the turbine operates only during a small fraction of the time at its nominal power.

Conclusion

This paper proposes a method for calculating WTB relative damage over an extended period while considering a larger set of parameters. It takes into account 10-minute SCADA data, TI, wind shear, and the forces generated by the blade mass. For this calculation, flapwise and edgewise bending moment responses, as well as the axial force on the blade, are simulated using FAST for various constant wind speeds, and then decomposed into two signals, namely, alternating and continuous. Subsequently, the moment and force signals are reconstructed over a 10-minute period, considering a high-frequency wind signal, $V_{H F}$ , simulated via Turbsim for all mean wind speeds ( $V_{m e a n}$ ) and TIs that the WT may encounter. The resulting $d_{10 m i n}$ damage from these high-frequency solicitation simulations over a 10-minute period is then calculated using the Miner’s rule before being recorded in a database. Then, by reading the available 10-minute SCADA data, $d_{10 m i n}$ is selected based on the measured $V_{m e a n}$ and TI for each 10-minute period and compiled to obtain the overall damage, $D_{t o t}$ .

Furthermore, by repeating the process with different WT nominal powers, $P_{n o m i n a l}$ , it was possible to evaluate the impact of nominal power limitation on the resulting WTB fatigue damage, $D_{t o t}$ . It was computed that a 20% limitation of the nominal power for a 5 MW WT could reduce the damage in the flapwise direction by 61.5% and by 27.9% in the edgewise direction, with a loss in energy production of only 8.1%. This aspect might be particularly interesting for wind farm operators, as this tool enables them to visualize the impact of WT nominal power limitation on the RUL and energy production. This way, wind farm operators could have a clearer idea of the ideal operational conditions to adopt concerning energy production, the RUL of the WTs they operate, and the maintenance schedule.

However, it is important to keep in mind that this tool only provides an evaluation of the relative damage of the WTB due to the numerous uncertainties regarding the properties of the WTB. Quantifying the uncertainty in WTB damage estimations remains a significant challenge. To our knowledge, no Miner’s rule-based study on WTB damage estimation has successfully compared its results with observations on actual WT. This issue should be the subject of future research. If it becomes possible to quantify the uncertainty of our damage model, then it would be possible to calibrate it accordingly.

Another aspect to consider in transforming this relative damage evaluation tool into an absolute damage evaluation tool is the inclusion of other environmental factors affecting WTB fatigue. In the present study, we have limited the number of environmental factors taken into account. However, it has been proven that temperature and humidity significantly impact the fatigue behavior of composite materials (Ziane et al., 2016). The formation of ice on the WTB adds weight to the structure, increasing fatigue (Lagdani et al., 2022). Additionally, other environmental factors are more localized on specific parts of the WTB, such as leading-edge erosion. This phenomenon is related to the impact of dust, sand particles, or water droplets on the WTB surface and is more likely to damage the outer sections of the blade due to their higher relative speed (Hu et al., 2021). If the focus is on fatigue at the blade root section, leading-edge erosion might not be a significant concern due to the low relative speed. However, for a more comprehensive WTB fatigue damage evaluation tool, leading-edge erosion must be considered, as it can damage the WTB structure at the outer sections in the long term.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the author(s) used ChatGPT in order to correct the grammar. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.

ORCID iD

Antoine Chrétien

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Impact of wind turbine nominal power limitation over wind turbine blade remaining useful life and its economic consequences

Abstract

Keywords

Introduction

Resources and hypothesis

Resources

Environmental effects on wind turbine damage

Hypothesis

Evaluation of WTB damage

Simulation of high-frequency wind V H F

Creation of the WTB damage database over 10-minute periods considering V H F

Results and discussion

Conclusion

Footnotes

Appendix

Declaration of conflicting interests

Funding

Declaration of generative AI and AI-assisted technologies in the writing process

ORCID iD

References

Simulation of high-frequency wind $V_{H F}$

Creation of the WTB damage database over 10-minute periods considering $V_{H F}$