Estimating long-term annual energy production from shorter-time-series data: methods and verification with a 10-year large-eddy simulation of a large offshore wind farm

Atmospheric large-eddy simulation (LES), a computational fluid-dynamics technique that resolves turbulence in the atmospheric boundary layer, is increasingly used for wind resource assessment (WRA), by including wind turbine parametrizations and using external weather data as initial- and boundary conditions. The large computational costs of doing such a 'real-weather' LES, however, limits length of the simulation to < 1 year; whereas long-term, multi-year, mean power production values are of high interest to many parties in the wind energy sector. To address this need, this work presents several methods to estimate long-term mean power production/annual energy production and wind from a < 1 year LES run, by applying Bayes' theorem on short-term LES output and long-term ERA5 reanalysis data. A 10 year LES run of a hypothetical large offshore wind farm is performed in order to validate these 'long-term correction' methods, in three scenarios of increasing complexity. First, long-term correction of 365 consecutive days gives estimates of long-term mean power with a mean absolute error of 0.35 %, and 95th percentile of the absolute error within 0.8 % of the long-term mean, reducing the uncertainty by an order or magnitude. Second, in the scenario when the simulation period is not fixed, using several simple day selection techniques to select the simulation period can reduce the error further. Then, only around 200 days are needed to arrive at the same error values. The results indicate that long-term correction is insensitive to the particulars of the day selection methods, but that including a diverse set of days from different years and seasons is essential. Third, a method to also include wind observations in the long-term correction is presented and tested. This requires an additional 'free stream' LES run without active turbines, and gives estimates of long-term power and wind that are corrected for a potential LES bias. Although validation of this final approach is difficult in the employed modelling strategy, it gives valuable insights, and fits within the common WRA practice of combining models and observations.The presented techniques are based on physical arguments, computationally cheap, and simple to implement; and as such could be a useful extension to the diverse set of modelling, observational, and statistical techniques used in WRA.

The decarbonisation of energy sources requires additional investments in renewable technologies, including the installation of onshore and offshore wind farms. For wind energy to remain competitive, wind farms must continue to provide low-cost power even when covering larger areas. Inside very large wind farms, winds can decrease considerably from their free-stream values to a point where an equilibrium wind speed is reached. The magnitude of this equilibrium wind speed is primarily dependent on the balance between turbine drag force and the downward momentum influx from above the wind farm. We have simulated for neutral atmospheric conditions, the wind speed field inside different wind farms that range from small (25 km2) to very large (105 km2) in three regions with distinct wind speed and roughness conditions. Our results show that the power density of very large wind farms depends on the local free-stream wind speed, the surface characteristics, and the turbine density. In onshore regions with moderate winds the power density of very large wind farms reaches 1 W m−2, whereas in offshore regions with very strong winds it exceeds 3 W m−2. Despite a relatively low power density, onshore regions with moderate winds offer potential locations for very large wind farms. In offshore regions, clusters of smaller wind farms are generally preferable; under very strong winds also very large offshore wind farms become efficient.

Offshore wind farms extend a distance from an onshore grid to increase their generating power, but long distance and high power transmissions raise a lot of cost challenges. LFAC (Low Frequency AC) transmission is a new promising technology in high power and low cost power transmission fields against HVDC (High Voltage DC) and HVAC (High Voltage AC) transmissions. This paper presents an economic comparison of LFAC and HVDC transmissions for large offshore wind farms. The economic assessments of two different transmission technologies are analyzed and compared in terms of wind farm capacities (600 MW and 900 MW) and distances (from 25 km to 100 km) from the onshore grid. Based on this comparison, the economic feasibility of LFAC is verified as a most economical solution for remote offshore wind farms. Keywords: LFAC, HVDC, Offshore, wind farm I. INTRODUCTION In recent years, energy systems based on wind power have rapidly enlarged their application areas, especially towards large offshore wind farms (over 100 MW) and micro grid systems. The conventional onshore wind farms have small power generation and short distance power transmission to a power grid. However, for a large remote wind farms, a new power transmission system is required to provide high energy density and low loss power transmission characteristics with low investments. So, how to connect large remote wind farms to the onshore micro grid with low power losses and economic benefits is the prime concerns of researchers, and its economic power system and wind farm layouts for transmitting high power and long distance has gained more attentions. The conventional HVAC (High Voltage AC) system consists of wind generators, transformers, transmission cables and reactive power compensators, and the generated power is converted to a very high voltage (154 kV or 345 kV) by transformers. The HVAC power system transmits the power through 3 cores XPLE cables through underwater, but the transmission distance of the HVAC power system is the most critical factor against power transmission capability because reactive power losses are proportional to the distance. Therefore, HVAC transmission system is not adequate to long distance large offshore wind farms. Recently, new technologies for power systems have been reported [1]-[15] to provide alternative ways to maximize the power transmission capability. The most outstanding technology is HVDC power system, which has high economic benefits for long distant applications because HVDC power system has no limitation of the transmission capability. HVDC Transmission does not suffer from the reactive losses found in the transmission of HVAC system. However, in order to transmit DC power from a remote wind farms the generated AC power must be converted to the DC power and must be converted back to the AC power for a grid connection. Converting the AC power into the DC power requires an expensive AC to DC converter station to be installed at the remote wind farm area as well as a DC to AC power converter station at a receiving end, prior to the grid. An alternative technology is LFAC (Low Frequency AC) transmission system. LFAC transmission system uses lower frequency (50/3 Hz or 60/3 Hz) than a grid frequency (50 or 60 Hz) and requires no offshore power converter stations but an onshore frequency converter station. LFAC transmission system has an ability to extend a transmission distance and capability rather than the conventional HVAC transmission system. However, LFAC system can generate some audible noises and have transformer saturation and size problems. To adopt a best power system topology for large remote offshore wind farms, an economic analysis about HVDC and LFAC system should be performed. However, economic investments are directly dependent on a power system configuration, a distance and transmission capability. Therefore, this paper proposes HVDC and LFAC power system configurations and presents an economic assessments and comparison of LFAC and HVDC transmissions for large offshore wind farms. The economic assessments of two different transmission technologies are analyzed based on the proposed power configurations and compared in terms of wind farm’s capacities (600 MW and 900 MW) and distances (from 25 km to 100 km) from the onshore grid. From the comparison, the economic feasibility of LFAC is verified as a most economical solution for the large offshore wind farms.

Abstract. Wind farm parameterizations (WFPs) are used in mesoscale models for predicting wind farm power production and its impact on wind resources while considering the variability of the regional wind climate. However, the performance of WFPs is influenced by various factors including atmospheric stability. In this study, we compared two widely used WFPs in the Weather Research and Forecasting (WRF) model to large-eddy simulations (LES) of turbine wakes performed with the same model. The Fitch WFP and the explicit wake parameterization were evaluated for their ability to represent wind speed and turbulent kinetic energy (TKE) in a two-turbine wind farm layout under neutral, unstable, and stable atmospheric stability conditions. To ensure a fair comparison, the inflow conditions were kept as close as possible between the LES and mesoscale simulations for each type of stability condition, and the LES results were spatially aggregated to align with the mesoscale grid spacing. Our findings indicate that the performance of WFPs varies depending on the specific variable (wind speed or TKE) and the area of interest downwind of the turbine when compared to the LES reference. The WFPs can accurately depict the vertical profiles of the wind speed deficit for either the grid cell containing the wind turbines or the grid cells in the far wake, but not both simultaneously. The WFPs with an explicit source of TKE overestimate TKE values at the first grid cell containing the wind turbine; however, for downwind grid cells, agreement improves. On the other hand, WFPs without a TKE source underestimate TKE in all downwind grid cells. These agreement patterns between the WFPs and the LES reference are consistent under the three atmospheric stability conditions. However, the WFPs resemble less the wind speed and TKE from the LES reference under stable conditions than that under neutral or unstable conditions.

Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform large-eddy simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, 2020, p. A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on both the array density and turbine layout. An analytical model derived from the two-scale momentum theory predicts the impact of array density very well for all 50 farms investigated and can therefore be used as an upper limit to farm performance. We also propose a new method to quantify turbine-scale losses (due to turbine–wake interactions) and farm-scale losses (due to the reduction of farm-average wind speed). They both depend on the strength of atmospheric response to the farm, and our results suggest that, for large offshore wind farms, the farm-scale losses are typically more than twice as large as the turbine-scale losses. This is found to be due to a two-scale interaction between turbine wake and farm induction effects, explaining why the impact of turbine layout on farm power varies with the strength of atmospheric response.

To simulate the large-scale impacts of wind farms, wind turbines are parameterized within mesoscale models in which grid sizes are typically much larger than turbine scales. Five wind-farm parameterizations were implemented in the Weather Research and Forecasting (WRF) Model v4.3.3 to simulate multiple operational wind farms in the North Sea, which were verified against a satellite image, airborne measurements, and the FINO-1 meteorological mast data on 14 October 2017. The parameterization by Volker et al. underestimated the turbulence and wind speed deficit compared to measurements and to the parameterization of Fitch et al., which is the default in WRF. The Abkar and Porté-Agel parameterization gave close predictions of wind speed to that of Fitch et al. with a lower magnitude of predicted turbulence, although the parameterization was sensitive to a tunable constant. The parameterization by Pan and Archer resulted in turbine-induced thrust and turbulence that were slightly less than that of Fitch et al., but resulted in a substantial drop in power generation due to the magnification of wind speed differences in the power calculation. The parameterization by Redfern et al. was not substantially different from Fitch et al. in the absence of conditions such as strong wind veer. The simulations indicated the need for a turbine-induced turbulence source within a wind-farm parameterization for improved prediction of near-surface wind speed, near-surface temperature, and turbulence. The induced turbulence was responsible for enhancing turbulent momentum flux near the surface, causing a local speed-up of near-surface wind speed inside a wind farm. Our findings highlighted that wakes from large offshore wind farms could extend 100 km downwind, reducing downwind power production as in the case of the 400-MW Bard Offshore 1 wind farm whose power output was reduced by the wakes of the 402-MW Veja Mate wind farm for this case study. Significance Statement Because wind farms are smaller than the common grid spacing of numerical weather prediction models, the impacts of wind farms on the weather have to be indirectly incorporated through parameterizations. Several approaches to parameterization are available and the most appropriate scheme is not always clear. The absence of a turbulence source in a parameterization leads to substantial inaccuracies in predicting near-surface wind speed and turbulence over a wind farm. The impact of large clusters of offshore wind turbines in the wind field can exceed 100 km downwind, resulting in a substantial loss of power for downwind turbines. The prediction of this power loss can be sensitive to the chosen parameterization, contributing to uncertainty in wind-farm economic planning.

Wind turbine wakes for wind energy

Planned offshore wind farm clusters have a rated capacity of more than 10 GW. The layout optimization and yield estimation of wind farms is often performed with computationally inexpensive, analytical wake models. As recent research results show, the flow physics in large (multi-gigawatt) offshore wind farms are more complex than in small (sub-gigawatt) wind farms. Since analytical wake models are tuned with data of existing, sub-gigawatt wind farms they might not produce accurate results for large wind farm clusters. In this study the results of a large-eddy simulation of a 15 GW wind farm are compared with two analytical wake models to demonstrate potential discrepancies. The TurbOPark model and the Niayifar and Porté-Agel model are chosen because they use a Gaussian wake profile and a turbulence model. The wind farm has a finite size in the crosswise direction, unlike as in many other large-eddy simulation wind farm studies, in which the wind farm is effectively infinitely wide due to the cyclic boundary conditions. The results show that new effects like crosswise divergence and convergence occur in such a finite-size multi-gigawatt wind farm. The comparison with the wake models shows that there are large discrepancies of up to 40% between the predicted wind farm power output of the wake models and the large-eddy simulation. An energy budget analysis is made to explain the discrepancies. It shows that the wake models neglect relevant kinetic energy sources and sinks like the geostrophic forcing, the energy input by pressure gradients and energy dissipation. Taking some of these sources and sinks into account could improve the accuracy of the wake models.

Abstract. 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 and tested for the application of RANS simulations of large wind farms. Second, a RANS-based wind farm parameterization 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 of less than 1 % in terms of the wind farm power of the downstream wind farm. Most importantly, a reduction in CPU hours of 75.1 % 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, 92.3 % and 99.9 % for the double wind farm case and for a wind farm cluster case consisting of three wind farms, respectively. If the wind farm thrust and power coefficient inputs are derived from RANS-AD simulations, then the CPU time reduction is still 82.7 % for the wind farm cluster case. 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, but the models are in agreement with the inflow wind speed of the downstream wind farm. The RANS-AD-AWF model is also validated with measurements in terms of wind farm wake shape; the model captures the trend of the measurements for a wide range of wind directions, although the measurements indicate more pronounced wind farm wake shapes for certain wind directions.

Abstract. Wind farms affect local weather and microclimates; hence, parameterizations of their effects have been developed for numerical weather prediction models. While most wind farm parameterizations (WFPs) include drag effects of wind farms, models differ on whether or not an additional turbulent kinetic energy (TKE) source should be included in these parameterizations to simulate the impact of wind farms on the boundary layer. Therefore, we use aircraft measurements above large offshore wind farms in stable conditions to evaluate WFP choices. Of the three case studies we examine, we find the simulated ambient background flow to agree with observations of temperature stratification and winds. This agreement allows us to explore the sensitivity of simulated wind farm effects with respect to modeling choices such as whether or not to include a TKE source, horizontal resolution, vertical resolution and advection of TKE. For a stably stratified marine atmospheric boundary layer (MABL), a TKE source and a horizontal resolution on the order of 5 km or finer are necessary to represent the impact of offshore wind farms on the MABL. Additionally, TKE advection results in excessively reduced TKE over the wind farms, which in turn causes an underestimation of the wind speed deficit above the wind farm. Furthermore, using fine vertical resolution increases the agreement of the simulated wind speed with satellite observations of surface wind speed.

Abstract. Germany's expansion target for offshore wind power capacity of 40 GW by the year 2040 can only be reached if large portions of the Exclusive Economic Zone in the German Bight are equipped with wind farms. Because these wind farm clusters will be much larger than existing wind farms, it is unknown how they will affect the boundary layer flow and how much power they will produce. The objective of this large-eddy simulation study is to investigate the wake properties and the power output of very large potential wind farms in the German Bight for different turbine spacings, stabilities and boundary layer heights. The results show that very large wind farms cause flow effects that small wind farms do not. These effects include, but are not limited to, inversion layer displacement, counterclockwise flow deflection inside the boundary layer and clockwise flow deflection above the boundary layer. Wakes of very large wind farms are longer for shallower boundary layers and smaller turbine spacings, reaching values of more than 100 km. The wake in terms of turbulence intensity is approximately 20 km long, in which longer wakes occur for convective boundary layers and shorter wakes for stable boundary layers. Very large wind farms in a shallow, stable boundary layer can excite gravity waves in the overlying free atmosphere, resulting in significant flow blockage. The power output of very large wind farms is higher for thicker boundary layers because thick boundary layers contain more kinetic energy than thin boundary layers. The power density of the energy input by the geostrophic pressure gradient limits the power output of very large wind farms. Because this power density is very low (approximately 2 W m−2), the installed power density of very large wind farms should be small to achieve a good wind farm efficiency.

Abstract. The flow inside and around large offshore wind farms can range from smaller structures associated with the mechanical turbulence generated by wind turbines to larger structures indicative of the mesoscale flow. In this study, we explore the variation in turbulence structures and dominant scales of vertical entrainment above large offshore wind farms located in the North Sea, using data obtained from a research aircraft. The aircraft was flown upstream, downstream, and above wind farm clusters. Under neutrally stratified conditions, there is high ambient turbulence in the atmosphere and an elevated energy dissipation rate compared to stable conditions. The intensity of small-scale turbulence structures is increased above and downstream of the wind farm, and it prevails over mesoscale fluctuations. But in stable stratification, mesoscale flow structures are not only dominant upstream of the wind farm but also downstream. We observed that the vertical flux of horizontal momentum is the main source of energy recovery in large offshore wind farms, and it strongly depends on the magnitude of the length scales of the vertical wind velocity component. The dominant length scales of entrainment range from 20 to ∼60 m above the wind farm in all stratification strengths, and in the wake flow these scales range from 10 to ∼100 m only under near-neutral stratification. For strongly stable conditions, negligible vertical entrainment of momentum was observed even just 2 km downstream of large wind farms. We also observed that there is a significant lateral momentum flux above the offshore wind farms, especially under strongly stable conditions, which suggests that these wind farms do not satisfy the conditions of an “infinite wind farm”.

A new wind farm parameterization has been developed for the mesoscale numerical weather prediction model, the Weather Research and Forecasting model (WRF). The effects of wind turbines are represented by imposing a momentum sink on the mean flow; transferring kinetic energy into electricity and turbulent kinetic energy (TKE). The parameterization improves upon previous models, basing the atmospheric drag of turbines on the thrust coefficient of a modern commercial turbine. In addition, the source of TKE varies with wind speed, reflecting the amount of energy extracted from the atmosphere by the turbines that does not produce electrical energy. Analyses of idealized simulations of a large offshore wind farm are presented to highlight the perturbation induced by the wind farm and its interaction with the atmospheric boundary layer (BL). A wind speed deficit extended throughout the depth of the neutral boundary layer, above and downstream from the farm, with a long wake of 60-km e-folding distance. Within the farm the wind speed deficit reached a maximum reduction of 16%. A maximum increase of TKE, by nearly a factor of 7, was located within the farm. The increase in TKE extended to the top of the BL above the farm due to vertical transport and wind shear, significantly enhancing turbulent momentum fluxes. The TKE increased by a factor of 2 near the surface within the farm. Near-surface winds accelerated by up to 11%. These results are consistent with the few results available from observations and large-eddy simulations, indicating this parameterization provides a reasonable means of exploring potential downwind impacts of large wind farms.

<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.

<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.