Jensen Wake Model Research Articles

Improved Design of a Large Offshore Wind Farm by Using Biogeography based Optimization

This paper investigates optimal placement of wind turbines (WTs) within a large offshore wind farm (LOFWF). 88 wind farm (WF) configurations are invested to search the optimal layout for the Horns rev 1 offshore WF using twenty years of wind data knowing that wind characteristics are modeled from long term reanalysis data based on MERRA-2. The regular and the irregular placement of the Horns Rev 1 (HR1) offshore WF are investigated with Jensen wake model. Therefore, the objective is to assess the effect of wind turbine spacing (WTS) on the power output loss in a LOFWF and, also to find the best configuration that gives the maximum power with minimum investment cost. The use of the Biogeography based optimization (BBO), as a bio-inspired evolutionary approach, represents the advantage of being effective on strongly non-convex spaces such as a large offshore WF. Due to the iterative process applied to the initial population, and the multiplicity of the population, the BBO process limit the risk of getting stuck in a local optimum, by distributing the individuals in the whole solution space. The results obtained show that the wind data extracted from MERRA-2 can be applied reliably to any existing WF to simulate wind power production. The results also demonstrate that significant power losses occur when the turbines are arranged in a condensed manner and the significant power gains are not obtained from too large configurations, but rather from the best placement in configurations. The proposed approach shows promise in terms of applicability with MERRA-2 and is effectively suitable for arranging turbines and assessing wind resources in an offshore wind farm project (OFWFP). https://dorl.net/dor/20.1001.1.13090127.2021.11.2.27.6

Layout optimization for offshore wind farms in India using the genetic algorithm technique

Abstract. Wind Farm Layout Optimization Problem (WFLOP) is a critical issue when installing a large wind farm. Many studies have focused on the WFLOP but only for a limited number of turbines and idealized wind speed distributions. In this study, we apply the Genetic Algorithm (GA) to solve the WFLOP for large hypothetical offshore wind farms using real wind data. GA mimics the natural selection process observed in nature, which is the survival of the fittest. The study site is the Palk Strait, located between India and Sri Lanka. This site is a potential hotspot of offshore wind in India. A modified Jensen wake model is used to calculate the wake losses. GA is used to produce optimal layouts for four different wind farms at the specified site. We use two different optimization approaches: one where the number of turbines is kept the same as the thumb rule layout and another where the number of turbines is allowed to vary. The results show that layout optimization leads to large improvements in power generation (up to 28 %), efficiency (up to 34 %), and cost (up to 25 %) compared to the thumb rule due to the reduction in wake losses. Optimized layouts where both the number and locations of turbines are allowed to vary produce better results in terms of efficiency and cost but also leads to lower installed capacity and power generation. Wind energy is growing at an unprecedented rate in India. Easily accessible terrestrial wind resources are almost saturated, and offshore wind is the new frontier. This study can play an important role while taking the first steps towards the expansion of offshore wind in India.

Development and validation of a prediction model for the multi-wake of tidal stream turbines

The proposed analytical wake model which is proposed for multi-wake predictions of tidal stream turbines. This analytical wake model is developed referring to the classical Jensen wake model, reanalyzing the equations used in predicting the velocity distribution of ship propeller jets, and expressing the wake decay coefficient as a function of the ambient turbulence intensity. Coupled with three types of multi-wake combination models, the reliability of the proposed wake prediction model is evaluated through comparing with experimental and numerical data of two wakes interaction. It is found that the wake deficit predicted by the proposed wake model exhibit pleasant agreement with the numerical results as well as the experimental measurements. The developed model also provides reasonable predictions of power output in the cases five aligned turbines under two different turbulence conditions.

Configuration of wind farm in Kaberten region: wind potential and optimal capacity

The configuration of a wind farm depends mainly on the wind potential and the disposition of the wind turbines in this park. The windiest site is the most favorable for a future installation of wind turbines for the production of electricity, also, in this same site, a too dense arrangement would lead to considerable of power losses under the effect of wake. In this context, it is presented a research work that consists of determining the installation conditions of a wind farm; evaluating the wind farm through measurements of wind speed and the location of wind turbines in the park to minimize the effect of wind turbine interference. In order to do this, an evaluation study of the wind potential for the implementation of a wind farm based on the quantification of the wind in speed and directions firstly proposed. Secondly, a method for optimizing the positioning of wind turbines in a wind power farm is used based on the introduction of the Jensen wake model and the application of the iterative pseudo-random distribution approach of the turbines in the site. Simulation results are presented and discussed using data from the Kaberten site in Algeria and the characteristics of the GAMESA G52 wind turbine.

Validation of wind turbine wake environment modelling

The widely used wake environment models in engineering are validated according to wind tunnel experiment in this paper, namely the Jensen wake model, Frandsen wake model, the Larsen wake model and simplified vortex wake model. From the validation results, it can be found that the wake expansion are overestimated, namely the expansion efficient still needs to be further investigated. In Jensen and Frandsen models, the assumption of uniform distribution of wake speeds along radius differs from the experimental data, with low precision. The wake speed with an approximate Gaussian distribution adopted by Larsen model improves the accuracy. But for all these wake models, due to the overestimation of wake expansion, the wake profiles are definitely calculated with error, thereby lowering the precision of power prediction of wind farms. It is suggested that these models needs to be improved based on more measurement/experimental data.

A New Bi-Level Planning Approach to Find Economic and Reliable Layout for Large-Scale Wind Farm

This paper presents a bi-level planning approach to find an optimal layout for a large-scale wind farm (WF) from economic and reliability perspectives. The upper level of the planning approach is formulated as constrained multi-objective optimization (MOO) to obtain the optimal WF layout, where two conflicting objectives are optimized simultaneously. Two objectives for MOO are i) yearly gross energy production and ii) annual loan repayment (for cable and land area of the WF), where the first objective is maximized and the second objective is minimized. Jensen's wake model is used to calculate the wake effect, and to evaluate the multiple wake effect within a WF, a coordinate-transformation-based approach has been adopted in this study. An efficient hybrid multi-objective metaheuristic algorithm, which is based on nondominated sorting multi-objective particle swarm optimization and improved archive multi-objective simulated annealing, has been proposed to find the optimized WF layout. The superiority of the Pareto front obtained by the proposed algorithm for the large-scale WF layout is supported by its comparison with different powerful and well-established MOO algorithms. In the lower level of the proposed approach, economic and reliability analyses of the solutions (WF layout), obtained in the Pareto front by the proposed hybrid algorithm, have been done. In this context, two performance metrics, a) generation economy index and b) expected wind energy generation (EWEG), have been considered. A sequential Monte Carlo simulation has been developed to calculate the EWEG considering random failure of both wind turbines and cables in this paper. The most suitable WF layout is selected by trading off between economy and reliability using a fuzzy decision-making approach.

Local turbulence parameterization improves the Jensen wake model and its implementation for power optimization of an operating wind farm

Abstract. In this paper, a new calculation procedure to improve the accuracy of the Jensen wake model for operating wind farms is proposed. In this procedure, the wake decay constant is updated locally at each wind turbine based on the turbulence intensity measurement provided by the nacelle anemometer. This procedure was tested against experimental data at the Sole du Moulin Vieux (SMV) onshore wind farm in France and the Horns Rev-I offshore wind farm in Denmark. Results indicate that the wake deficit at each wind turbine is described more accurately than when using the original model, reducing the error from 15 % to 20 % to approximately 5 %. Furthermore, this new model properly calibrated for the SMV wind farm is then used for coordinated control purposes. Assuming an axial induction control strategy, and following a model predictive approach, new power settings leading to an increased overall power production of the farm are derived. Power gains found are on the order of 2.5 % for a two-wind-turbine case with close spacing and 1 % to 1.5 % for a row of five wind turbines with a larger spacing. Finally, the uncertainty of the updated Jensen model is quantified considering the model inputs. When checked against the predicted power gain, the uncertainty of the model estimations is seen to be excessive, reaching approximately 4 %, which indicates the difficulty of field observations for such a gain. Nevertheless, the optimized settings are to be implemented during a field test campaign at SMV wind farm in the scope of the national project SMARTEOLE.

Investigation of offshore wind farm layouts regarding wake effects and cable topology

Offshore wind energy is emerging as a large contributor to installed renewable energy capacity. In order to continue the momentum of its development, the offshore wind industry is looking to continually lower the levelized cost of electricity (LCOE). One area being explored in an effort to lower the LCOE of offshore wind generation is the optimization of the wind farm layout. Many of the offshore wind farm layout designs that exist today are structured in a rectilinear form where turbines are spaced evenly along columns and rows. This research explores the economic advantages of removing rectilinear constraints and optimizing the positions of the individual turbines within an offshore wind farm. At the core of achieving the research objective was the development of a model that is capable of simulating an existing offshore wind farm by converting representative wind farm data into an LCOE. The positions of the turbines within the wind farm can be modified using an optimization framework with the intent to minimize the LCOE. The model comprised of the Jensen Wake Model, a hybrid cable layout heuristic and a cost scaling model. The wind farm layout was optimized using a genetic algorithm. The cost estimation model and optimization framework were applied into two case studies to analyze the results of the wind farm layout optimization of two wind farms, Horns Rev and Borssele. In both case studies the optimized layouts provided higher AEP, shorter intra-array collection cable lengths and ultimately a lower LCOE than the baseline rectilinear layouts.

Optimization of wind farm layout considering wake effect and multiple parameters

The output power of wind farms in real world applications is lower than the theoretical output which is largely due to wake effect. So as to maximize the output power, the wake effect of upstream wind turbines on downstream ones should be attenuated. Thus, arrangement of wind turbines in a wind farm is an essential issue that needs to be tackled. This study pursues the aim of finding an optimal layout. Initially, Jensen wake model is applied to simulate the wake effect. Then, genetic algorithm is employed to optimize the wind farm layout considering multiple factors that include different hub heights, rotor diameters, variable induction factors, power and capacity factor curves. Three cases including constant wind–constant direction, constant wind–variable direction and variable wind–variable direction are studied and compared with previous studies. The results indicate that the efficiency of the wind farm for case 1 is 96.71% which is a high record comparing to the previous literature. For Case 2 and 3, the annual wind farm capacity factor (CF) is found to be 97.96 and 97.51%. The power output of Case 1, 2, and 3 are 5.6855 × 108 kWh, 5.6694 × 108 kWh, and 4.5572 × 108 kWh, respectively. © 2019 American Institute of Chemical Engineers Environ Prog, 38:e13146, 2019

Fast Processing Intelligent Wind Farm Controller for Production Maximisation

A practical wind farm controller for production maximisation based on coordinated control is presented. The farm controller emphasises computational efficiency without compromising accuracy. The controller combines particle swarm optimisation (PSO) with a turbulence intensity–based Jensen wake model (TI–JM) for exploiting the benefits of either curtailing upstream turbines using coefficient of power ( C P ) or deflecting wakes by applying yaw-offsets for maximising net farm production. Firstly, TI–JM is evaluated using convention control benchmarking WindPRO and real time SCADA data from three operating wind farms. Then the optimised strategies are evaluated using simulations based on TI–JM and PSO. The innovative control strategies can optimise a medium size wind farm, Lillgrund consisting of 48 wind turbines, requiring less than 50 s for a single simulation, increasing farm efficiency up to a maximum of 6% in full wake conditions.

Study on three wake models’ effect on wind energy estimation in Hong Kong

Wake effect is one of the most vital factors in wind farm layout design and energy output estimation. Some wake models have been used to improve the power generation estimation precision. In this study, three typical wake models (Jensen wake model, two-dimensional (2D) Jensen wake model and Jensen-Gaussian wake model) are compared and adopted to estimate the offshore wind energy output in Hong Kong. Both the total electricity generation and power output from each wind turbine are compared when different wake models are used. The results show that the three different wake models have not produced significant different results on their total energy output estimations. The estimation error from the 2D Jensen wake model and Jensen-Gaussian wake model compared with the Jensen wake model are 1.55% and 0.38%, respectively. However, the wake’s effect on each wind turbine’s power estimation cannot be ignored, which is important to wind turbine’s structural study. Based on the 2D Jensen wake model, an assumption of 3D Jensen-Gaussian wake model is discussed at the end of this paper, which is supposed to be studied in the near future. In conclusion, this study contributes to wake model selection, wind farm layout design and wake model’s further development.

Tidal Turbine Array Optimization Based on the Discrete Particle Swarm Algorithm

In consideration of the resource wasted by unreasonable layout scheme of tidal current turbines, which would influence the ratio of cost and power output, particle swarm optimization algorithm is introduced and improved in the paper. In order to solve the problem of optimal array of tidal turbines, the discrete particle swarm optimization (DPSO) algorithm has been performed by re-defining the updating strategies of particles’ velocity and position. This paper analyzes the optimization problem of micrositing of tidal current turbines by adjusting each turbine’s position, where the maximum value of total electric power is obtained at the maximum speed in the flood tide and ebb tide. Firstly, the best installed turbine number is generated by maximizing the output energy in the given tidal farm by the Farm/Flux and empirical method. Secondly, considering the wake effect, the reasonable distance between turbines, and the tidal velocities influencing factors in the tidal farm, Jensen wake model and elliptic distribution model are selected for the turbines’ total generating capacity calculation at the maximum speed in the flood tide and ebb tide. Finally, the total generating capacity, regarded as objective function, is calculated in the final simulation, thus the DPSO could guide the individuals to the feasible area and optimal position. The results have been concluded that the optimization algorithm, which increased 6.19% more recourse output than experience method, can be thought as a good tool for engineering design of tidal energy demonstration.

Large-eddy simulation study of multi-rotor wind turbines

A novel wind turbine configuration comprising of four identical rotors mounted on a single tower is studied using large-eddy simulation (LES) with turbine forces modeled using an actuator drag-disk model. The characteristics of the wakes of the multi-rotor turbine are compared to those of the wake of a conventional turbine comprised of a single rotor per tower. The single-rotor turbine has twice the diameter and the same thrust coefficient as the rotors of the multi-rotor turbine. Several multi-rotor configurations, with varying horizontal and vertical spacings between the four rotors, are evaluated. The multi-rotor turbine wakes are found to recover faster, while the turbulence intensity in the wake is smaller, compared to the wake of the conventional turbine. The mean velocity profiles obtained from the LES results are predicted accurately by a semi-analytical model assuming Gaussian radial profiles of the velocity deficits, and either linear or quadratic superposition of multiple wakes. The classical Jensen wake model, assuming top-hat radial profiles, with quadratic superposition of wakes is also found to accurately predict the decay of the axial mean velocity in the streamwise direction. The interaction between multiple multi-rotor turbines is contrasted with that between multiple single-rotor turbines by considering wind farms with five turbine units aligned perfectly with each other and the wind direction and separated by four single-rotor diameters. The wake losses are found to be significantly smaller in such a wind farm comprising of multi-rotor turbines as compared to single-rotor turbines. The top-hat analytical model is employed to quantify the benefits of the multi-rotor configuration over the conventional single-rotor configuration for a wide range of thrust coefficients and axial spacings. These results suggest that a larger planform energy flux can be achieved without significantly increased fatigue loads by using multi-rotor turbines instead of conventional, single-rotor turbines.

Optimization of wind turbines siting in a wind farm using genetic algorithm based local search

Abstract The present work is devoted to search for the optimum wind farm layout using binary real coded genetic algorithm (BRCGA) based local search (LS); gathering robust single wake model with suitable wake interaction modeling. The binary part of genetic algorithm (GA) is used to represent the location of turbines; while the real part is used to give the power generated by each turbine at its location. In addition, the solution quality is improved by implementing LS technique; where it intends to find the optimal solution near the approximated solution obtained by BRCGA. The Jensen wake model along with the sum of squares model are used to obtain the available power for each turbine; where it is considered one of the most common analytical models used for wind farm optimization. Siting improvement is achieved, as compared with earlier studies.

Wake and Turbulence Analysis for Wind Turbine Layouts in an Island

There is a big wind energy potential in supplying the power in an island and most of the islands are off-grid. Due to the limited area in island(s), there is need to find appropriate layout / location for wind turbines suited to the local wind conditions. In this paper, we have considered the wind resources data of an island in Trøndelag region of the Northern Norway, situated on the coastal line. The wind resources data of this island have been analysed for wake losses and turbulence on wind turbines for determining appropriate locations of wind turbines in this island. These analyses are very important for understanding the fatigue and mechanical stress on the wind turbines. In this work, semi empirical wake model has been used for wake losses analysis with wind speed and turbine spacings. The Jensen wake model used for the wake loss analysis due to its high degree of accuracy and the Frandsen model for characterizing the turbulent loading. The variations of the losses in the wind energy production of the down-wind turbine relative to the up-wind turbine and, the down-stream turbulence have been analysed for various turbine distances. The special emphasis has been taken for the case of wind turbine spacing, leading to the turbulence conditions for satisfying the IEC 61400-1 conditions to find the wind turbine layout in this island. The energy production of down-wind turbines has been decreased from 2 to 20% due to the lower wind speeds as they are located behind up-wind turbine, resulting in decreasing the overall energy production of the wind farm. Also, the higher wake losses have contributed to the effective turbulence, which has reduced the overall energy production from the wind farm. In this case study, the required distance for wind turbines have been changed to 6 rotor diameters for increasing the energy gain. From the results, it has been estimated that the marginal change in wake losses by moving the down-stream wind turbine by one rotor diameter distance has been in the range of 0.5 to 1% only and it is insignificant. In the full-length paper, the wake effects with wind speed variations and the wind turbine locations will be reported for reducing the wake losses on the down-stream wind turbine. The Frandsen model has been used for analysing turbulence loading on the down-stream wind turbine as per IEC 61400-1 criteria. In larger wind farms, the high turbulence from the up-stream wind turbines increases the fatigues on the turbines of the wind farm. In this work, we have used the effective turbulence criteria at a certain distance between up-stream and down-stream turbines for minimizing the fatigue load level. The sensitivity analysis on wake and turbulence analysis will be reported in the full-length paper. Results from this work will be useful for finding wind farm layouts in an island for utilizing effectively the wind energy resources and electrification using wind power plants.

Analysis of Series-DC Offshore Wind Plants with Aerodynamic Wake Effects

In series-dc wind plants, variations in power output among turbines due to aerodynamic effects may lead to violations of operational limits of electric machines and power electronic converters. Turbine wakes constitute the predominant cause of such variations. It is, therefore, imperative to incorporate wake models during analysis of wind plant-level issues and control strategies. In this paper, two candidate energy conversion configurations previously proposed for series-dc connected turbines are considered. They are analyzed in the context of a notional offshore wind plant using the Jensen wake model. An optimization problem is formulated for maximizing total plant power output. A key finding is that this objective is attainable without any turbine violating operational limits for arbitrary wind direction and speed. This, however, may require variation of transmission voltage or current as a function of prevailing wind conditions by means of the onshore converter interfacing the plant with the terrestrial power grid.

A Markovian wind farm generation model and its application to adequacy assessment

Wind profile, wake effect, and wind turbine outage create considerable impact on the energy production of a wind farm. This paper proposes a Markovian wind farm generation model that incorporates these factors. This model considers the wind farm as a generating unit with multiple generation states. The probability, frequency of occurrence, and transition rate of each state can be obtained using the collected wind profile data and wind turbine reliability parameters. The power output of each state is calculated using Jensen wake model and enumerated wind farm layouts. The proposed model is verified by a sequential Monte Carlo simulation approach using a test wind farm and recorded wind profile data from four different sites in North Dakota, USA. A state merging technique is developed to enable the application of the proposed model to adequacy assessment. The Roy Billiton Test System with a test wind farm is used to demonstrate the application of the proposed model and the procedure to adequacy assessment. Moreover, this paper investigates the influence of wake effect, peak load, seasonal wind pattern, wind turbine reliability parameters, and wind turbine type on system adequacy.

Review of Reactive Power Dispatch Strategies for Loss Minimization in a DFIG-based Wind Farm

This paper reviews and compares the performance of reactive power dispatch strategies for the loss minimization of Doubly Fed Induction Generator (DFIG)-based Wind Farms (WFs). Twelve possible combinations of three WF level reactive power dispatch strategies and four Wind Turbine (WT) level reactive power control strategies are investigated. All of the combined strategies are formulated based on the comprehensive loss models of WFs, including the loss models of DFIGs, converters, filters, transformers, and cables of the collection system. Optimization problems are solved by a Modified Particle Swarm Optimization (MPSO) algorithm. The effectiveness of these strategies is evaluated by simulations on a carefully designed WF under a series of cases with different wind speeds and reactive power requirements of the WF. The wind speed at each WT inside the WF is calculated using the Jensen wake model. The results show that the best reactive power dispatch strategy for loss minimization comes when the WF level strategy and WT level control are coordinated and the losses from each device in the WF are considered in the objective.

Statistical meandering wake model and its application to yaw-angle optimisation of wind farms

The wake produced by a wind turbine is dynamically meandering and of rather narrow nature. Only when looking at large time averages, the wake appears to be static and rather broad, and is then well described by simple engineering models like the Jensen wake model (JWM). We generalise the latter deterministic models to a statistical meandering wake model (SMWM), where a random directional deflection is assigned to a narrow wake in such a way that on average it resembles a broad Jensen wake. In a second step, the model is further generalised to wind-farm level, where the deflections of the multiple wakes are treated as independently and identically distributed random variables. When carefully calibrated to the Nysted wind farm, the ensemble average of the statistical model produces the same wind-direction dependence of the power efficiency as obtained from the standard Jensen model. Upon using the JWM to perform a yaw-angle optimisation of wind-farm power output, we find an optimisation gain of 6.7% for the Nysted wind farm when compared to zero yaw angles and averaged over all wind directions. When applying the obtained JWM-based optimised yaw angles to the SMWM, the ensemble-averaged gain is calculated to be 7.5%. This outcome indicates the possible operational robustness of an optimised yaw control for real-life wind farms.

Qualitative analysis of wind-turbine wakes over hilly terrain

In this work, wind-turbine wakes are studied over flat and hilly terrains. Measurements made by using stereoscopic PIV are compared to data obtained from numerical simulations using RANS equations and an actuator-disc method. The numerical and experimental data show similar qualitative trends, indicating that the wind-turbine wake is perturbed by the presence of the hills. Additionally, a faster flow recovery at hub height is seen with the hilly terrain, indicating that the hills presence is beneficial for downstream turbines exposed to wake-interaction effects. The Jensen wake model is implemented over the hilly terrain and it is shown that this model cannot accurately capture the wake modulations induced by the hills. However, by superimposing a wind-turbine wake simulated over flat terrain on the hilly-terrain flow field, it is illustrated that the commonly-used wake-superposition technique can yield reasonable results if the used wake model has sufficient accuracy.