Techno-economical Layout and Turbine Type Optimization for Floating Offshore Wind Farms: A ScotWind Portfolio Study

This paper explores state-of-the-art modelling and optimization methods for floating offshore wind farms. A case study is performed on three ScotWind lease areas, where the optimal turbine type and layout is assessed in terms of Annual Energy Production (AEP) using a multiple-step optimization strategy. The numerical setup relies on TopFarm (DTU), ORBIT (NREL) and Peak Wind’s in-house codes and expertise. The portfolio study reveals that across all sites, using wind turbines of higher single capacity (15MW against 11MW and 14MW) is more optimal, as the scaling-up of the nameplate power allows to save costs. The LCOE decreases to around 100$/MWh, which is consistent with the predictions for commercial floating wind projects in the coming years. The optimal layouts show an alignment of the turbines perpendicularly to the prevailing wind direction, in which their spacing is also greater to minimize the wake losses. Sensitivity analyses are carried out on key project-specific parameters and optimization inputs, such as the initial positions of the turbines, showing how a multiple-start strategy explores the whole design space and allows to validate the optima found.


Introduction
In the strive to limit global warming to 1.5 • C compared to pre-industrial levels, drastic reductions in greenhouse gas emissions are necessary.Using cost-effective and reliable low-carbon electricity generation sources is key.Floating Offshore Wind (FOW) allows to exploit strong and stable winds, despite being still a relatively immature technology.ScotWind's seabed tender sets a significant milestone in the commercial deployment of FOW farms.Among the 25GW of offshore wind capacity awarded in January 2022, more than half of it concerns FOW [1].For such projects to be profitable, wind farm optimization becomes crucial.
This paper develops a framework to investigate the most optimal Wind Turbine Generator (WTG) and layout for different ScotWind lease areas, based on state-of-the-art algorithms.Following a system engineering approach, the trade-offs in terms of performance and cost are assessed at different levels, from the WTG to the wind farm and across the sites at portfolio level.The overall goal is to maximize the AEP and decrease the Levelized Cost of Energy (LCOE).
Figure 1: ScotWind lease areas.Adapted from [2] Among the 15 plan options pinpointed by the Sectoral Marine Plan (illustrated in Figure 1), three ScotWind areas have been chosen as case studies.Differences in the capacity and size of the floating wind farm, the location (distance to port), the wind resource (average wind speed and wind rose) and the bathymetry of each site have driven the choice.Some of these parameters are captured in Table 1.given the wind resource from the Global Wind Atlas [4].The optimization algorithm relies on TopFarm, based on Open-MDAO (Multidisciplinary Design Analysis and Optimization) [5].Once an optimal layout with respect to the AEP is found, the Offshore Renewables Balance of system Installation Tool (ORBIT) computes the costs of the project.The model was developed by the National Renewable Energy Laboratory (NREL) and adapted using PEAK Wind's expertise and modelling.Finally, the LCOE is computed, which can be used for the project final decision regarding the layout.

Wake models
The engineering wake model is crucial for the AEP computation.The first models only assumed mass conservation, such as Jensen's top-hat shaped wake [6].However, the representation of the velocity field by such wake models is not realistic [7].Improvements can be achieved using a Gaussian-shaped velocity deficit with the momentum and mass conservation equations, as shown by Bastankhah and Porte-Agel [7] (referred to as Bastankhah model hereafter).

Wind turbines
Following a benchmark of the commercial WTGs available, three different types have been chosen for this portfolio optimization.The parameters are listed in Table 2.The power and thrust curves are approximated using an analytical model implemented in PyWake based on diameter, nominal power, hub height, air density and turbulence intensity.Regarding the station-keeping system, the choice to use semi-submersible floaters is made mainly because of the medium-ranged water depth across the sites and installation ports.A catenary mooring system with three mooring lines and drag embedded anchors is adopted.Except for the mooring footprint driving the spacing constraint, floating-specific parameters are not considered within the optimization loop, but in the cost model calculations.

Optimization strategy
There are several optimization methods.Gradient-based algorithms rely on the evaluation of the derivatives of the objective function [8].The Sequential Least Squares Quadratic Programming algorithm (SLSQP) that uses the SciPy Python library is one of those [9].These methods can become computationally heavy.Gradient-free heuristic methods such as the Random Search (RS) algorithm (DTU Wind Energy by Ju Feng) follow semi-empirical rules and are more powerful with complex optimization problems i.e. many local minima, concavities, flatness [10].The convergence towards a local optimum is usually quicker.Engineering wake model with power and thrust curves A multiple-step strategy was carried out, as done in [11].This allows to combine the strengths of both algorithms, i.e. to explore the whole design space and consolidate the optimum found, as it will be further elaborated in Section 3. The parameters are listed in Table 4.As it will be discussed in 4.1, the initial layout influences the final optimal layout found.The results presented in Section 3 are based on randomly generated initial positions of the WTGs inside the site boundaries and complying with the inter-turbine minimum distance constraint.

Results
This portfolio optimization focused on three ScotWind lease areas.The outcomes for two of them are presented in this paper: Site No. 10 (500MW) and Site No. 2 (2610MW).The results for Site No. 11 (3000MW) showed similar trends, and thus they are not presented here for the sake of conciseness.

Site No. 10 -500MW
The optimization of the smallest project was carried out for each WTG using the multiple-step strategy described in Subsection 2.4.Figures 3 and 4 show the optimized layouts with AEP per turbine and the flow maps (simulated wind from the west) for two of the three configurations: 45 SG 11MW turbines or 33 Vestas 15MW turbines.The case with 35 SG 14MW turbines showed similar results.Each configuration is within the cap capacity of 500MW.
Following trends are observed: first, the WTGs occupy the maximum space so as to maximize the energy capture (no neighbouring wind farms were considered).Indeed, the WTGs placed close or even on the buffer borders produce more energy than the ones towards the inside, as they face stronger winds that are not subject to wake losses for the predominant wind directions (from the south and west, as shown in the wind rose in Figure 3).The turbines that are on the lower and left bounds generate higher single AEPs, around 2.7% more than the ones on the inside of the lease area or close to the north-east boundary.As visible in the flow maps of Figures 3 and 4, the wind speed is slowed down behind the WTGs, going from around 12 m/s to 11 m/s in the far wake.Some turbines face even larger wind speed losses when in the wake of others.
The optimal layout is not a regular grid, but the WTGs can be seen as relatively aligned perpendicularly to the south-west direction, which is the dominant wind direction.Their spacing in this windward direction is greater.This is in accordance with the literature [15].On top of that, by being slightly out of step with each other, the WTGs can produce even more energy, taking advantage of the higher winds blowing from the south-west.
As shown by Figure 5, the highest gross AEP (i.e.including only wake losses) is obtained using 15MW WTGs, but the 11MW WTGs turn out to produce more energy than the 14MW ones for the same cap capacity.This illustrates the non-linearity of the AEP with respect to the WTG size.As it is commonly believed that upscaling the WTGs allows to increase the energy production for the same cap capacity, this is shown to be not the case for this site, comparing the AEP of the 11MW against the 14MW WTGs, due to the complex interactions with the incoming flow.
Overall, having less WTGs but of higher single capacity (15MW) is still more beneficial.The AEP is higher because the WTGs are spaced more, allowing for the wake to recover and thus the WTGs face higher winds.
Computing the total CAPEX for the three WTG configurations, it appears that the costs decrease with the increase of nameplate capacity.This is due to the fact that less turbines result in saved costs, mainly with respect to the system (procurement of the WTGs, substructures, less mooring lines and anchors needed, shorter cable routes).
As the CAPEX is one of the main drivers, the LCOE also decreases, with a drop of almost 5.7% going from 11MW WTGs to 15MW WTGs.Thus, even though the 14MW WTGs produce less AEP than the 11MW WTGs (as highlighted earlier), the costs counterbalance this, leading to a decreased LCOE for the 14MW WTGs.Overall, the LCOE ranges between 104$/MWh and 110$/MWh, which is consistent with the projections for the coming years [16].However, it is important to note that the LCOE is highly sensitive to project-specific parameters such as the Weighted Average Cost of Capital (WACC) that depends on the financing scheme.In this study the LCOE is mostly to be considered in a relative scale between the projects and the WTG configurations.

Site No. 2 -2610MW
This study site is the second biggest floating offshore wind project of all ScotWind areas with a cap capacity of 2610MW.The same multiple-step optimization strategy was carried out and similarly, the number of WTGs is selected such that the cap capacity is not surpassed, that is either 237 SG 11MW turbines, or 186 SG 14MW turbines, or 174 Vestas 15MW turbines.Figure 6 shows the optimized layouts with AEP per turbine for the SG 11MW configuration, the other two cases show similar patterns.Compared with the previous site, the WTGs are not spread across the whole area.Some spots are left with no WTGs, e.g. the lower left corner.This indicates that the optima found are local and not global ones.Indeed, the non-convex and irregular geometry of the site combined with the huge power capacity increase the complexity of the optimization, as the design space is more hilly and multimodal with respect to the AEP (i.e. with many local minima).A way of mitigating this is to use the multiple-start strategy, i.e. rerun the optimization using other initial positions.This is further investigated for Site No. 10 in Subsection 4.1.Regarding the optimized AEP, CAPEX and LCOE, the trends are the same as for site No. 10, with the results summarized in Figure 7.A reduction of 1% in gross AEP is obtained when switching from 11MW to 14MW WTGs, but the 15MW WTGs still achieve a slightly higher AEP (+0.89% compared with 11MW WTGs), as the higher spacing allows an increase in relative wind speed.Costs are saved when upscaling the WTGs (-5.5% from 11MW to 15MW WTGs), consequently leading to a drop in the LCOE.Again, the 15MW WTGs result in the lowest cost of energy and that configuration would thus be the most optimal one.

Sensitivity analysis. Site No. 10
The results shown in the previous section are further analyzed for site No. 10 by means of a sensitivity analysis.The aim is to understand the impact of critical inputs on the optimized layout and the associated AEP.As illustrated with Site No. 2, the need to re-run the optimization several times and use multiple-start strategies are crucial to compare different optimized layouts, thus mitigate the local optimal issue and improve the power capture.The results also show the robustness of the model used as well as the relative importance of each parameter.A summary is given in Table 5.The main parameters influencing the AEP are clearly the wake model used and the turbulence intensity.The following sections focuses on the initial conditions, i.e. the layout that is used as an input to the optimizer.Minimum distance constraint 720 m 1000 m +0.2%

Sensitivity to the initial layout
Several initial layouts are tested to understand their effect on the final AEP following the optimization strategy previously described.A total of ten random layouts are generated for each case.The results for the reference scenario can be observed in Figure 8a.The seeds have been sorted and colored from lowest to highest initial AEP.For each optimization step a mean value is calculated, AEP , as well as the standard deviation, σ.
The mean value increases in a similar magnitude after both optimization steps, it is however important to notice the significantly low computational effort of the RS method compared to the SLSQP one.The standard deviation decreases in both optimization steps.One possible explanation is the similarity regarding in the local optima, which is then exploited by the gradient-based algorithm.
Four seeds are plotted separately in Figure 8b to better understand the correlation between the initial and the final AEP.The largest initial AEP does not lead to the largest final AEP, showing a low level of correlation between the final and initial AEP.The understanding obtained is that several initial conditions should be explored.This multiple-start optimization strategy allows to obtain significant gains in the AEP, especially considering that small improvements can be gained by extending the SLSQP optimization (i.e.increasing the maximum number of iterations or the tolerance).The ten optimized layouts obtained previously in the sensitivity study are analyzed to understand the correlation between the optimal locations.A regularly-spaced mesh is generated, the number of WTGs falling within each mesh cell are counted and summed for the ten layouts.The amount of WTGs per cell is normalized with the largest value.
As Figure 9 shows, some locations are chosen consistently, especially in the corners of the site and along the boundaries, due to the reduced wake effects.Some areas in the inner space are left empty (dark purple).These results are consistent with the optimized layout shown in Figure 3.For all seeds, the optimizer finds as many optimal locations on the borders as possible and the positions of the inner WTGs are changed to avoid wake effects in the predominant wind directions.

Conclusion
Overall, this optimization study across three Scotwind lease areas revealed that using WTGs of higher single capacity leads to a decrease in the LCOE, ranging between 100-110$/MWh.The scaling-up of the FOWTs thus seem to be a key driver.Considering only the energy output, nevertheless, non-linearities in the AEP with respect to turbine capacity were brought to light, showing how increasing it from 11MW to 14MW actually reduced the energy output of the wind farm (keeping the same cap capacity).Also, the optimized layouts were correlated with the wind resource of the sites.Indeed, considering no neighbouring wind farms, the WTGs tend to be placed on the borders.To further minimize the wake losses, the optimal layouts show an aligment of the WTGs perpendicularly to the prevailing wind direction.In this direction, they also have a greater spacing and are slightly misaligned to step out of the wake of the WTG in front.
As the complexity of the optimization increases with the number and capacity of the WTGs (shown with the 2610MW Site No. 2), it becomes crucial to perform several rounds of optimization and to test the framework against various initial positions and different wake models.It allows to mitigate the local optima issue and investigate the design space more broadly.This was performed in Section 4 as part of the sensitivity analyses.The multiple-step optimizations were ran with ten initial positions.The final and initial AEP were not related, showing how using different initial conditions allow to explore the whole design space, with a gain of up to 0.3%.Nevertheless, the optimized layouts were spatially correlated, especially on the site boundaries, validating the trends in the layouts observed in Section 3.
Uncertainties in the resulting AEP can be attributed among others to the wake model used (about 5% changes) and the site turbulence intensity (3%).Further studies should focus on understanding the model uncertainties related to the met-ocean conditions with site data.
In summary, the paper highlights the power of optimization in the early-stage design phase of a FOW project.It is not a straight-forward method, as several strategies and algorithms need to be investigated specific to each site and set of constraints, to select the most robust and fit-for-purpose optimization framework.Also, there is not only one optimized layout but several ones.This specific analysis has shown how the multiple-step and multiple-start optimization strategies can be valuable to this end.

Figure 2 :
Figure 2: Overview of the model

Figure 3 :
Figure 3: Optimized layout and flow map for the 11MW WTGs

Figure 4 :
Figure 4: Optimized layout and flow map for the 15MW WTGs

Figure 7 :
Figure 7: AEP, CAPEX and LCOE comparison for Site No. 2, using Bastankhah wake model, for three different WTGs (SG11, SG14 and V236-15) Seed Highest Initial AEP Seed Highest RS AEP Seed Highest final AEP Seed (b) Evolution of the AEP for selected seeds

Figure 8 :
Figure 8: Sensitivity to the initial conditions for Site no. 10, with Bastankhah wake model and SG11 WTGs

Figure 9 :
Figure 9: Heatmap of normalized number of WTGs in each cell.

Table 1 :
Characteristics of the study sites.Site No. Cap capacity [MW] Area [km 2 ] 2. Methodological Framework 2.1.OverviewA holistic wind farm layout optimization model has been developed by PEAK Wind (PW) using existing tools and its own expertise.Figure2provides a summary of the model.

Table 4 :
Optimization parameters for each optimization stage.

Table 5 :
Summary of sensitivity analysis performed, with Site No. 10 as a reference.