What are the benefits of lidar-assisted control in the design of a wind turbine?

This paper explores the potential benefits brought by the integration of lidar-assisted control (LAC) in the design of a wind turbine. The study identifies which design drivers can be relaxed by LAC, and by how much these drivers should be reduced by LAC before other conditions become the drivers. A generic LAC load-reduction model is defined and used to redesign the rotor and tower of three turbines, differing in terms of wind class, size and power rating. The load reductions enabled by LAC 5 are used to save mass, increase hub height or extend lifetime. For the first two strategies, results suggest only modest reductions in the levelized cost of energy, with potentially benefits essentially limited to the sole tower of a large offshore machine. On the other hand, lifetime extension appears to be the most effective way of exploiting the effects of LAC.

the loads that are generated in that condition. Table 1 presents a classification of the DLCs considered here, including a description of the corresponding operating condition. PEMs are obtained via a two-step procedure.
First, the (active) design constraints that determine the sizing of a given wind turbine component are identified; these are termed design drivers. Design constraints are introduced in the structural design process of a wind turbine component to 95 guarantee structural safety during its lifetime, ensuring that admissible values for stress, strain and fatigue damage are never exceeded. Additional constraints are enforced to avoid resonant conditions, to guarantee a safe clearance and avoid collisions between blade and tower, to prevent buckling, and to ensure all other desired characteristics from the resulting design (Bottasso and Bortolotti, 2019). These constraints are functions of the key quantities resulting from the various DLCs, augmented by safety factors as prescribed by the norms. 100 Second, all key quantities responsible for design-driving constraints are analysed, ranked in descending order, labelled with the indication of the originating DLC, and classified as modifiable or blocking. Clearly, the maximum value of a key quantity can only be reduced by LAC if its ranking is led by a modifiable DLC.
For each key quantity, its PEM is defined as the difference between its maximum value and the value of the highest ranked blocking DLC. However, to make the analysis less specific to a given particular implementation, a LAC load-reduction model was used here instead of re-running all DLCs with a given LAC controller in the loop. The load-reduction model is simply represented by 110 a coefficient smaller than one, defined for each key quantity associated with a modifiable DLC. The reduction coefficient is based on results reported in the literature, as more precisely discussed in §2.2.1.
The application of a LAC load-reduction model lowers some of the key quantities, in turn deactivating the associated designdriving constraints. To exploit the slack generated by LAC in the formerly active constraints, a redesign is performed to determine the structure that minimizes a desired figure of merit while guaranteing structural integrity, in turn reactivating the 115 constraints.

LAC load-reduction model
The load-reduction model is based on a literature survey. The study reported in Bossanyi et al. (2014)  that are modifiable -in the sense that they can be affected by a change in the controller-, and also DLC 1.4 (extreme wind 130 direction), 1.5 (extreme wind shear), and 2.1 (control system fault or grid disconnection) should be considered. The first two of these DLCs are not considered in the LAC load-reduction model, because they do not typically generate design driving loads.
The case of DLC 2.1 is however different: here, maximum loads are typically generated during a shutdown, triggered by an extreme ambient condition change, a fault or a grid disconnection. When this happens, the entity of the generated loads will be largely dictated by the behavior of the shutdown procedure, which here is assumed not be assisted by a lidar for safety reasons.

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On the other hand, loads generated during a shutdown might also depend to some extent on the state of the turbine at the time the shutdown was triggered, which does depend on the behavior of the LAC controller. A precise quantification of the effects of LAC on these DLCs would therefore require simulations with LAC in the loop, which are however outside of the scope of the present preliminary work. Hence, LAC-induced load reductions were assumed to be null for these DLCs, which is a conservative choice.

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Clearly, differences in the formulation and tuning of a LAC controller will generally imply different reductions of key quantities. To estimate these effects, the results obtained from various authors were compared. The most complete set of results was found for DLC 1.  To address the conundrum posed by the scatter of the results reported in the literature, a pragmatic approach was used here.
First, Bossanyi et al. (2014) was chosen as reference, because it presents a comprehensive list of effects on several components obtained by using a fairly plain implementation, which might be representative of an initial conservative deployment on production machines. Second, two additional sets of coefficients were added to the baseline ones of Bossanyi et al. (2014), to represent optimistic and pessimistic scenarios. The optimistic scenario is obtained by multiplying the baseline coefficients by 155 a factor of 1.5, whereas the pessimistic one is obtained by using a factor of 0.5. Here again, it is worth remembering that the present study does not target one specific LAC controller, but aims at understanding basic trends.
A distinction must be made between the application of load-reduction coefficients to ultimate loads and deflections, which is straightforward, and to fatigue loads. The former simply consists in the correction of the key quantities obtained by a non-LAC controller with the corresponding coefficients of the load-reduction model. Combined loads -for example at tower base or at 160 the main and blade pitch bearings-are computed from the corrected individual load components.
For fatigue damage, the following procedure is used. Site-weighted DELs are computed as where f (v) is the Weibull probability density function at a wind speed v, while the damage equivalent load at that same wind speed is expressed as where m is the Wöhler coefficient, S r,i is the load range of a cycle i, n is the total number of cycles and N eq the equivalent number of cycles (Hendriks and Bulder, 1995).
To compute LAC-reduced DELs, it is assumed that load reductions are independent of wind speed and load range. This way, the Weibull-weighted DEL reductions reported in the literature can be applied directly to the load time histories obtained 170 here with a non-LAC controller by aeroelastic simulations. Next, transient combined loads are computed from the relevant components (for example, combining fore-aft and side-side components at tower base, and similarly combining the associated components at the main and pitch bearings), and then processed by rainflow counting to obtain DELs, finally searching for the point in the cross section of interest with the maximum damage. is used for offshore turbines. The blade cost for both onshore and offshore models is computed based on the SANDIA model exchange rate. The comparison of the various designs is based on LCOE, which is computed as Aeroelastic analyses are performed with the Blade Element Momentum (BEM) based aeroelastic simulator Cp-Lambda , coupled with a conventional non-LAC controller (Riboldi et al., 2012). The aeroelastic simulator

Economic evaluation
Cp-Lambda is also the core of the wind turbine design suite Cp-Max (Bottasso and Bortolotti, 2019;Bortolotti et al., 2016).
This code can perform the combined preliminary optimization of a wind turbine, including both rotor and tower sizing.
The optimization of the blade aeroelastic characteristics can be divided into two coupled sub-loops, which size the external 190 aerodynamic shape and the structural components. In this work, the aerodynamic shape of the blade is kept frozen, and the rotor is redesigned only from the structural point of view.
The blade structural optimization algorithm aims at minimizing cost, while guaranteeing structural integrity and other requirements by enforcing a set of constraints that include, among others, extreme conditions, fatigue damage, buckling, tower clearance, frequency placement, manufacturability and transportation. The optimization variables include the thickness of the The tower structural sizing aims at minimizing tower cost, while satisfying constraints from extreme loads, buckling, fatigue damage, as well as geometric constraints for manufacturing and transportation. The optimization variables include the diameter and thickness of the different tower segments for given material characteristics.

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The formal description of the design algorithms can be found in Bottasso et al. (2012) and Bortolotti et al. (2016). Optimization is based on Sequential Quadratic Programming (SQP), where gradients are computed by means of forward finite differences.

Results
The potential benefits of adopting LAC in the early stages of the design of the rotor and tower of different wind turbines are 205 analyzed next, following the approach described in Section 2.
are reported in Table 4, while additional details can be found in the corresponding references. These turbines are reasonable 210 representatives of current products available on the market.  turbine, even if slightly higher for some figures, are also in reasonable agreement with the US reference. For the offshore case, a bottom-fixed 5 MW machine is compared to the 10 MW used in the present study. Larger differences are found here, for instance in the OPEX costs, due to the very different rating of the two turbines, although the LCOEs are relatively similar.

Assessment of potentially exploitable design margins
A reduced set of DLCs (IEC, 2005) is identified as the one producing design drivers for the three considered turbines. The 220 set includes power production with normal turbulence (DLC 1.1), extreme turbulence (DLC 1.3), loss of electrical network in normal turbulence (DLC 2.1) and with extreme operating gusts (DLC 2.3). Additionally, parked conditions are also considered in yaw misalignment (DLC 6.1), with grid loss (DLC 6.2) and with extreme yaw misalignment (DLC 6.3).

Tower
A first analysis of the loads and constraints driving the design of the three towers unveils a significant potential that could be by modifiable DLCs. This key quantity for all three turbines is first blocked by DLC 2.1, leading to PEMs between 8% (WT1, ranking position 7) and 21% (WT2, ranking position 28).
The sizing of the shell skin is mainly driven by the fatigue damage constraint (Fig. 3c). This is also the main driver in the design of the webs, elements made of sandwich panels that carry shear. Fatigue damage is driven by the modifiable DLC 1.2.

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However, here the reduction potential is limited by technological constraints that bound from below the thickness of these elements. The load ranking of the combined blade root moment (CBRM) is shown in Fig. 4b, highlighting potential reductions.

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This section aims at quantifying the benefits of integrating LAC within the design of the blade and tower of the three reference wind turbines. To this end, the rotor and tower of each turbine is reoptimized, considering loads and elastic deflections as reduced by the coefficients of the load-reduction model, using the factors of  Both towers of WT1 and WT3 enjoy significant benefits from large reductions in fatigue damage, which decrease mass between 5% for the pessimistic scenario and 17% for the optimistic one. In turn, the lighter weight induces significant reductions 280 in the ICC of both turbines. On the other hand, the annual operating expenses (AOE) show a different behavior. Indeed, the additional expenses generated by the maintenance of a lidar system do not significantly add to the already high O&M costs of the offshore turbine WT1. For the onshore machines WT2 and WT3, where these costs play a larger role, AOE increases by approximately 2%. For all turbines, AEP is essentially unaffected. In the end, the combination of these various effects produces a reduction in LCOE of about 1.2% for WT1, and a very slight increase of 0.1% for this same figure of merit for WT3 (Fig. 5).

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The WT2 tower presents a different trend. Indeed, the upper segment of this tower is driven by buckling. Even though this constraint presents a significant PEM of about 20% (see Fig. 2a Figure 5. Effects of LAC on the redesign of the tower with respect to the initial baselines. Solid bars: load-reduction model of Table 2; whiskers: range of the pessimistic and optimistic scenarios. to the load-reduction model ( Table 2). As a consequence, the redesign is only capable of a limited mass reduction that, in combination with the significant lidar costs, leads to an increase in LCOE.

Taller tower redesign 290
Instead of reducing tower mass (and hence cost), LAC-based improvements in fatigue damage and ultimate loads can be exploited to design taller towers. In fact, by reaching higher above ground, the rotor is exposed to faster wind speeds, thus increasing AEP; thanks to LAC, this can be achieved without significantly increasing the cost of the tower. To explore the effects of this concept, towers of increasing heights were designed. The study assumes that LAC performance does not depend on tower height.

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Here again the study is performed in two steps. First, the tower structure is sized with a non-LAC controller for a given height.
The design objective is minimum mass, constrained to guarantee structural integrity. Next, the design is repeated by reducing the key quantities according to the load-reduction model, according to the nominal, pessimistic and optimistic scenarios. The procedure is repeated for increasing tower heights, until no further improvements are possible or an upper limit of 15% height increase with respect to the baseline is reached.

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The effects on mass, ICC, AEP, AOE and LCOE for the three reference machines are reported in Fig. 6.
Different trends are observed for the three turbines. The offshore machine WT1 shows a larger potential: for each of the analyzed heights, mass reductions with respect to the non-LAC configuration always translate into decreases in ICC. At the same time AEP increases, whereas AOE remains mostly constant due to the already high O&M costs. LCOE decreases gradually as tower height is increased. However, most of the gains are already achieved for a height increase of 5%, which is associated 305 with an LCOE decrease of about 1.5% (Fig. 6e).  Table 2; whiskers: range of the pessimistic and optimistic scenarios.
An opposite trend is obtained with the tower of WT2: because of its different design drivers, this machine does not benefit from a taller tower, as already noted in §3.2.1. The trend indicates that some LCOE improvements might be possible for very tall towers, which were however deemed unrealistic past the upper bound of a 15% height increase.
Similarly, a taller tower appears not to be very promising even for the onshore fatigue-driven WT3 turbine, although for 310 different reasons. Here, although a 5% height increase lowers tower mass and ICC and improves AEP by about 2%, these benefits are offset by an increase in AOE, resulting in marginal -if not completely negligible-benefits in LCOE.

Tower redesign for longer lifetime
Instead of aiming for less expensive or taller towers, as done so far, yet another way to try and exploit the load benefits brought by LAC is to extend the tower lifetime.

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In this case, the baseline towers are first designed for a 20 year lifetime based on the key quantities resulting from a non-LAC controller. Next, the towers are redesigned for increasing lifetime, based on key quantities modified by the load-reduction model. WT2 is excluded from this analysis, because of the very limited importance of fatigue in the sizing of its tower, as shown earlier.
The tower mass of both WT1 and WT3 increases substantially when sizing for a longer lifetime without using LAC. This  Table 2; whiskers: range of the pessimistic and optimistic scenarios.
It should be remarked that these trends are obtained under the assumption of a 100% lidar availability; additionally, because of the approximations implicit in the assumed load-reduction model, these results can only be regarded as preliminary rough trends. However, the use of LAC to design towers with longer lifetimes seems to be much more promising than the alternative strategies of aiming for reduced costs or improved AEP by taller hub heights. Indeed, since the tower cost plays a large role in ICC, reductions in LCOE could be expected by the installation of towers with a longer lifetime. Alternatively, the towers 330 could be reused to support more modern rotor-nacelle assemblies, playing the role of long term support structures that do not necessarily have to be upgraded at the same pace of the rest of the turbine.

Rotor redesign
Only rather modest mass reductions are achieved for the blades of all models and for all scenarios, due to the moderate influence of LAC in design-driving constraints. The situation is more precisely illustrated by Fig. 8, which shows the largest 335 improvements for WT1 and essentially no effect for WT2.
Indeed, the load-reduction model reported in Table 2 shows a larger effect of LAC in fatigue damage mitigation than in the reduction of ultimate loads and deflections. Although webs and shear webs are both driven by fatigue, they are already thin structures with limited reduction potential before the thickness technological constraints become active. In turn, this leads to the fatigue PEMs not being fully exploited. The design of the spar caps is also not largely affected by LAC. In principle, a 340 significant PEM is present for tip deflection, but unfortunately here again the LAC load-reduction model has only modest 2% improvements for this key quantity.  Table 2; whiskers: range of the pessimistic and optimistic scenarios.
For all three turbines, the reduction in ICC generated by the use of LAC in the redesigned rotors is not significant enough to compensate for the increase in AOE. Therefore, LCOE increases for all onshore machines and decreases in a negligible way for the offshore turbine.

Cost sensitivity analysis
Finally, a sensitivity analysis is performed to understand to what extent the purchase and maintenance costs of a lidar system can influence the reduction in LCOE. Baseline values of 100,000 e and 2,500 e/year, respectively for purchase and maintenance, are gradually modified until reaching the limit of ±100% variations. It is assumed that lidar-related yearly maintenance costs are constant throughout the wind turbine lifetime, and are therefore not affected by external factors, such as the replacement of 350 the lidar system. Purchase price includes both the cost and the number of lidar systems required throughout the wind turbine lifetime. The analysis considers the nominal LAC load-reduction model of Table 2 applied only to WT1 and WT3, as WT2 did not seem to have any real potential for improvement.
It should be noticed that purchase and maintenance costs are treated here as two independent variables. In reality, purchase price could be correlated with performance, and therefore it might affect load reductions. Additionally, purchase price could 355 be correlated with maintenance: a higher cost of the lidar could imply a more sophisticated device, which might be more costly to maintain, but it could also be correlated with build quality, which then might be inversely related to maintenance cost. Such considerations would require a sophisticated cost model of the lidar, which was however unfortunately not available for this research. The present analysis, being based on the simple change of the two independent quantities purchase and maintenance costs, could then be interpreted as a price positioning study, where the lidar manufacturer tries to understand the correct price 360 range for the device to make it appealing to customers. Figure 9a shows that only a modest effect in LCOE can be achieved for WT1 when purchase and maintenance costs are modified. On the other hand, an order of magnitude larger effect is observed for WT3 (Fig. 9b), where the incidence of the lidar-associated costs is more prominent given the smaller size and rating of this turbine.
Break-even is indicated in both figures as a dotted line, located in the white area that separates reductions (blue) from Overall, results indicate that only modest reductions in LCOE are possible, even with very low LAC-induced costs. This paper has presented a preliminary analysis on the potential benefits of integrating LAC within the design of the rotor and tower of a wind turbine. The design was performed as a constrained optimization based on aeroelastic simulations, conducted in close accordance with international design standards.
The benefits generated by the use of a lidar in the control of a turbine were quantified through a load-reduction model 380 derived from the literature, considering a variable performance of the LAC system within pessimistic and optimistic scenarios.
This approach, in contrast to the use of an actual LAC controller in the loop, was chosen in order to draw conclusions on trends, rather than on the effects of a specific LAC controller and implementation. Realizing that any such redesign exercise is probably highly problem specific, the study was conducted considering three turbines of different class, size and rating.
Based on the results of this study, the following conclusions can be drawn.

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First, a significant improvement potential was observed when the design is driven by fatigue. Indeed, fatigue damage is primarily generated in power production in turbulent wind conditions. Here, the lidar-generated preview of the wind that will shortly affect the rotor is clearly beneficial: as the controller "sees" what will happen, it can anticipate its action. This is in contrast to the case of a pure feedback controller that, since it can only operate in response to a phenomenon that has already taken place, is by definition "late" in its reaction. In turn, the lidar preview information leads to a general reduction of load 390 fluctuations, and hence of fatigue damage.
On the contrary, the improvement potential is only very limited for components driven by ultimate conditions (such as maximum stresses, strains or blade tip deflection). Indeed, these ultimate conditions cannot always be modified by LAC. In addition, even when LAC plays a role, other factors may have an even larger effect; for example, this is the case of shutdowns, where the pitch-to-feather policy may have a dominant role in dictating the peak response. But even when LAC does relax a 395 driving constraint, an even more general question still remains: shall one design a component based on a driver that was reduced by LAC? If so, what are the extra precautions that should be taken in order to hedge against faults, inaccuracies, misses, or unavailability of the lidar? These issues were not considered here, which is a limitation of the present study. However, it is possible that -at least in some of the cases analyzed in this work-the improvements to ultimate conditions brought by LAC would have to be completely neglected when these additional aspects are considered, or that extra costs would have to be 400 added, for example to ensure redundancy by the use of multiple lidars.
It was also found that, for fatigue-driven towers, significant benefits in mass can be obtained by the use of a LAC controller (on average by about 12% for the cases considered here). However, these benefits are largely diluted by looking at the more general metric LCOE. In fact, only a large offshore machine showed some improvements for this figure of merit: since O&M costs are already high for an offshore turbine, the extra costs due to the lidar play a lesser role. For smaller turbines the situation 405 is different, and the benefits in mass do not repay for the costs of the lidar.
Instead of simply reducing mass, LAC can be used to either increase hub height (which increases power capture in sheared inflow) or to extend lifetime. Both approaches were considered here. The most interesting results were again obtained for fatigue-driven offshore towers. Indeed, a 15% taller tower was found to present approximately the same mass of the baseline, mass than the baseline.
The situation for the rotor is less promising. In principle, spar caps -which are the main contributors to blade mass-could greatly benefit from LAC when tip deflection is the main driver. Here again lidar preview can clearly help when maximum deflections are triggered by strong wind gusts. On the other hand, stiffness requirements caused by the placement of the flap frequency can substantially reduce this margin of improvement, as this is a non-LAC modifiable effect. Additionally, one would 415 have again to guarantee that the safety-critical tip clearance constraint is always satisfied during operation, which might require redundancy of the lidar or other measures. Webs and shell skin are often driven by fatigue, a condition that could in principle be exploited by LAC. However, the improvement potential is limited due to the already limited thickness of these components.
In summary, the integration of LAC into the design of the rotor does not seem to lead to significant benefits in terms of LCOE.
Finally, a simple parametric study on the purchase and O&M costs of a lidar system was performed. As previously observed, 420 the study shows that LCOE is largely independent from the LAC purchase and O&M costs in the offshore case. Although a larger effect is visible in the onshore case, improvements in LCOE caused by reductions in the lidars costs are still quite modest.
This might indicate that, instead of targeting price reductions, lidar research and development should focus on performance. On the other hand, significant price reductions might allow for redundancy, which in turn would enable the targeting of ultimate conditions.

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The present work is based on a number of assumptions, and further work should be performed before more definitive conclusions can be drawn. First, only three turbines were considered; although these machines are reasonable approximations of contemporary products, it is clear that design drivers are quite turbine specific, and a more ample range of cases should be investigated. Second, there was no attempt here to consider radar availability, faults and possible redundancy; an analysis of these aspects would help in clarifying whether ultimate conditions can indeed benefit from LAC or not. Finally, it should 430 be remarked that the use of a generic load model implies some significant approximations. Although this was done here on purpose with the goal of making the study more general, it is also clear that the performance of different LAC systems can be very different, depending on the lidar characteristics and on the controller formulation and tuning. Therefore, here again, more specific studies could find niches of applicability of LAC missed by the present general analysis.
Notwithstanding the limitations of this study, in the end it appears that the answer whether LAC is beneficial or not might 435 not be so clear cut, and in reality the situation is much more complex and varied (and also interesting). In hindsight, this is also a useful reminder that apparently obvious improvements do not always necessarily translate into real system-level benefits. For example, reducing some loads might be irrelevant if the design is driven by other factors, or might not pay off if the cost of that reduction neutralizes its benefits. This also stresses once more the central importance of systems engineering and design for the understanding of the true potential of a technology.

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Author contributions. HC performed the analysis on potentially exploitable margins and conducted the design studies; SL prepared the lidar load-reduction model and assisted in the application of the model in the design framework; CLB formulated the analysis methodology based