A concept for a Safety and Reliability Control Engineering (SRCE) including a supervisory reliability controller, which uses information about the current state of health, was introduced in and further discussed, for example, in and . In a reliability controller based on the health index, used as a measure for the stat of health, for a mechatronic system was implemented and validated. On the one hand, the application of such an approach for wind energy systems has a high potential due to the highly individual site and turbine-specific operating and environmental conditions as well as ageing characteristics of various components . On the other hand, the complexity of the coupled system, the interaction of wind turbines in a wind farm as well as constraints from operating and maintenance strategies, market conditions, grid requirement and certification processes, nevertheless lead to a challenging interaction between different areas. One of the major aspects for the operation of a reliability controller in a closed loop is the information about the state of health of the considered system. While wind turbines are equipped with various sensors and associated condition monitoring systems (CMS) or structural health monitoring (SHM) systems, the prognosis of the actual state of health and the associated remaining useful lifetime (RUL) still requires a lot of research and development. In , an overview of signal-based monitoring methods with a focus on the usage for online fault detection and advanced control is provided. In , an overview of management and control strategies for wind turbines based on health prognostics is provided. Both papers clearly state that further investigation is needed to determine the state of health. Additionally, the stringent requirements for an adaptive controller due to the multiobjective nature of the problem under various loading conditions is also mentioned. Nevertheless, the full advantage of health monitoring combined with advanced reliability control strategies can only be fully exploited with further development in each of the fields, which can later be combined into an integrated approach.

There are two major advantages which result from the use of closed-loop structure for controlling the reliability. On the one hand, it enables a synchronization with maintenance strategies or planned decommissioning. On the other hand, it allows extending the lifetime of a system by switching to a load-reducing control configuration at any point in time. The latter point is specifically addressed in the concept of life-extending control, for which a concept was introduced in . This concept is more oriented towards fatigue damage and thus also well applicable for wind turbines. The approach was pursued for wind turbine operation in and the associated patent . In the study, the wind turbine actuators are directly modified by a model predictive control algorithm, which receives setpoints for the degradation of the turbine from a supervisory control loop. Comparable concepts based on an online fatigue accumulation using online rainflow counting were also followed by and . The latter is clearly related to the concept of reliability adaptive control, which was explained above. In all three of the applications, the controllers are tested on rather short time frames of at maximum 600 s such that long-term benefits from these methods cannot yet be fully considered. Long-term effects of adapting control strategies during operation for lifetime extension are examined in and . In , the concept of reliability control is implemented by switching between different down- and uprating configurations to follow a predetermined desired degradation for several years. Dependent on the desired target, a lifetime extension by several years can be reached. While the concept of directly adapting the turbine actuators according to the desired planning targets might have a higher theoretical potential because its reaction is more flexible, the concept of switching between different configurations seems to be more straightforward to implement for existing structures for wind turbine and wind farm control concepts. It also facilitates a guarantee for a safeguarded operation in all of the selected configurations. The combination of both concepts might offer additional advantages in the future.

In all of the mentioned work, the aspect of planning the operation up until the end of a wind turbine's lifetime has not yet been addressed in much detail. This becomes even more relevant in the context of wind farm control where the higher-level constraints like the market prices, maintenance strategies and planning of decommissioning are relevant. In , the results of several participants on showcases for wind farm flow control under consideration of electricity prices are discussed. The influence of operation on loads and damage is only considered by one of the five participants for a single turbine. In general, wind farm control has gained growing interest of research and also industry in recent years. One major focus of research was the mitigation of wake effects, which decrease power production but increase loads on downstream turbines . Wake steering by yaw misalignment, but also derating

In general, there are various terms for reducing the power of a wind turbine and the usage often depends on the context. In wind farm control, the term “axial-induction control” is often used. Also, “down-regulation” or “curtailment” are prominent terms. The latter term is often referred to in the context of requests by the grid operator. The term “derating” is used throughout this work.

We assume a basic setup for a supervisory reliability control loop of a wind turbine or a complete wind farm by separating into different stages acting on different timescales. On the real-time stage, the dynamic loads of a wind turbine result from the interaction between the real-time wind turbine controller and the external conditions from the environment and the grid. Those loads slowly induce damage to the wind turbine. The supervisory reliability control loop acts on a time scope of 10 min up to several days because such a time scope allows for an appropriate performance evaluation of the wind turbine in terms of damage progression and power production. On this operating stage, setpoints are sent to the real-time controller of the wind turbine. The planned desired operation determines the targets for this stage which result from the long-term reliability objectives, i.e. the planned damage progression. Because of the dependency between reliability and operation, the desired operation already needs to consider the influence of adaptive control on the damage while at the same time focusing on long-term planning decisions and economic benefits. An overview of a wind farm which is operated using adaptive operation on these two stages is given in Fig. . The long-term planning (”Planning stage” on the left side of the figure) can either be used in an open-loop by providing setpoints to the wind turbine controller for specific input conditions or a target damage progression of the reliability control loop. In both cases, it should cover most relevant deterministic effects on long-term damage progression in an optimal way. Through a closed-loop behaviour on the operating stage, it is additionally possible to react to the actual performance of the wind turbine, including the current state of health and additional current inputs from weather or market price conditions (right side of the figure). At the same time, the long-term objectives are still met. A re-adaption of the planning required when large deviations of the original planning occur or if the long-term objectives change. Thus, it is not a real closed-loop operation, but it can also be applied when open-loop setpoints are sent to the real-time controller. It should just be applied after longer time periods of months or several years.

The long-term objectives for wind turbine operation are specifically driven by fatigue damage progression, which is an important failure mode for wind turbine principal components like the tower and the blades. For an optimal material usage, fatigue budget is ideally fully used up at the desired lifetime while a maximum amount of energy has been produced during this time. Thus, balancing the trade-off between induced damage and power production over the whole range of external conditions and under consideration of their frequency of occurrence is required. The goal is to find a planning method which distributes the fatigue damage optimally over the planned operating time by saving the fatigue budget where it pays off most, i.e. where loads are high but energy production is low. This is possible because of the nonlinear relationship between external conditions, load reducing control features and induced damage. When a turbine is subjected to high wake-induced turbulence, for example, the relationship between induced damage and produced energy is definitely worse than for a turbine operating at the same wind speed at a low turbulence. The key question for an optimally planned target distribution is to decide by how much the damage should be reduced through adaptive control so that the long-term objectives are met. To answer this question, a method to find an optimal planning through mathematical optimization for an individual wind turbine is developed.

In order to create a planning method which fulfils the objectives, the complete process from an adaptation of real-time wind turbine control to the evaluation of long-term goals and requirements needs to be covered. During this process, the influence on damage progression of relevant deterministic external conditions is just as important as that of real-time controller setpoints.

The key part of our proposed method consists of the formulation of a mathematical optimization problem, where the aim is to meet long-term objectives, such as maximum power or revenue over the entire lifetime, by finding an individual trade-off between induced damage and power production for each relevant operational condition.

For application of our method to a given system, it is crucial to know how it interacts with its environment. For this, the system boundary must be well defined beforehand. It forms the basis for definition of environmental inputs, for setpoints of the real-time controller, as well as for the damage of different failure modes and performance measures such as energy production.

We identified a four-step process to create the optimal planning for this well-defined system within its boundaries (Fig. ). For optimizing the distribution of the fatigue budget over the system's lifetime, it must be possible to evaluate the effect of changes in the setpoints of the adaptable real-time controllers with low computational effort. The setpoints of the real-time controller of the system directly influence the trade-off between induced damage and energy production. Once the adaptable real-time controller is provided, surrogate models can be set up. They represent the relationship between external conditions and setpoints of the controller to damage and energy. These steps 1 and 2 are necessary but existing prerequisites for the long-term optimization of the operation. They need a careful selection and have a strong influence on the quality and the validity of the results. The optimal operational planning is found by steps 3 and 4 of the process. Both of the steps are part of the proposed long-term planning method which we name value-integrated optimization of lifetime asset operation (VIOLA). The optimization problem is developed in step 3. This step still yields multiple results, where each one represents an individual trade-off between energy production and damage. The selection of a single optimal planning becomes possible by evaluating economic aspects of the results from step 3. The four steps not only allow for a feasible computation time, but they also lead to an easily explainable result after each step, which is in high contrast to more integrated approaches. The four steps can principally be applied to any system which is subject to a strong coupling of control setpoints and external conditions. Due to the high influence of wind conditions on the fatigue damage to wind turbines, wind energy systems represent a prime example for its application.

The above-mentioned four-step process forms the core of the remaining paper. At first, the theoretical background and a more in-depth explanation for the approach are given in Sect. . The process is demonstrated with an application example. The focus of the example is to effectively reduce power of a considered turbine under conditions where high loads are induced from wake-induced turbulence of neighbouring turbines. In Sect. , the considered system is defined. Also, its prerequisites are introduced and implemented, resulting in surrogate models usable for the optimization. Afterwards, the long-term optimization process VIOLA is presented and applied to the example in Sect. . The process and the results are discussed in Sect.  before the findings are concluded, and an outlook is given in Sect. .

We focus on optimal operation of a single turbine within a wind farm. This means that effects from the surrounding wind farm have to be taken into account as well. These include mainly the wake effects from other turbines, which act on the considered turbine and are, under normal operation, a significant driver of its loads. Each single considered turbine will thus be able to react to the wake effects from the surrounding turbines, but the effect from changes in control on the wake cannot be considered yet.

The primary objective of a wind turbine controller is to maximize power production while meeting the requirements of a grid operator . Additionally, secondary objectives, such as load reduction, are pursued during control design. This can be achieved, for example, by implementing features for reduction in loads on specific components. Examples are exclusion zones to reduce tower vibrations or individual pitch control (IPC) to reduce fluctuations in blade root bending moments. However, these secondary objectives usually force the controller to deviate from optimal operation with regard to its primary objectives. Some secondary objectives might even compete with one another, e.g. blade root loads and pitch actuator activity for IPC. We now assume that the balance between primary objective and secondary objectives can be selected externally by adapting the controller through a control setpoint.

In Sect. , we already introduced the control setpoint as u(x). We assume this to be an abstract value which can be selected based on the external input conditions x. Thus, u is a vector of controller setpoints, which in turn reacts by adjusting its own internal parameters. In a larger wind farm system, which is composed of multiple turbines, which uses wake steering or wake reduction, u(x) could be the yaw angle or the amount of power derating . Within the remainder of this paper, we assume a one-dimensional control setpoint for the power derating of a single turbine. This is a commonly available input, as reduced power capability is also requested by grid operators to mitigate grid congestion. There are several studies which investigate derating methods with respect to various objectives. These methods include power regulation for the grid, wake reduction or loads. In , several studies on derating (or axial-induction control) are summarized and sorted into the mentioned categories. Many studies investigate load reduction as a side effect, while the main objective is either the power regulation or reducing the wake on the downstream turbine.

Within the system boundaries of this study, the main objective is not to determine the best fitting derating method for the generic wind turbine, but to show the benefits of using derating for an optimal planning. Therefore, the choice is conducted based on the findings from the literature and from previous experience with the generic IWT7.5 wind turbine, and not through an extensive study and tuning of the controller under various conditions. Also, no additional features, such as individual pitch control or active dampers, are activated. For a real-world application, fine-tuning the controller for every derating configuration would be beneficial and could lead to an improved performance with respect to loads and power. The IWT7.5 is controlled with the IWES research controller . The derating method is implemented such that it reduces power in partial and in full load by a percentage factor δP∈ [δPmin=50%,100%]. Such a derating method is referred to as proportional delta control in or percentage reserve in .

In partial load, both tower and blade fatigue loads should be decreased. To do so, the constant-λ method is implemented , because we expect a positive effect on these loads based on the literature, and we avoid potential negative effects like a near-stall operation as, for example, by using the minimum-thrust strategy. This is achieved by finding the steady-state pitch angle β so that the reduced power coefficient δPcp is found while λ is kept constant. From these values, the parameters for derated operation can be computed.

In the full load region, the torque setpoint is normally reduced for derating. This allows for a fast recovery of power when derating is no longer required, and is thus beneficial for ancillary services . However, it only has a minor effect on the fatigue loads of the blade and the tower. Reducing the generator speed mainly has a strong positive effect on the blade loads in the flapwise direction , while reducing the torque has a positive influence on the driving torque loads . The effect on the tower loads are quite turbine dependent because a reduction in generator speed can reduce oscillations to some extent but often also increases them due to the lowered aerodynamic damping . Therefore, a mixed method between reducing torque and speed might be advantageous, again depending on individual objectives and turbine characteristics. Both methods are combined for reducing the rated generator torque Mr and ωr.

In Fig. , the operating points of the controller for the selected setpoints are presented. Figure a shows the speed–torque curve of the controller. The end point of the curves always determines the combination of Mr and ωr. By comparing the progression of these curves, the effect of both strategies can be observed. In partial load, the constant-λ strategy determines a specific combination of parameters including the static pitch angle. The steady-state operating points of the pitch-angle are plotted over the wind speed in Fig. b. In combination, this results in the steady-state power curves which are shown in Fig. c.

The control setpoints can then be used as optimization variables in the formulation of a mathematical optimization problem. However, using them directly within an optimization requires full simulation of respective load cases, which is not feasible due to the required computational effort. Instead, surrogate models can be set up which abstract the whole turbine–controller interaction.

Surrogate models, sometimes also called meta-models, are a necessary prerequisite for evaluating and optimizing different influences on damage over long periods of time. For wind turbines, they have gained growing research interest to cover the influences of various external conditions and control on fatigue damage. They have in common that aero-elastic simulations are used to create a database of fatigue loads for various input conditions. In Fig. , those aero-elastic simulation models are denoted more generally as higher fidelity models on the seconds scope. The surrogate model is created by performing multiple simulations for a pool of input samples. Due to the relationship between damage increments and DELs, the surrogate models can be calculated on the basis of the short-term DELs. Thus, the strong nonlinearity due to the Wöhler exponent does not have to be considered, and the damage increments can be calculated using Eq. (). The short term DEL DELfmst(z) is obtained through aero-elastic simulations of the wind turbine model and a subsequent evaluation using the rainflow counting algorithm and Eq. ().

By using surrogate models to compute damage and energy increment, additional uncertainties are inevitable when calculating long periods of time. At the same time, the load calculation of wind turbines is always associated with uncertainties due to the stochastic influences of the wind . This must be taken into account when creating surrogate models. Depending on the application and effort, different requirements are made on the surrogate models. For example, more accurate models are required for fatigue tracking or for calculating the remaining service life than for use in an optimization. Here, fast evaluation and good mapping of the correlations between optimization variables and initial values are of particular importance.

In this work, the surrogate is considered as an existing prerequisite with various suitable approaches from the literature ranging from Gaussian regression (often referred to as kriging) to polynomial chaos expansion to artificial neural networks . A good overview of different surrogate methods and a comparison of their performance is given in . Despite their known lower accuracy compared with some of the other methods, we select multidimensional polynomial regression models for the DELs due to their suitability for optimization, their simple usage, their differentiability and their fast training and evaluation time. For the electrical power, a linear interpolation is used.

The pool of input conditions is created with a full-factorial sampling for the wind conditions x together with the percentage power u(x)=δP(x). The sampling values are provided in Table . While wind speed and power are sampled equidistantly, the sampling of the TI values is selected so that the distance between the samples increases exponentially, as indicated by the formula in Table . This reduces simulation time and still creates enough data in situations with high occurrence. To account for the randomness in the incoming wind, various realizations of the same mean input characteristics are usually simulated; those are determined through pseudo-random seeds. For the simulations performed in this work, 6 simulations of 10 min on the seconds scope are performed to obtain a damage increment on the minutes scope with the time increment Δt=60 min = 1 h as is standard for DEL calculations.

To obtain the parameters of the polynomial regression model for the DELs, a least squares approach is used. The maximum order of the polynomial is set to 5. The value is found by cross validating different orders of the polynomial between 1 and 8. For the further usage of the surrogate models, it is particularly important that the influence of the derating setpoint at the different input condition be correctly represented. For all three failure modes, a general agreement of the surrogate model to the data can be observed. Figures  and exemplarily show the evaluated surrogate model (solid lines) as well as the simulated training data (dots in same colour as solid line) when one of the input conditions is set to a fixed value. The DELs are normalized with respect to the fixed values (v= 8 m s-1 and TI =16 %) at the nominal percentage power δP=100 %. The power is not explicitly shown here because its behaviour, dependent on wind speed, directly derives from the control setpoints (cf. Fig c). In general, the accuracy of the fit for the flapwise BM and the tower base BM is lower than that of the edgewise BM. These loads are more strongly influenced by the turbulence of the wind and thus also have a higher uncertainty in the simulated DELs. Especially for the tower, the high variation in the simulation data makes it difficult to create a surrogate model. Also, the relative mean error on the complete dataset is highest for the tower BM (error = 3.88 %), compared with the error in the flapwise BM (2.32 %) and the edgewise BM (0.23 %).

The behaviour of the DELs depending on the control setpoints will now be briefly discussed. Figure  shows the results with the wind speed v on the x axis for different values of percentage power δP=100 % with a fix TI = 16 %. Both, the flapwise and the tower DELs (DELflapst and DELtowerst), strongly increase with the wind speed (cf. Fig. b and c), while the DELs of the edgewise BM DELedgest reduce when the rated wind speed is reached at 12 m s-1 and the turbine starts pitching (cf. Fig. b). The reduction in DELedgest depending on δP=100 % directly relates to the lower rotational speed through the control setpoints at each wind speed. Thus, it has a stronger effect at 90 % and 80 % when the rotor speed is lowered by a higher amount than the generator torque to achieve the power setpoint. The decrease in DELedgest is also rather small compared with the other two failure modes, where the relative difference in DELs is much higher. The DELflapst can be reduced for almost all wind speeds (cf. Fig. b), but not by the same amount. The DELs of the tower BM show a much less clear relation to the percentage of power. For low wind speeds, the values of DELtowerst also decrease with the lower values of δP=100 %, but with some significant variation within the simulated data points. For higher wind speeds, reducing the power can even increase the tower loads, and the relation is not completely deterministic. This effect is caused by the reduced aero-dynamic damping due to the rotor speed reduction or from resonance effects.

Figure  shows results with TI on the x axis for different values of δP with a fix wind speed v= 8 %. The DELedgest is not significantly influenced by the turbulence. The load reduction in the edgewise DEL is low compared with the other two failure modes. For the flapwise bending moment and the tower bending moment, the strongest relative reduction can be achieved by reducing the power to 90 %, but more derating still decreases the DELs slightly further. The relative load reduction also increases with increasing turbulence.

The results presented in this section show several aspects which are relevant for the optimal planning approach. The selected method for derating is suitable to reduce the short-term DELs and thus the damage increments of all the failure modes. Also, the surrogate models are able to cover the nonlinearity sufficiently to be used for further optimization. The optimal planning approach can make use of this to determine when a load reduction should be favoured over a higher energy production. This can especially be done by exploiting the fact that higher turbulence significantly increases loads, but the power production remains almost the same. This effect is even strongly enforced from the relation of the short-term DEL to the damage increment because the value is raised to a higher power by the Wöhler exponent (see Eq. ).

Developing the mathematical optimization process for finding the operational strategies is the central part of this work. Neglecting economic factors and other influences and restrictions for the total value of a farm at first, it is ecologically most beneficial to get the maximum amount of energy over the lifetime τlife of the turbine while the fatigue budget of each component is fully used up. Therefore, the total energy for a given target damage budget is maximized over the fixed reference time τref. The operational strategy u‾={u(xj)}j=1Bx is optimized for each of the external conditions which were previously selected by the definition of the system boundaries. It follows that the number of selected independent control setpoints, defined by Dim(U) and the number of bins which are used for the external conditions Bx, determine the number of optimization variables, which is equal to Bx⋅Dim(U). Within the scope of this work Dim(U) is equal to 1 because a single derating strategy will be applied. With a fixed known target fatigue budget Dfmtarget for failure mode fm∈F, the optimization problem is formulated as 22maxu‾∑j=1BxP(xj,u(xj))href(xj)subsetto∑j=1Bxdfm(xj,u(xj))href(xj)≤Dfmtarget,∀fm∈F. Using this simple and compact formulation, it is possible to spare the fatigue budget when the damage increment is high compared with the energy increment. When the damage of all failure modes is reduced compared with a baseline operation u‾ref, i.e. Dfmtarget≤Dfmref, the turbine can be operated for a longer time and ultimately more energy can be produced.

The optimization problem is solved by using the gradient-based interior point algorithm for constrained nonlinear optimization problems . The process itself is formulated with Python and the optimizer is interfaced through the library pygmo , which builds on the C++ library pagmo . Gradients are computed using finite differences. Optimization runs were executed on a laptop with an Intel i7 four-core processor, 2.1 GHz speed and 32 GB RAM. The execution time of each run ranges from several minutes to several hours, depending on the specified target damages. The optimizer typically needs between 100 and 500 iterations to converge. As starting values, the reference strategy with 100 % power production at each turbine was always used, which is a nonoptimal but feasible solution. All optimization runs show plausible results in terms of an improved relationship between the energy increment and damage increment. For this reason, no explicit variations of the starting values were required to check for convergence to local minima.

Clearly, the solution strongly depends on the selected failure modes, their behaviour with regard to the damage rate determined from the surrogate models and on the target fatigue budget. When several failure modes should be optimized simultaneously, it might be impossible to fulfil the constraints and no solution can be found. Therefore, the selection of the target budget strongly depends on the specific problem which relates to a specific wind farm or wind turbine. The formulation in Eq. () provides a clear separation of the technical aspect from the economic aspect and therefore allows investigating the relationship between damage progression and energy production for different components under consideration of the operational strategies over long periods of time. It can also directly be used to create a Pareto front between damage and energy production by principally applying the epsilon constraint method for multiobjective optimization , i.e. by fixing various combinations of the target values Dfmtarget. We pursue this approach in this work and select a specific strategy based on further information in the final step 4.

With the presented optimal planning approach, higher total energy yield can be achieved with lifetime extension, which is made possible by accepting lower annual energy production throughout the lifetime. This reduction in annual energy has a significant impact on the overall value of the wind farm, especially when taking into account economic factors that include loan repayments and the value of the money. This aspect is considered for the evaluation and selection of the operational strategies under consideration of a basic financing model. Through this first evaluation, the difference between a pure maximization of energy from the materials used and additional factors can be emphasized. We use the net present value (NPV) for this.

The optimization process builds on the usage of surrogate models. They implement the deterministic relationship from inputs to damage and energy increments on the minutes scope. Within these models, the limits and uncertainties of various partial effects are aggregated. This includes the modelling of input conditions, the high-fidelity simulation model on the seconds scope, the calculation of damage increments and finally the selection and training of the surrogate models themselves. The modelling approach for each of these is very closely linked to the specified system boundaries.

For the application example, we have limited ourselves to two main environmental conditions and one controller setpoint as considered input conditions. These inputs define a subset and can be extended for both, environmental conditions and the possible setpoints. Fatigue damage of structural components is represented by three main failure modes. (Discussing the complexity of fatigue damage modelling goes beyond the scope of this paper; instead, readers are referred to, for example, , which provides an overview about developments in this field.)

Regarding the environmental conditions, further influences like wind shear, yaw misalignment and wave effects for offshore wind farms can be considered. In addition, the wake effects of surrounding wind turbines can be modelled with a higher level of detail to cover effects like partial wake overlap or wake meandering. This requires an extension of the models on the minutes as well as the seconds scope.

The control setpoints of the real-time controller act as inputs to the surrogate model and as influencing variables for the optimizer. Thus, by extending the number of controller features which can be adapted and used as optimization variables, the possibilities for balancing damage under various environmental conditions increase. It would be ideal to directly optimize the control parameters under all influencing load conditions and select the trade-off according to the overall objectives, including their frequency of occurrence. Such an approach is not computationally feasible due to the need for load simulations under each condition in combination with a control parameter. Therefore, extending the possibilities of the real-time controller combined with a smart pre-selection of further control setpoints, such as allowing for partial overload or wake steering, will lead to more degrees of freedom for the long-term operational planning. With limited computational capacities, a balance between accuracy, degrees of freedom, interpretability of results and also enhancement of the approach needs to be found for specific use cases and for the optimization process itself. To assess the importance of various influences on the results, sensitivity analysis could be performed, but this is beyond the scope of this paper.

While partial models could theoretically be improved until they provide a perfect representation of reality, the forecasting over long periods of time will always be subject to remaining uncertainties. Therefore, prediction of the future always contains assumptions, which are usually modelled by a probabilistic approach. For the long-term forecast, one can distinguish between the technical part, where the forecast of environmental conditions influences the fatigue damage calculation, and the forecasting of the economic developments. This is affected by many unknowns from the global market and even politics.

Regarding the technical part, we use the classical approach for the computation of fatigue damage by covering the long-term forecast by a relative frequency distribution derived from site-specific measurements from the past. In combination with partial safety factors, such an approach is suitable for estimating a conservative design fatigue budget. Nevertheless, they neglect some important influences like annual variations of the wind . Also, long-term changes in the weather due to climate change could become relevant. found an insignificant influence on fatigue life compared with other influences but pointed out their potential influence with improved methods. For a more detailed estimation for each individual turbine, probabilistic approaches for the fatigue damage prediction using surrogate models can be used, e.g. by using Monte Carlo simulations with a representative time series or by using stochastic distributions for modelling the uncertainty . Due to the high computational effort, such approaches are less suitable for the use within an optimization loop. The probabilistic approach for fatigue life prediction is strongly connected with the choice of inputs for the models. One also needs to distinguish between conditions which can be influenced by control setpoints of the controller, and conditions which cannot be influenced (e.g. idling) but which nevertheless contribute to the overall damage process. Therefore, it is also possible to reduce uncertainties with further details in the models. To determine the overall risk, it is required to assess the uncertainties of the partial models and the forecasts.

In our current implementation of the proposed method, a very basic approach for the financial part, i.e. computing the asset value, is implemented. Regulatory and legal framework conditions are excluded from the model, as they can change over time and are strongly dependent on the specific location. Also, our focus is on showing the technical feasibility. Covering all regulatory aspects and expected, planned or coming legislation is a highly specialized but separate task. Nevertheless, the current approach can be supplemented with further inputs to reduce the uncertainties. Also, other value metrics, such as the cost of valued energy (COVE), could be integrated . A highly significant influence is the price of electricity, which is not constant over the entire lifetime.

In summary, the amount of detail in the mathematical optimization process has to be a deliberate decision. This decision also depends on other parameters like the available computational power and the optimization method. With the current subdivision into two parts – the technical, deterministic optimization in step 3 and the subsequent selection based on additional (economic) factors in step 4 – the mathematical optimization problem can be solved with low computational effort, and the deterministic solutions are well understandable and interpretable. Nevertheless, several drawbacks to our approach remain and are discussed next.

Without any limitations on computational power and time, the robust optimization approach which directly maximizes the asset value as an objective containing further inputs like, for example, reliability models, component replacement costs and forecasts of the market, including their probabilistic uncertainties, would be ideal. To approach such an ideal solution within given boundaries, several smaller steps can be made.

The deterministic optimization method is currently limited to a single turbine. The influence of the turbine controller on the wake and thus on surrounding turbines is neglected. To extend our approach to an entire wind farm two possible solutions exist. The first way is to optimize operation of all turbines once, but this could increase the size of the optimization problem beyond feasibility. The second solution could be to iteratively cycle through computing inflow conditions for an individual turbine from a wind farm flow model and then optimize operation for each turbine separately for their respective inflow conditions. We expect such an approach to converge after a few cycles while keeping computational requirements at bay and scaling well. Both solutions allow a combination with farm control solutions, such as wake steering.

Overall, any deterministic solution of a single turbine or an entire wind farm requires the specification of an individual target damage for each selected failure mode. Here, the specification of a desired target reliability level for the components of each wind turbine could be covered by probabilistic reliability methods. Further research is required to assess how this can be integrated with the current method. It also needs to be investigated how the computation of any value metric can be integrated into the optimization approach, either directly within the mathematical optimization or for a subsequent selection of Pareto-optimal operational strategies.

To cover the forecast of volatile market prices within the deterministic mathematical optimization, the annual frequency distribution of input conditions can be extended with another dimension for price and thus a combined probability for wind and price, similar to the approach in . In addition, an annual selection of the trade-off between energy and damage could be integrated into the optimization. This way, it would be possible to allow for a higher damage progression at the beginning to reduce the interest burden and to reduce the damage progression of the turbine later.

One aspect, which cannot be covered by the current planning approach, is considering sequence effects, i.e. dependencies of future damage progression on previous damage. With the use of frequency distributions for long-term effects, linearity of damage progression is inherently assumed. To consider sequence effects, the current approach can at least be used as an initial planning step, partially covering the linear part of a damage progression process.

Regardless of the limitations, the results of the application example show how a condition-based long-term planning approach can realize a targeted fatigue damage progression. It balances the trade-off between induced damage and energy production under the given system boundaries and constraints of the application example optimally. It is possible to apply the method to a real-world scenario when the system boundaries are well defined and adapted to the specific use case. In a first step, the provided planning strategy can be used in an open-loop scenario, where the turbine follows the planned setpoints. The open-loop approach can also be used to extend the lifetime after the turbine has already been operating for a significant time span. If the approach is applied during the design process, it could be used to save material through a less conservative design or to optimize the power curve as part of the real-time controller. In a second step, the approach could be further developed into reliability-adaptive control, where measurements of turbine operation are fed back into continuous re-planning, thus forming a closed-loop controller as presented on the right side of Fig. .