Wind farm optimization with multiple hub heights using gradient-based methods

This article presents a framework to integrate and optimize the design of large-scale wind turbines. Annual energy production, load analysis, the structural design of components and the wind farm operation model are coupled to perform a system-level nonlinear optimization. As well as the commonly used design objective levelized cost of energy (LCoE), key metrics of engineering economics such as net present value (NPV), internal rate of return (IRR) and the discounted payback time (DPT) are calculated and used as design objectives, respectively. The results show that IRR and DPT have the same effect as LCoE since they all lead to minimization of the ratio of the capital expenditure to the energy production. Meanwhile, the optimization for NPV tends to maximize the margin between incomes and costs. These two types of economic metrics provide the minimal blade length and maximal blade length of an optimal blade for a target wind turbine at a given wind farm. The turbine properties with respect to the blade length and tower height are also examined. The blade obtained with economic optimization objectives has a much larger relative thickness and smaller chord distributions than that obtained for high aerodynamic performance design. Furthermore, the use of cost control objectives in optimization is crucial in improving the economic efficiency of wind turbines and sacrificing some aerodynamic performance can bring significant reductions in design loads and turbine costs.

Offshore wind energy development along the East Coast of the US is proceeding quickly as a result of large areas with an excellent wind resource, low water depths and proximity to large electricity markets. Careful planning of wind turbine deployments in these offshore wind energy lease areas (LA) is required to maximize power output and to minimize wake losses between neighboring wind farms as well as those internal to each wind farm. Here, we used microscale wind modeling with two wake parameterizations to evaluate the potential annual energy production (AEP) and wake losses in the different LA areas, and we developed and applied a levelized cost of energy (LCoE) model to quantify the impact of different wind turbine layouts on LCoE. The modeling illustrated that if the current suite of LA is subject to deployment of 15 MW wind turbines at a spacing of 1.85 km, they will generate 4 to 4.6% of total national electricity demand. The LCoE ranged from $68 to $102/MWh depending on the precise layout selected, which is cost competitive with many other generation sources. The scale of the wind farms that will be deployed greatly exceed those currently operating and mean that wake-induced power losses are considerable but still relatively poorly constrained. AEP and LCoE exhibited significant dependence on the precise wake model applied. For the largest LA, the AEP differed by over 10% depending on the wake model used, leading to a $10/MWh difference in LCoE for the wind turbine layout with 1.85 km spacing.

Floating offshore wind, far less constrained by water depths than bottom-fixed, has great potential in the Mediterranean Basin. The levelised cost of energy (LCOE) is arguably the single most reliable metric to measure the viability of energy projects. In this work, the levelised cost of energy for floating offshore wind is mapped for the first time in the European and Eastern Mediterranean with a detailed cost breakdown and a focus on semi-submersible platforms. A multi-parameter analysis is conducted in a case study to discern the effects of specific elements on the LCOE. Expressions are formulated as functions of site-specific variables: distance to shore, water depth and annual energy production. The latter is estimated accurately by combining the power curve of an exemplar wind turbine with hindcast, site-specific wind data. The mapping shows the paramount importance of the wind climate, i.e., the resource, for the LCOE. The lowest values (~95 €/MWh) occur where the wind resource is most abundant, i.e., the Gulf of Lion and the Aegean Sea. The highest values (>250 €/MWh) are found where the resource is scarce, i.e., around the Balearic Islands and in the North Adriatic, Tyrrhenian and Levantine Seas. Moderate values of the LCOE (130–180 €/MWh) occur off South Spain (Alboran Sea), Sardinia, Sicily and Malta, and in the South Adriatic. In addition to the local wind resource, other parameters that play a relevant role in the LCOE are those related to the production of energy (number of turbines in the wind farm and installed power), on the one hand, and to substantial sources of costs (cost of turbines and substructure), on the other, as well as the project lifetime and discount rate. These results identify hotspots for the deployment of floating offshore wind in the Mediterranean and opportunities for cost reductions, and contribute to decision-making in a region much in need of renewable energy.

This study compares the performance of two wind farm sites located in Northern Europe: an onshore site and an offshore area in the eastern Baltic Sea region. This study investigates the optimisation of wind farm performance within a fixed project area by maximising annual energy production (AEP) and increasing energy density. Three wake-loss scenarios (≤10%, ≤15%, and ≤20%) were examined to assess the sensitivity of layout optimisation to aerodynamic interaction constraints. Several layout configurations were analysed to reduce wake losses and enhance overall energy output. Wind conditions were assessed using NORA3 reanalysis data, and wake interactions were modelled using the Jensen wake model to estimate AEP. Both wind farms were further compared across key criteria, including cost, power generation efficiency, installation and maintenance requirements, and site availability. Offshore wind farms achieve 1.5–1.7 times higher energy density under similar spatial conditions. However, offshore levelised cost of energy (LCOE) remains roughly 25% higher due to higher capital and infrastructure costs, while onshore LCOE demonstrates better economic performance, driven by lower CAPEX and O&M expenses. The findings highlight the trade-offs between cost efficiency and wake-driven energy performance for onshore and offshore wind development in the eastern Baltic Sea region.

Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9% reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2%. Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.

Unravelling historical cost developments of offshore wind energy in Europe

In this study, economic evaluation of large-scale floating offshore wind farms(OWF) is conducted. The floating wind turbine is not limited by water depth, so it can be installed in the sea far from the coast, and also expected to increase the productivity of electricity energy due to higher mean wind speed. As the cost of the project increases as the distance to shore increases and the capacity of the power generation complex increases. However, as the distance to shore increases and the capacity of the offshore wind farm increases, the project cost will be increased. Therefore this research is needed to confirm whether it is economically sustainable. The case models to be evaluated are a 400㎿ and 480㎿ wind farm. The cost model is composed of the installation and operating cost of the floating offshore wind farm. In particular, the electricity production and income are calculated by applying the wind speed model according to the transmission line distance and the electricity energy price according to the renewable energy certificate(REC) weight. Economic analysis is evaluated on annual energy production(AEP), net present value(NPV), cost-benefit ratio(B/C ratio), and levelized cost of energy(LCOE).

This study explores the smoothing effect on the uncertainty of the wind power fluctuations that affect a power system at points of common coupling. Set pair analysis is applied to evaluate the similarity between the power fluctuations of a single wind turbine and those of all aggregated wind turbines, based on which a quantitative index describing the wind power smoothing effect is proposed. The smoothing effect characteristics of a wind farm cluster are investigated for different numbers of wind turbines, different wind speeds, different seasons, and multiple sampling intervals. A significant smoothing effect is usually observed at a shorter sampling interval and a higher wind speed, and the smoothing effect index increases with an increase in the numbers of wind turbines and farms. Additionally, the correlation between the smoothing effect of aggregated wind farms and the forecast accuracy for the corresponding aggregated power output is examined. The experimental results indicate that the wind power forecast accuracy varies with the smoothing effect index, which is influenced by the number of wind farms. Furthermore, the aggregated output from a wind farm cluster with a higher smoothing effect index exhibits better forecasting performance than that from a single wind farm, showing that the trend of the wind power series becomes smoother due to the smoothing effect, thus enabling one-step-ahead wind power forecasting with higher accuracy.

Differences in wind farm energy production based on the atmospheric stability dissipation rate: Case study of a 30 MW onshore wind farm

<strong class="journal-contentHeaderColor">Abstract.</strong> Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses; hence, there is a need for numerical models that can properly simulate wind farm interaction. This work proposes a Reynolds-averaged Navier-Stokes (RANS) method to efficiently simulate the effect of neighboring wind farms on wind farm power and annual energy production. First, a novel steady-state atmospheric inflow is proposed. This inflow model is well suited for RANS simulations of large wind farms because it does not lead to the development of nonphysical wind farm wakes. Second, a RANS-based wind farm parametrization is introduced, the actuator wind farm (AWF) model, which represents the wind farm as a forest canopy and allows to use of coarser grids compared to modeling all wind turbines as actuator disks (ADs). When the horizontal resolution of the RANS-AWF model is increased, the model results approach the results of the RANS-AD model. A double wind farm case is simulated with RANS to show that replacing an upstream wind farm with an AWF model only causes a deviation less than 1 % in terms of wind farm power of the downstream wind farm. Most importantly, a reduction in CPU hours of 74.4 % is achieved, provided that the AWF inputs are known, namely, wind farm thrust and power coefficients. The reduction in CPU hours is further reduced when all wind farms are represented by AWF models; namely 89.3 % and 99.9 %, for the double wind farm case and for a wind farm cluster case consisting of three wind farms, respectively. For the double wind farm case, the RANS models predict different wind speed flow fields compared to output from simulations performed with the mesoscale Weather Research and Forecasting model (WRF), but the models are in agreement with the inflow wind speed of the downstream wind farm. The double wind farm case is also simulated with the TurbOPark engineering wake model. Similar wake shapes are reproduced by TurbOPark but the model predicts a larger wind farm wake magnitude compared to RANS and WRF. TurbOPark predicts much better results when its ground model is switched off and a wake expansion coefficient of 0.06 is used. The RANS-AD-AWF model is also validated with SCADA measurements in terms of wind farm shape; the model captures the trend of the measurements for a wide range of wind directions, although the SCADA measurements indicate more pronounced wind farm wake shapes for certain wind directions.

Reduced-order models for mesoscale current energy converter (CEC) modeling allow for tractable computation times for investigations of array configurations on power performance and environmental effects to support design optimization. The CEC representation in these models take the form of actuator discs in codes such as SNL-Delft3D-CEC-FM treating the rotating CEC blades as momentum sinks. In the first-of-its-kind, whole-plant optimization software, DTOcean, the hydrodynamic modelling of CECs is reduced one step further by superimposing wake models based on normalized CFD simulations onto a set of pre-computed velocity fields, to provide power estimates. DTOcean is a new tool and the amount of verification and validation evidence gathered is presently limited. To gain additional confidence and industry buy-in to the software penetration, this study investigated a primary component of levelized cost of electricity (LCOE) calculation, annual energy production (AEP), through an analytic calculation of power using the results of an identical simulation in SNL-Delt3D-CEC-FM. Three configurations of an 8-turbine array are studied with DTOcean where two rows of 4-turbines are spaced (unstaggered) 5-, 10-, and 20-Diameters apart and the AEP was calculated; The energy calculation in SNL-Delft3D-CEC-FM were more computationally expensive for the mesoscale domain making the optimization of solely an arrays power production using the wake superposition method implemented DTOcean attractive. The codes however are complementary as SNL-Delft3D-CEC-FM simultaneously investigates environmental effects of varying array configurations while DTOcean considers all aspects of array costs through its lifetime to optimize LCOE from a whole-plant perspective.

The wind at 50 m above ground level (a.g.l) was measured for 22 months. The mean wind speed predicted by Wind Atlas Analysis and Application Program (WAsP) at Lapaha was 6.39 m/s and the power density were 279 W/m2. The prevailing wind direction at Lapaha site was East and Southeast direction with a low turbulence. The WAsP wind map indicated that Lapaha has a good wind potential for power production. A wind farm consisting of four Vergnet 275 kW wind turbines at Lapaha site is expected to pay itself back in 9 years with a Benefit to Cost Ratio (BCR) of 1.74, a Levelized Cost of Energy (LCoE) in Tongan Pa’anga (TOP) of 0.10/kWh compared to TOP 0.86/kWh presently charged to domestic consumers. The expected internal rate of return (IRR) would be 50% and with a life time of 25 years. The expected cost saved from the wind farm is TOP 1.3 million per year, which is equivalent to 1.3 million liters of diesel saved, resulting in 535 tons less CO2 emitted annually. The proposed wind farm is expected to decrease diesel consumption by 20% annually.

Spreadsheets have been used to collect and understand existing solar thermal central receiver design data. Correlation of these data has led to the development of many useful algorithms. The algorithms provide the basis for calculating performance efficiencies, annual energy production, plant cost, and levelized energy cost. Variations in design details are evaluated with example results of the effect of plant location, collector field dield size, efficiencies for North and surround configurations as a function of field size, efficiencies of external and cavity receivers for similar operating conditions, and interactions of the collector field and receiver design. Examples are also presented for the plant total capital investment and levelized energy cost as a function of the annual energy produced. Sensitivities to various parameters affecting the net annual energy production and levelized energy cost are also discussed. The performance and cost characteristics of large and small plants are considered. Use of the spreadsheet analysis is demonstrated where one possible design utilizes modular solar systems. The design includes a single steam generator and turbine plant. This optimizes the performance and cost attributes of both small solar and large non-solar systems to arrive at a more cost-effective plant.

Background: During the whole life cycle of an offshore wind farm, from cradle to grave, logistics is needed. Particularly during wind turbine construction, vessels are intensively used. However, no study has been found to evaluate logistics costs during this particular turbine construction phase. Objective: In order to close this gap, this paper aims to propose an Offshore Logistics Cost (OLC) framework, evaluate OLC impact on total cost and identify recommendations to reduce this impact. Methodology: This study considers two quantitative approaches to evaluate OLC share. First quantitative approach is based on cost information found in twenty related studies from literature. Second quantitative approach was developed in two steps. A first step is a bottom up calculation model. This model performs OLC calculations for each scenario identified. In a second step, OLC results are used as input to two existing calculation models: National Renewable Energy Laboratory (NREL) simplified model and commonly accepted model developed by Megavind. Variance of results are then analyzed to determine a representative range for OLC impact on total cost. Results: Using some related values from literature review, this study assesses wind turbine construction offshore logistics to represent around 1.2% of Levelized Cost of Energy (LCOE). Using bottom up approach, this study evaluates offshore logistics during wind turbine construction with a broader contribution, conservatively from 0.6 to 7.6% of LCOE for offshore wind turbines over 4 MW power rating. It is also demonstrated that the higher the wind turbine size, the lower offshore logistics impact on LCOE. Conclusion: Offshore wind logistics costs during construction phase can represent between 0.6 and 7.6% of LCOE and it appears necessary to optimize these costs to contribute to a competitive LCOE. As main offshore logistics cost drivers have been identified, areas to reduce LCOE impact are suggested: increasing weather limits to reduce waiting on weather costs, minimizing work offshore, improving processes, using economy of scale and optimizing vessel use.

With the rapid advancement of clean energy, wind farm planning and construction are expanding worldwide, increasing the demand for accurate resource assessments. This study investigates the influence of vertical wind characteristics on wind farm siting and energy production, using measured meteorological data from the Hangjinqi wind farm. Results show that both mean wind speed increase substantially with altitude, indicating that upper layers provide richer and more stable wind resources. The estimated annual energy production of the site reaches 23,500 MWh, with capacity factors ranging from 35% to 42%, well above the national average. Seasonal and diurnal variations are evident: wind speeds strengthen during winter and spring, particularly at night, while turbulence intensity peaks in the daytime and decreases with height. Carbon dioxide (CO2) reduction also increases with hub height, with the most pronounced seasonal reductions in spring (3367.6–5041.1 tCO2, +49.7%) and winter (3215.7–5380.0 tCO2, +67.4%), equivalent to several thousand tons of standard coal per turbine annually. Optimal performance is observed at 100–140 m, demonstrating efficient utilization of mid- to high-altitude resources. Nevertheless, discrepancies in turbine performance at different hub heights suggest untapped potential at higher elevations. These findings highlight the importance of incorporating vertical wind characteristics into wind farm siting decisions, and support the deployment of turbines with tower heights ≥140 m alongside intelligent scheduling and forecasting strategies to maximize energy yield and economic benefits.