Wind Farm Power Output Research Articles

Regression learner machine learning approach to predict wind speed considering various parameters and integration of DG in mesh distribution system through GWO

ABSTRACT The escalating global demand for electricity is driving a significant expansion in the size and complexity of electric power systems. Explosive growth strains power distribution, creating challenges for operators. Among these challenges, the imperative to minimise power losses is crucial. To enhance power efficiency and quality, Distributed Generation (DG) technology, particularly wind energy, is being integrated into distribution systems. However, the variable nature of wind speed poses a significant challenge to the seamless integration of wind energy into grids. To address this challenge, wind speed prediction methods are explored. In this work, a Machine Learning framework is employed for multivariate wind speed forecasting in Tamil Nadu, India 8.0883 ∘ N , 77.5385 ∘ E . Key performance metrics, such as Root Mean Square Error (RMSE) and Mean Absolute Percentage Error values (MAPE), are used to assess the accuracy of the wind speed predictions. The predicted wind speed data is then utilised to estimate wind farm power output which is seamlessly integrated into the distribution system. Load Flow analysis is conducted using the robust and straightforward current injection method, focusing on IEEE-33 and IEEE-69 bus-balanced Mesh distribution systems. The aim is to determine the impact of wind-powered Distributed Generation on power losses within these systems.

A teaching-learning-based optimization algorithm with reinforcement learning to address wind farm layout optimization problem

As the global demand for renewable energy continues to rise, wind energy has received widespread attention as an eco-friendly energy source. Wind power generation is regarded as one of the key means to reduce carbon emissions and achieve sustainable development. Usually, a mass of turbines works together to produce electricity in a wind farm. However, downstream turbines will inevitably be influenced by the wake generated by upstream turbines, resulting in unused wind energy being lost. To reduce the negative effects of the wake, maximization of wind farm output power, and minimization of wind farm cost, a teaching-learning-based optimization algorithm with reinforcement learning is proposed in this paper. The improvements of the proposed algorithm mainly include the following three points: i) the original serial structure of the algorithm is changed to a parallel structure to accelerate the convergence and improve the efficiency of the algorithm. ii) the parameter F, which is adjusted by RL, is proposed to adjust the selection of the updating phase due to the design of a parallel structure. iii) in the modified learner phase, an individual is added to participate in the update, and a selection probability is proposed to improve the ability of the algorithm to retain the information of superior individuals. To study the performance of the modified algorithm, it was first tested against 10 other advanced algorithms on a benchmark testing suite. They then ran numerical experiments on four hypothetical wind farm cases under two simulated wind conditions. Finally, the superiority of improved algorithm over others and the effectiveness of addressing wind farm layout problem are demonstrated by experimental results.

Collective large-scale wind farm multivariate power output control based on hierarchical communication multi-agent proximal policy optimization

Wind power is becoming an increasingly vital source of renewable energy worldwide. However, controlling power generation in wind farms faces significant challenges due to the inherent complexity of these systems. To address this issue and maximize power output, we propose a novel communication-based multi-agent deep reinforcement learning approach for large-scale wind farm control. We introduce a multivariate power model for wind farms to analyze the impact of wake effects on power output. This model considers controllable variables such as axial induction factor, yaw angle, and tilt angle. To coordinate the continuous controls in large-scale wind farms, we propose the hierarchical communication multi-agent proximal policy optimization (HCMAPPO) algorithm. The wind farm is divided into multiple wind turbine aggregators (WTAs), and neighboring WTAs can exchange information through hierarchical communication to optimize power output. Our simulation results demonstrate that the multivariate HCMAPPO approach significantly increases wind farm power output compared to traditional PID control, coordinated model-based predictive control, and the multi-agent deep deterministic policy gradient algorithm. The HCMAPPO algorithm can be trained using a thirteen-turbine wind farm environment and effectively applied to large-scale wind farms. Importantly, as the wind farm scale increases, there is no significant increase in wind turbine blade fatigue damage from wake control. This multivariate HCMAPPO control strategy enables the collective maximization of power output in large-scale wind farms.

Strategy for mitigating wake interference between offshore vertical-axis wind turbines: Evaluation of vertically staggered arrangement

Wake interference between wind turbines potentially decreases the power output of offshore wind farms. While the staggered arrangement shows promise for mitigating this interference, the understanding of the impact of vertically staggered setup remains ambiguous, especially in the case of vertical-axis wind turbines (VAWTs). Also, the difference between horizontally and vertically staggered arrangements needs to be clarified. This study aims to shed light on these ambiguities, systematically evaluating the effectiveness of vertically staggered arrangement in mitigating wake interference between offshore VAWTs. High-fidelity computational fluid dynamics simulations are used to investigate the wake interference between two vertically staggered MW-class VAWTs. Typical separation distances (3D ≤ LS ≤ 7D) and different vertically staggered distances (−0.25H ≤ LV ≤ 0.75H) are considered, where D and H denote the turbine diameter and blade span length, respectively. Employing the Taguchi method, the effectiveness of horizontally and vertically staggered arrangements is compared, and the relatively optimal layout of the turbine array is identified. The results show that the vertically staggered arrangement significantly improves the power performance of the downstream turbine, e.g., the power output increases by 75.96% when LS = 7D and LV = 0.25H. When dealing with smaller LS (e.g., 3D), a negative LV is suggested, which reduces the tower cost while preserving the performance improvement. The vertically staggered arrangement has a greater impact on wake interference than the horizontally staggered arrangement. In terms of the relatively optimal layout, the power output of the turbine array is increased by 46.27%. These findings would contribute to the layout design of offshore wind farms.

Elman short-term wind power prediction based on the optimized seagull algorithm

Accurate prediction of wind farm power output can relieve the pressure of grid frequency regulation and peak regulation and improve grid stability. With the goal of improving power prediction accuracy and reducing overall prediction error, this paper proposes an Elman short-term wind power prediction model on the basis of an optimized seagull algorithm. Firstly, the Elman network is used as the base prediction model, and the seagull algorithm is applied to seek the best values for its weights. Secondly, the chaotic circle mapping with better initial characteristics is improved to equalize its sequence distribution for optimizing the population initialization. Then, to address the lack of local search capability, an optimized iterative approach using the sine cosine operator is used to achieve a balance between local exploitation ability and global search capability. Finally, after simulation and analysis of the actual data set, it is verified that the model has a better prediction effect.

A data driven based adaptive unit protection for transmission line integrated with large penetrated wind farms

The dynamic fault current characteristics, transient behaviour, and changing output power of large-scale doubly fed induction generator-based wind farms (WFs) have severe influence on transmission line conventional current differential schemes. Under normal conditions, the current difference between two ends of transmission line grows as its length increases. The capacitive charging current then might equal load current if power output of WF is low. In the presence of WFs, Traditional differential protection techniques are experiencing challenges. In order to ascertain the possible impacts of various scenarios with substantial offshore wind farms connected to transmission lines on differential relay characteristics, a data-driven approach is proposed in this paper. The STMPM based signal reconstruction method is used to compute the per-phase differential current and then their first and second-order derivatives are estimated to find the net change in the current magnitude. Finally, the Euclidean distance between these first and second derivative components are calculated and employed as a disturbance detection index (DDI). The conducted PSCAD/EMTDC simulation studies demonstrate satisfactory operation of proposed startergy for a wide range of disturbances, including external and internal faults, fault resistance, variable fault location, change in WF penetration, and various kinds of non-fault switching events.

Modelling the impact of trapped lee waves on offshore wind farm power output

Abstract. Mesoscale meteorological phenomena, including atmospheric gravity waves (AGWs) and including trapped lee waves (TLWs), can result from flow over topography or coastal transition in the presence of stable atmospheric stratification, particularly with strong capping inversions. Satellite images show that topographically forced TLWs frequently occur around near-coastal offshore wind farms. Yet current understanding of how they interact with individual turbines and whole farm energy output is limited. This parametric study investigates the potential impact of TLWs on a UK near-coastal offshore wind farm, Westermost Rough (WMR), resulting from westerly–southwesterly flow over topography in the southeast of England. Computational fluid dynamics (CFD) modelling (using Ansys CFX) of TLW situations based on real atmospheric conditions at WMR was used to better understand turbine level and whole wind farm performance in this parametric study based on real inflow conditions. These simulations indicated that TLWs have the potential to significantly alter the wind speeds experienced by and the resultant power output of individual turbines and the whole wind farm. The location of the wind farm in the TLW wave cycle was an important factor in determining the magnitude of TLW impacts, given the expected wavelength of the TLW. Where the TLW trough was coincident with the wind farm, the turbine wind speeds and power outputs were more substantially reduced compared with when the TLW peak was coincident with the location of the wind farm. These reductions were mediated by turbine wind speeds and wake losses being superimposed on the TLW. However, the same initial flow conditions interacting with topography under different atmospheric stability settings produce differing near-wind-farm flow. Factors influencing the flow within the wind farm under the different stability conditions include differing, hill and coastal transition recovery, wind farm blockage effects, and wake recovery. Determining how much of the differences in wind speed and power output in the wind farm resulted from the TLW is an area for future development.

Optimal control of wind farm power output with delay compensated nested-loop extreme seeking control

In this paper, we propose to enhance the nested-loop extremum seeking control (NLESC)-based wind farm control strategy with the predictor-based delay compensation in order to improve its convergence characteristics under fluctuating wind. Earlier work has shown the effectiveness of NLESC for region-2 wind farm operation, i.e., maximizing the total power output of cascaded wind turbine array, while its convergence speed is highly limited by the delay of power output for downstream turbines due to wake propagation along the wind direction. By utilizing the delay compensated ESC proposed by Oliveira and Krstic, the delay compensated NLESC (DCNLESC) wind farm control is proposed, allowing the dither frequencies to be of similar magnitude as that in the single-turbine ESC. This can significantly improve the convergence speed of optimum tracking for real-time wind farm control. The wake propagation delay is estimated from turbine power outputs using cross correlation and proper filtering. Using the SimWindFarm platform, the proposed DCNLESC strategy is simulated with both a single-column three-turbine array and a 2 × 3 turbine array, under different wind speeds. The results show that the convergence speed toward the calibrated optimum is significantly improved over the NLESC operation. The convergence time for the upstream turbines' torque gain is reduced by 55%–14% in terms of integral time-weighted absolute error, while the impact on turbine fatigue loads is as low as no more than 3.5% increase on turbine tower and shaft.

A study on behavior of producers, retailers and speculators in futures and day-ahead markets: A Nash equilibrium model

Uncertainties in different parameters such as the output power of renewable energy sources, available capacity of generators, or the condition of grid lines in the future, face market players with financial risks in the power system. Futures contracts are used in parallel with the day-ahead electricity markets to protect market players against financial risks of undesirable price fluctuations. Supplying a demand by both futures and day-ahead markets leads to mutual impacts between these two markets. In this paper, a Nash equilibrium approach is introduced to model the interactions between the futures and day-ahead markets. The proposed model includes producers, retailers, and speculators as market players, the uncertainty in the output power of wind farms (WFs), the possibility of the financial settlement of contracts, market players' risk preferences, and transmission system limitations. Using this approach, the optimal strategy of market players in futures and day-ahead markets, the effects of transmission system congestion on the Nash equilibrium of the system, and the role of the financial settlement of contracts in dealing with the uncertainty of WFs' output power and transmission lines capacity are discussed. Eventually, the behavior of speculators and their impacts on the gaming of other market players are evaluated. Simulation results highlight the role of the financial delivery feature in the effective utilization of futures contracts and the behavior of market players.

Study on boundary conditions of k-ε-fp turbulence model for wind turbine wake simulation

ABSTRACT Wind turbine wake has a great impact on the power output and fatigue damage of the whole wind farm. As a result, wind turbine wake simulation has attracted attention from both researchers and engineers for decades, in which turbulence modeling is the key point. Among all the turbulence modeling methods for wind turbine wake, k − ε − f P , a RANS model proposed by Laan in 2015, can balance well between efficiency and accuracy. In the current research, the boundary conditions of k − ε − f P turbulence model have been studied comprehensively. It was found that the boundary conditions of the model are affected by the wind conditions of the actual wind turbine, resulting in poor simulation accuracy under high wind shear conditions. Five simulation cases have been carried and compared with field measurement results. It was found that the roughness length z 0 is the most important factor for the determination of boundary conditions. Considering the wind shear conditions around wind turbine rotor, a new determination method for roughness length z 0 of the ground has been constructed, which corrects the wind profile prediction under high wind shear conditions. This research will contribute to the micro-sitting of future large wind farms.

Large-eddy simulation of a 15 GW wind farm: Flow effects, energy budgets and comparison with wake models

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.

Development of a reliable simulation framework for techno-economic analyses on green hydrogen production from wind farms using alkaline electrolyzers

The present study investigates the feasibility of coupling the intermittent electric power generation from a wind farm with alkaline electrolyzers to produce green hydrogen. A physically accurate model of commercial electrolytic modules has been first developed, accounting for conversion efficiency drop due to modules’ cool down, effects of shutdowns due to the intermittence of wind power, and voltage degradation over the working time frame. The model has been calibrated on real modules, for which industrial data were available. Three commercial module sizes have been considered, i.e., 1, 2 and 4 MW. As a second step, the model has been coupled with historical power datasets coming from a real wind farm, characterized by a nominal installed power of 13.8 MW. Finally, the model was implemented within a sizing algorithm to find the best combination between the actual wind farm power output and the electrolyzer capacity to reach the lowest Levelized Cost Of Hydrogen (LCOH) possible. To this end, realistic data for the capital cost of the whole system (wind farm and electrolyzers) have been considered, based on industrial data and market reports, as well as maintenance costs including both periodic replacements of degraded components and periodic maintenance. Simulations showed that, if the right sizing of the two systems is made, competitive hydrogen production costs can be achieved even with current technologies. Bigger modules are less flexible but, by now, considerably cheaper than smaller ones. A future economy of scale in alkaline electrolyzers is then needed to foster the diffusion of the technology.

Flywheel energy storage controlled by model predictive control to achieve smooth short-term high-frequency wind power

The use of energy storage systems to improve the fluctuation of wind power generation has garnered significant in the development of wind power. However, the fluctuation of the signals in the high-frequency part of the wind turbine output is particularly drastic and short in duration. As a kind of physical energy storage device, the flywheel energy storage device has a fast response speed but higher requirements on the control system. In order to improve the control effect of the flywheel energy storage device, the model predictive control algorithm is improved in this paper. First, the high-frequency components of the wind farm output power data are extracted by the wavelet packet decomposition algorithm, and the high-frequency components are optimized by mathematical interpolation as the data basis. Secondly, a mathematical model of the flywheel energy storage system applied in the model predictive control algorithm is proposed, and the model predictive control algorithm is used to configure the flywheel energy storage device to achieve a smooth output power of the wind farm. Finally, the simulation is performed in MATLAB and the experimental parameters are adjusted. The experimental results show that the configuration of the flywheel energy storage system based on the model predictive control algorithm can effectively smooth the fluctuation of the high-frequency component of the output power data of the wind farm. The experimental results take the wind power data of different time periods for energy storage configuration, and the comparison verifies the reliability of the system designed in this paper.

Impacts of Uncertain Geomagnetic Disturbances on Transient Power Angle Stability of DFIG Integrated Power System

When geomagnetic disturbances (GMDs) occur, the reactive power loss (GIC-Q) caused by geomagnetically induced currents (GICs) flowing through transformers can lead to system instability. Previous studies have been focused on the impacts of GMD on the static stability of conventional systems, while transient stability of hybrid systems left unexplored. In this article a hybrid system based on wind and conventional energy sources are proposed as a research object. The wind farm output power and GIC-Q are equivalent to the grounding impedance. Considering the uncertainty of GMD, based on establishing the random fuzzy model of induced geomagnetic fields, the expected value of critical clearing angle and acceleration/deceleration area is calculated by using credibility theory. Then the influence of GMD on the transient stability under the different proportions of wind farm output power is analyzed quantitatively by using transient stability margin. Taking the Mengdong power grid under four operation modes as an example, the results show that no matter which operation mode, the transient stability of the system is reduced when GMDs occur. Under heavy loading conditions in summer and when the proportion of wind farm output power reaches 50%, the transient stability of the system is the lowest. The research results provide a basis for disaster prevention and control of GMDs.

Turbulent entrainment in finite-length wind farms

In this article, we present an entrainment-based model for predicting the flow and power output of finite-length wind farms. The model is an extension of the three-layer approach of Luzzatto-Fegiz & Caulfield (Phys. Rev. Fluids, vol. 3, 2018, 093802) for wind farms of infinite length, and assumes dependence of key flow quantities, such as the wind farm bulk velocity, on the streamwise distance from the farm entrance. To assist our analysis and validate the proposed model, we undertake a series of large-eddy simulations with different turbine spacing arrangements and layouts. Comparisons are also made with the top-down model with entrance effects of Meneveau (J. Turbul., vol. 13, 2012, N7) and data from the literature. The finite-length entrainment model is shown to be capable of capturing the power drop between contiguous rows of turbines as well as describing the advection and turbulent transport of kinetic energy in both the entrance and fully developed regions. The fully developed regime is approximated only deep in the wind farm, after approximately 15 rows of turbines. Our data suggest that for the cases considered in this study, the empirical coefficients that can be used to describe turbulent entrainment and transfers above the wind farm exhibit little dependence on the farm layout and may be considered constant for modelling purposes. However, the flow field within the wind farm layer can be strongly modulated by the turbine density (spacing) as well as the array layout, and to that extent it can be argued that they are both primary factors determining the wind farm power output.

Numerical Investigations on the Fluid Behavior in the Near Wake of an Experimental Wind Turbine Model in the Presence of the Nacelle

Accurate predictions of the near wake of horizontal-axis wind turbines are critical in estimating and optimizing the energy production of wind farms. Consequently, accurate aerodynamic models of an isolated wind turbine are required. In this paper, the steady-state flow around an experimental horizontal-axis wind turbine (known as the MEXICO model) is investigated using full-geometry computational fluid dynamics (CFD) simulations. The simulations are performed using Reynolds-Averaged Navier-Stokes (RANS) equations in combination with the transitional k-kl-w turbulence model. The multiple reference frame (MRF) approach is used to allow the rotation of the blades. The impacts of the nacelle and blade rotation on the induction region and near wake are highlighted. Simulation cases under attached and detached flow conditions with and without the nacelle were compared to the detailed particle image velocimetry (PIV) measurements. The axial and radial flow behaviors at the induction region have been analyzed in detail. This study attempts to highlight the nacelle effects on the near wake flow and on numerical prediction accuracy under various conditions, as well as the possible reasons for these effects. According to simulation results, the rotation of blades dominates the near wake region, and including the nacelle geometry can improve both axial and radial flow prediction accuracy by up to 15% at high wind speeds. At low wind speeds, the nacelle effects can be ignored. The presence of the nacelle has also been shown to increase flow separation at the trailing edges of the blade airfoils, increasing both root and tip vorticities. Finally, small nacelle diameters are recommended to reduce flow separation on the blades and increase the average velocity downstream of the rotor, thereby optimizing wind farm output power.

Gradient boosting-based approach for short- and medium-term wind turbine output power prediction

Being able to predict the output power of wind turbines and wind farms is crucial in the process of integrating such stochastic energy sources with power systems. To support stakeholders in short- and mid-term wind power prediction, a novel data-driven Machine Learning based approach is proposed. This approach relies on three Gradient Boosting (GB) regressor implementations. The novelty of our approach is also manifested in the fact, that it is respectively based on the use of MERRA-2 reanalysis data and GEOS FP meteorological forecasts in models training and wind power prediction. It makes the short- and mid-term prediction unique in enriching the results even for time horizon of 240 h with resolution of 1 h. The data preprocessing and cleaning, feature engineering, and training, testing and validation of the models are presented in details. The performances of the models and prediction accuracy are evaluated relying on a few absolute and relative error measures. The proposed methodology is implemented in the output power prediction of a wind turbine located in Poland. The results of predictions are compared with other Machine Learning algorithms. The results show that proposed GB implementations can capture accepted accuracy of prediction and outperform other investigated algorithms.

Optimization of wind farm portfolios for minimizing overall power fluctuations at selective frequencies – a case study of the Faroe Islands

Abstract. Hourly modeled wind turbine power output time series – modeled based on outputs from the mesoscale numerical weather prediction system Weather Research and Forecasting Model (WRF) – are used to examine the spatial smoothing of various wind farm portfolios located on a complex isolated island group with a surface area of 1400 km2. Power spectral densities (PSDs), hourly step-change functions, and duration curves are generated, and the 5th and 95th percentiles and the standard deviations of the hourly step-change functions are calculated. The spatial smoothing is identified from smaller high-frequency PSD amplitudes, lower hourly fluctuations, and more flat duration curves per installed wind power capacity, compared with single wind turbine outputs. A discussion on the limitation of the spatial smoothing for the region is included, where a smoothing effect is observed for periods of up to 1–2 d, although it is most evident at higher frequencies. By maximizing the smoothing effect, optimal wind farm portfolios are presented with the intention of minimizing overall wind power fluctuations. The focus is mainly on the smoothing effect on the 1–3 h timescale, during which the coherency between wind farm power outputs is expected to be dependent on how the regional weather travels between local sites, thereby making optimizations of wind farm portfolios relevant – in contrast to a focus on either lower or higher frequencies on the scale of days or minutes, respectively, during which wind farm power output time series are expected to be either close to fully coherent due to the same weather conditions covering a small region or not coherent as the turbulences in separate wind farm locations are expected to be uncorrelated. Results show that an optimization of the wind farm capacities at 14 pre-defined wind farm site locations has a minimal improvement on the hourly fluctuations compared with a portfolio with equally weighted wind farm capacities. However, choosing optimized combinations of individual wind farm site locations decreases the 1–3 h fluctuations considerably. For example, selecting a portfolio with four wind farms (out of the 14 pre-defined wind farm site locations) results in 15 % lower 5th and 95th percentiles of the hourly step-change function when choosing optimal wind farm combinations compared with choosing the worst wind farm combinations. For an optimized wind farm portfolio of seven wind farms, this number is 13 %. Optimized wind farm portfolios consist of distant wind farms, while the worst portfolios consist of clustered wind farms.

Flow characteristics analysis and power comparison for two novel types of vertically staggered wind farms

Reducing the wake effect to improve the power output of wind farms is identified as one of the grand challenges in wind energy science. To solve this problem, the windbreak and vertical axis wind turbine are added to the traditional aligned wind farm to form two novel types of vertically staggered wind farms (VSWF). A careful investigation is conducted to find the effect of crucial parameters on the power output and flow characteristics of proposed VSWFs. Results show that windbreak and VAWT both benefit the recovery of upstream wind turbine wake due to the mixing of wind flow and reducing wind shear, which increases the power output of VSWFs. Moreover, the power growth rate of VSWFs increases with the spacing. An interesting finding is that the larger tilt angle of the windbreak weakens the clockwise rotating vortex in the wake of the windbreak and increases the power output of the VSWF. Another important finding is that the power output of VSWF with VAWT is much greater than that of the windbreak, whose growth rate can achieve 13.1% (when LV = 6D). A possible explanation is that VAWT provides better wind penetrability and reduces surface roughness.

Monte-Carlo simulations based hub height optimization using FLORIS for two interacting onshore wind farms

This study focuses on finding the optimum hub height (i.e., tower height) distributions for two interacting on-shore wind farms that are located on relatively complex terrain. Different optimization scenarios are studied, which take into account both the wind farm power output and the relevant cost variations due to changing hub heights. Simulations are performed using the Flow Redirection and Induction in Steady State (FLORIS) framework, which is modified to represent significant variations in hub height levels due to elevation differences, hence partial wake interactions that are occurring as a consequence, are more realistically represented. Optimization is based on a systematic procedure that includes introducing definitions of overall evaluation criterion parameters for objective setting and generation of design of experiments tables and related data via FLORIS simulations to properly cover the design space. A Pareto analysis of generated data to find the most influential parameters is then performed, and response surfaces are generated to represent these variations, which are, in turn, used for Monte Carlo based simulations to determine the optimized hub height distributions. Overall, the optimized results show a reasonable increase can be achieved in wind farm power output levels, while total tower height levels (hence related cost levels) are either not changing or in some cases even getting reduced for the wind farms in consideration.