Weibull Wind Speed Distribution Research Articles

Uncertainty-Based Capacity Factors of Operational Wind Turbines Using the Generalized Likelihood Uncertainty Estimation (GLUE) Method

This study proposes a novel framework that couples the general likelihood uncertainty estimation (GLUE) method with a deterministic forecasting approach to conduct a new uncertainty analysis approach for assessing the energy production of operational wind turbines installed in the Jhongtun wind farm at Penghu (an island in the middle of Taiwan Strait). The 10-year measured data of wind speeds and energy output collected on these wind turbines is divided into two 5-year data sets for the present analysis framework of execution and validation to demonstrate the predictability of the GLUE method. The present study considers 15 scenario testing cases with various time periods, i.e., twelve months, the strong-wind (October-March) regime, the weak-wind (April-September) regime, and one year, for the framework to investigate the applicability of the GLUE method on long-term wind energy forecasting. In the execution framework, the 5-year measured data is used by the GLUE method to access the uncertainties involved in the deterministic approach (i.e., the shape and scale parameters of the Weibull wind speed distribution (WWSD), the performance curve, and the capacity factor) with two confidence intervals of 50% and 90%. The framework is then validated by the measured capacity factors in the last 5-year data and compared with the results of the uncertainty analysis approach by the Monte Carlo (MC) approach to discover the applicability of the new uncertainty analysis approach. From the simulated results, it is found that the proposed uncertainty analysis approach provides predictions of confidence intervals that match the measured data better than the MC-based uncertainty analysis approach. Specifically, the proposed approach can match the measured capacity factors in all the simulated scenarios. Conversely, the MC-based approach is found to create narrow confidence intervals that cannot completely capture the measured capacity factors, particularly for the strong-wind, weak-wind, and one-year scenarios. Therefore, this novel uncertainty analysis approach is proven to be useful in predicting the uncertainties of wind energy production.

Impact of Weibull Wind Speed Distribution on the Costs of Producing Power‐to‐X Products

AbstractA calculation method based on Weibull parameters and cost functions is presented to optimize the levelized cost of electricity and the costs for subsequent power‐to‐X (PTX) production from wind power. PTX products considered are methanol, ammonia, synthetic gasoline, and synthetic diesel as well as the hydrogenation of liquid organic hydrogen carrier. The onshore production sites Haru‐Oni in Chile, Tarfaya in Morocco, and Dornum in Germany were used for illustrative purposes. The model calculations show that the rated power of the installed wind turbines for power generation is generally optimal between 1 and 3 MWel in contrast to the current trend towards ever higher rated power. Also, it has been found that the recoverable wind energy increases with rising Weibull shape factor k if the wind speed at which the rated power is reached is smaller than the Weibull scaling factor A.

Techno-economic assessment of offshore wind energy potential at selected sites in the Gulf of Guinea

Offshore wind power has been found to stand out among the most dynamic renewable energy technologies. With its long coastal line, Nigeria has an overwhelming advantage in developing marine energy resources to relieve the power crisis effectively. This work analyzed and characterized observation data of sea-surface wind speed and direction at 30-minute intervals between 1979 and 2015 at five synoptic offshore stations in the Gulf of Guinea. The seasonal variations in hourly surface wind speed and directions as well as the Weibull distribution of wind speed and wind power at 100 m hub height were examined. The wind shears, capacity factors, and accumulated energy outputs for seven offshore wind turbine types were determined for the selected locations. In addition, the economic analysis of the selected offshore turbines using levelized cost of energy was carried out, while sensitivity analysis of the total levelized cost of energy to key input parameters was further determined. The results revealed large spatial and temporal variations in wind speed and wind power in the Gulf of Guinea. The most viable offshore site for wind energy exploitation was Agbami (the deepest offshore site), while Bonny (the shallow coastal site) had the least. The findings established very good fits (having mean bias (between −0.08 ms−1 and −2.44 ms−1), percentage bias (between −0.47% and −13.98%), correlation coefficients (between 0.97 and 0.98), Chi-square (between 0.2 and 1.2), and root mean square error (between 1.2 ms−1 and 3.1 ms−1)) between Weibull distribution and the actual wind data. The wind turbines with the highest and the lowest wind power densities, capacity factors, and power outputs across the seasons and sites were V236-15.0 MW and Siemens SWT113, respectively. The levelized cost of energy was considered for the deep waters due to the moderately high-capacity factors. The highest values ranged between 101.48 and 137.12 USD/MWh at Sea Eagle with V236-15 MW and V117-4.2 MW, respectively, while the lowest ranged from 52.29 to 69.66 USD/MWh at Agbami with V236-15 MW and Siemens (SWT113), respectively. The exploitation of Nigeria’s offshore wind resources could also be dedicated to producing renewable hydrogen and can serve to meet the country’s ambitious targets set for carbon neutrality by 2060.

Local flow and loads estimation on wake-affected wind turbines using graph neural networks and PyWake

The estimation of the flow conditions throughout a modern wind farm is a relevant albeit complex problem involving several different modelling scales. In this context, recent years have seen the rise of the demand - normally industry-driven - of quick, computationally inexpensive, wind farm flow field simulators upon which further calculations might be undertaken (e.g. power output, fatigue loads, etc.). Naturally, the trustworthiness of such models hinges upon their ability to accurately estimate wakes, under the evident trade-off between computational time and accuracy. One such simulator that has been recently gaining traction within the wind community is PyWake, a Python-based flow solver, with several possible add-ons and modularity options. Based on runs from PyWake, this contribution studies the applicability of graph neural networks (GNN) as a simultaneous wind turbine fleet, wind inflow and loads surrogate. As graphs are discrete mathematical sets of dependent objects, one can see how the layout-dependent interaction between wind turbines’ aerodynamics, from which wake arises, lends itself to be modelled as a graph. Thus, we introduce the use of GNNs for layout-agnostic joint modelling of rotor-averaged wind speed, turbulence intensity, power production and damage equivalent loads (DEL) on individual turbines of wind farms. To this end, probabilistic samples of inflow conditions from a Weibull distribution for wind speed, uniform wind direction and conditional normal distributions of wind shear and nacelle yaw angles are generated as main inflow properties in the numerical simulations. Additionally, arbitrary wind farm layouts are created based on varied geometric shapes with random parametrization (varying orientations, length/width ratio). Both the arbitrary layouts and the random inflow conditions are then used as inputs for PyWake. PyWake’s output, namely, rotor averaged wind speed, turbulence intensity, power production and DELs of each individual wind turbine in the wind farms, are used to train a general GNN model. We elect to implement an Encode-Process-Decode GNN as a graph learning model. We compare the performance of various approaches of the relational dependency representation (edge-forming techniques) amongst the nodes (wind turbines) on the graph, such as Delaunay triangulation, KNN, radius-based methods and fully connected scheme. In our analysis, we evaluate the accuracy of GNNs and its ability to generalize their joint predictions for unseen layouts and varying inflow conditions.

Using Observed and Modelled Heat Fluxes for Improved Extrapolation of Wind Distributions

Modelling the horizontal and vertical variation of wind speed is crucial for wind energy applications. A model frequently used for this purpose is part of the Wind Atlas Analysis and Application program (WAsP). Here, we modify the model in WAsP to account for local atmospheric stability parameters. Atmospheric stability effects are treated by using the impact of a temperature scale on the geostrophic drag law and the diabatic logarithmic wind profile. Using this approach, wind-direction dependent mean and standard deviation of a surface-layer temperature scale and a mean boundary-layer height scale can be obtained from either numerical weather prediction model output or observations to improve vertical extrapolations of Weibull wind speed distribution parameters. The modified atmospheric stability model is validated at six flat sites in northwestern Europe. The surface-layer temperature scale is available from sonic anemometer measurements at three of the sites. At all sites the temperature scale is also estimated from reanalysis data and from mesoscale model output. The modified model improves the aggregated estimations of power density distributions when extrapolating to nearby locations from 5.2 to 3%, when using the temperature scale derived from either observations or mesoscale/reanalysis output compared to the current model.

Multi model robust control design for a floating offshore variable speed wind turbine with tension leg platform

This paper presents a multi-model robust control (MMRC) design for an offshore variable speed wind turbine with tension leg platform. The proposed control scheme covers the model uncertainty in the above rated wind speed, and it provides a reliable control for power regulation while minimizing the mechanical loads on the wind turbine structure. For this purpose, the above rated wind speed region is divided into several wind speed groups, and a set of linearized models are obtained from the Fatigue, Aerodynamics, Structures, and Turbulence (FAST) simulator for various mean wind speeds of each group. Using Weibull wind speed distribution, a nominal model with additive uncertainty is generated for each wind speed group, to be used in the multi-model robust control design. The MATLAB/Simulink software environment is used to verify the performance of the proposed control strategy using the National Research Energy Laboratory (NREL) three-bladed horizontal axis 5-MW baseline wind turbine. The performance of the proposed multi-model robust controller is compared with the state-of-the-art gain-scheduling PI (GSPI) controller. The results show improvement in power regulation and platform movement minimization while reducing the mechanical loads of the wind turbine. By using the proposed control scheme, the severe oscillation in the blade pitch actuation and power output, which is due to the changes in the operating point of the wind turbine, decreases drastically.

Estimation methods for wind power potential with practical case study

The potential at any location of the world for wind power must be appraised before it can be used effectively. The current state of wind resource assessment studies is provided in order to find appropriate methodologies. The Weibull distribution is a two- or three-parameter distribution function by which the wind speed's frequency distribution can be fitted properly . This set of curves has been proven to fit wind speed readings extremely well. The Maximum likelihood method, the Modified maximum likelihood method, Error of approximation, Method of Moment and the Energy pattern factor method are all offered as methods for estimating the parameters of the Weibull wind speed distribution for wind energy analysis. A sample wind speed data set is used to demonstrate the use of each method, and statistical methods of analysis are used to compare the accuracy of each method. The research aids in identifying which method is most effective in finding Weibull distribution parameters and determining the wind energy resource. In grid-connected wind producing plants, wind power forecasting is crucial for demand-supply equilibrium. Many accurate and dependable weather forecasting models use a range of modern methodologies. The electricity prediction is primarily dependent on short-term to second-by-second forecasting, intermediate duration of 2-7 days and with long-term prediction and short-term duration of nearly 2 days, with the help of various models.

Impact of wind speed distribution and management strategy on hydrogen production from wind energy

Electrolytic hydrogen production using renewable sources can play a central role in global decarbonization. However, the direct coupling of electrolyzers with renewable energies can cause frequent shutdowns and high production fluctuations unless adopting electrical storage systems or using electricity from the grid that is generally not completely decarbonized. In this study, a system consisting of a wind turbine, short-term battery storage, and an alkaline electrolyzer was analyzed through annual simulations in MATLAB. A power management strategy sets the electrolyzer and battery operating conditions. Firstly, several battery and electrolyzer sizes were investigated for a given wind site for three scenarios (0%grid, 20%grid, and 100%grid) in which the grid guarantees the electrolyzer operation at a minimum load of 0%, 20%, and 100%, respectively. Secondly, the effect of the wind speed distribution on the system performance was investigated by comparing sixteen different wind sites in the 0%grid scenario. The battery presence always led to a LCOH increase. The 20%grid scenario represented a good compromise between the minimization of specific CO2 emissions, and the minimization of LCOH (that was always lower compared to the 0%grid scenario and the lowest without battery). The shape parameter of the fitted Weibull wind speed distribution did not affect the system. Instead, a greater scale parameter led to both greater hydrogen production and a lower LCOH.

Wind speed Weibull distribution and wind energy potential of Chandpur, Bangladesh

Weibull distribution goes particularly well with wind speed data and is necessary to assess wind energy harnessing potential at a site. For the best estimation of the statistical distribution parameters at Chandpur (23.21116° N; 90.64237° E), located at the southern part of Bangladesh, six models: graphical method, method of moments, power density method, Justus method, Lysen method and maximum likelihood method have been analyzed for 18.8 m, 40.2 m and 59.9 m above ground level (AGL) using measured wind speed data for 2014-2017. Out of the six models, Justus method has showed the best result for estimation of Weibull parameters at all heights AGL with average RMSE of 0.0082 and R2 of 0.9650. Further more to evaluate the wind energy potential at modern wind turbine hub height of 100 m, firstly the wind shear exponent at the site (the average value is 0.37 considering the 10 m elevation of the site above sea level) is estimated from the wind data of 3 heights; secondly average wind speed (4.88 m/s), wind power density (108.8 Wm-2), Weibull distribution parameters (shape factor 2.29 and scale factor 5.33 m/s) and wind turbine power curve related wind speeds (cut in 2.28 m/s, rated 9.33 m/s and cut out 21.03 m/s)have been extrapolated at the hub height. The average wind speed and wind power density values show that the class of the site is 1 in the worldwide accepted wind power classification, based on long term practical wind farm installation experiences; the low cut in speed (<3 m/s) shows that suitable wind turbines for the site are commercially unavailable for the site and turbines with 3 m/s cut in speed have average annual capacity factor of 16.62 %, less than the commercially viable capacity factor >25 %. The wind power class (< class 3) and capacity factor (<25 %) strictly reveals that Chandpur is not suitable for wind energy exploration in near future until a high technical improvement of wind turbines and reduction of relevant costs. DUJASE Vol. 6 (2) 99-108, 2021 (July)

Distributed Active Power Optimal Dispatching of Wind Farm Cluster Considering Wind Power Uncertainty

With the large-scale volatility and uncertainty of the centralized grid connection of wind power, the dimensionality disaster problem of wind farm cluster (WFC) scheduling optimization calculation becomes more and more significant. In view of these challenges, a distributed active power optimal dispatch model for WFC based on the alternating direction multiplier method (ADMM) is proposed, and the analytical description of the distribution characteristics of the active power output of wind farms is introduced into the proposed model. Firstly, based on the wake effect, the Weibull distribution of wind speed is transformed by the impulse function to establish an analytical model of the active output distribution of the wind farm. Secondly, the optimization goal is to minimize the expected sum of the deviations of the dispatch instructions and the output probability density function of each wind farm, constructing a WFC active power optimal dispatch model considering uncertainty. Finally, the proposed model is decoupled in space and time into sub-optimization problems, and the ADMM is improved to construct an efficient solution algorithm that can iterate in parallel and decouple a large number of decision variables at the same time. The model is compared with other current classical models through the evaluation of multiple recommendation evaluation metrics, and the experimental results show that the model has a 3–7% reduction in dispatched power shortfalls and a 4–21% improvement in wind power utilization. The optimization algorithm for model construction has extremely high computational efficiency and good convergence. The results show that when the update step size is three, the convergence is the fastest, and when the update step size is six, the convergence is the slowest; in addition, when the number of wind farms is greater than eight, the distributed computing efficiency has an incomparable advantage over the centralized one. It plays a helpful role in wind power consumption and the efficient calculation of the power grid and effectively improves the reliability of the power grid.

REGARDING THE CHARACTERISTICS OF THE WIND IN NORTHERN REGION DISTRICTS OF THE REPUBLIC OF MOLDOVA

The study is focused on three districts in the northern region of the Republic of Moldova – Briceni, Edinet and Ocnita. The maps were calculated and presented in terms of average annual wind speed and wind power density at a height of 100 m above ground level, wind rose and Weibull wind speed distribution. In the calculations performed for the three analyzed districts it was found that the average annual wind speed is between 6.84 and 7.35 m / s, and the wind power density – between 450 and 593 W / m2. The highest annual average speed equal to 7.35 m / s was identified in Ocnita district. At the same time, having the maps of the wind speed and the power density, the convenient locations for the construction of the wind farms can be selected. For each district involved in the study, a location with a pronounced wind potential was identified, recommended for the location of any wind farms.

Multi-year measurements of ripple and dune migration on Mars: Implications for the wind regime and sand transport

Aeolian sand dunes are observed across the Martian surface. The arrival of the HiRISE camera on Mars Reconnaissance Orbiter at Mars in 2006 enabled detection of modern-day movement of dunes and ripples from orbit for the first time. Since 2006, HiRISE collected a long timeseries of repeat imagery at a few Martian dune fields. We analyze this timeseries of imagery at two of these dune fields, using COSI-Corr for image registration and correlation, to study the movement and dynamics of dunes and meter-scale ripples at the Nili Patera and Meroe Patera barchan dune fields. We present measurements of whole-dune translational sand fluxes extracted at both dune fields via manual tracking of dune crestlines and slipfaces in HiRISE images. We also present a multi-Mars year timeseries of ripple flux measurements. Ripple migration shows a consistent pattern of seasonal variation, with maxima in flux during northern-hemisphere autumn and winter at both dune fields. Ripple migration is also observed to decrease away from the upwind margins of dune fields. We compare our observations with predicted sand transport using winds output from the MarsWRF atmospheric circulation model and theories of sand motion. The model predicts half-hourly, mesoscale winds, from which we estimate the 1 Hz, local-scale winds by assuming a Weibull distribution of wind speed, with parameters chosen based on landed wind data. This approach uses remote sensing observations of bedform migration, and comparisons with model output, to place constraints on the wind regime. Our measurements of the seasonal pattern of sand flux variation agree, to first order, with predictions based on modeled wind speeds. Comparison of the magnitudes of predicted and observed sand fluxes is not feasible due to the high uncertainties in our calculated sand fluxes caused by uncertainties in input parameters, most importantly the assumed fluid threshold for sand transport. However, we note that model predictions fit our observed sand fluxes best when relatively low values of the fluid threshold shear velocity of ~0.6–0.8 m/s (or shear stresses of O(10−3) Pa) are assumed.

Evaluation of projected decadal wind energy potential in Chiang Mai

One of the alternative energy sources which have globally pay more attention is wind power. In this research, the Weibull wind speed distribution was applied to evaluate wind energy potential during the period of 2081-2090. The projected wind datasets in this study were simulated by the Non hydrostatic Regional Climate Model (NHRCM). The boundary condition was the 20 km resolution MRI Atmospheric General Circulation Model (AGCM20) under the RCP8.5 scenario. The surface wind datasets in Chiang Mai were analyzed to 3-time intervals, i.e., May-August, September-December and January-April. Two averaged Weibull distribution parameters, i.e., k, shape parameter, and c, scale parameter were determined. The shape and scale parameters fluctuated 1.15 to 1.34 and 0.38 m/s to 0.74 m/s, respectively. It was found that the surface mean wind speed from May through August was stronger than from September through December.

Wind Climate and Wind Power Resource Assessment Based on Gridded Scatterometer Data: A Thracian Sea Case Study

The present analysis utilized the 6-hourly data of wind speed (zonal and meridional) for the period between 2011 and 2019, as retrieved from the Copernicus Marine Environmental Service (CMEMS), covering the Thracian Sea (the northern part of the Aegean Sea). Data were estimated from the global wind fields derived from the Advanced Scatterometer (ASCAT) L2b scatterometer on-board Meteorological Operational (METOP) satellites, and then processed towards the equivalent neutral-stability 10 m winds with a spatial resolution of 0.25° × 0.25°. The analysis involved: (a) descriptive statistics on wind speed and direction data; (b) frequency distributions of daily-mean wind speeds per wind direction sector; (c) total wind energy content assessment per wind speed increment and per sector; (d) total annual wind energy production (in MWh/yr); and (e) wind power density, probability density function, and Weibull wind speed distribution, together with the relevant dimensionless shape and scale parameters. Our results show that the Lemnos Plateau has the highest total wind energy content (4455 kWh/m2/yr). At the same time, the area to the SW of the Dardanelles exhibits the highest wind energy capacity factor (~37.44%), producing 7546 MWh/yr. This indicates that this zone could harvest wind energy through wind turbines, having an efficiency in energy production of 37%. Lower capacity factors of 24–28% were computed at the nearshore Thracian Sea zone, producing between 3000 and 5600 MWh/yr.

Combined effects of pitch angle, rotational speed and site wind distribution in small HAWT performance

Constant speed horizontal axis wind turbines operate at power coefficients different than its maximum due to operation at different tip speed ratios (TSRs). Whereas rotational speed and the site wind speed distribution determine the TSR range of the operation, the pitch angle is significant for the aerodynamic performance of the wind turbine. In this paper, a blade element momentum approach is used to study the power production effects of pitch angle and rotational speed of NREL Phase VI wind turbine at different site wind distributions (characterized by Weibull distributions). It is shown that the best combination of rotational speed and pitch angle always occurs at the same pitch angle, but for different rotational speeds (other than the best one) the best pitch angle may vary. The best rotational speed is found to be dependent on both form and scale factors of Weibull wind speed distribution. Improvements in turbine pitch angle and rotational speed are found to increase generated energy up to four times, but the increasing factor is highly dependent on wind speed distribution: For the studied turbine, high-wind-speeds sites can benefit more from the adjustment of these parameters than low-speed ones.

Applying Satellite Data Assimilation to Wind Simulation of Coastal Wind Farms in Guangdong, China

With the development of the wind power industry in China, accurate simulation of near-surface wind plays an important role in wind-resource assessment. Numerical weather prediction (NWP) models have been widely used to simulate the near-surface wind speed. By combining the Weather Research and Forecast (WRF) model with the Three-dimensional variation (3DVar) data assimilation system, our work applied satellite data assimilation to the wind resource assessment tasks of coastal wind farms in Guangdong, China. We compared the simulation results with wind speed observation data from seven wind observation towers in the Guangdong coastal area, and the results showed that satellite data assimilation with the WRF model can significantly reduce the root-mean-square error (RMSE) and improve the index of agreement (IA) and correlation coefficient (R). In different months and at different height layers (10, 50, and 70 m), the Root-Mean-Square Error (RMSE) can be reduced by a range of 0–0.8 m/s from 2.5–4 m/s of the original results, the IA can be increased by a range of 0–0.2 from 0.5–0.8 of the original results, and the R can be increased by a range of 0–0.3 from 0.2–0.7 of the original results. The results of the wind speed Weibull distribution show that, after data assimilation was used, the WRF model was able to simulate the distribution of wind speed more accurately. Based on the numerical simulation, our work proposes a combined wind resource evaluation approach of numerical modeling and data assimilation, which will benefit the wind power assessment of wind farms.

Data‐driven efficient reliability evaluation of power systems with wind penetration: an integrated GANs and CE method

The conventional Monte Carlo simulation may not be efficient enough for reliability evaluation of composite power systems. The cross-entropy (CE) algorithm is a promising state-of-the-art fast sampling method, while it has not been well developed in this field due to the implicit probability distributions of penetrated renewable energies. Specifically, the CE sampling requires the distributions of interest to be explicit and parametric, while some preconceived probabilistic distribution functions (PDFs) such as the Weibull distribution of wind speed make the results to deviate from the reality sometimes. In this study, a data-driven efficient approach for reliability evaluation of power systems with wind penetration is proposed utilising generative adversarial networks (GANs) and CE sampling. The distributions of wind speeds in multiple wind farms are estimated by GANs considering their spatial correlation without any prior knowledge. With the trained generative network mapping from the explicit Gaussian noise to the raw wind speed data, the CE sampling is successfully enabled to efficiently sample the system states with implicit PDFs, which are associated with wind speeds and component failures. A real wind speed dataset and the RTS testing system are utilised to verify the proposed integrated method, including the accuracy of distribution estimation and reliability evaluation result, as well as the speed-up efficiency of sampling.

A Dynamic Weighted Aggregation Equivalent Modeling Approach for the DFIG Wind Farm Considering the Weibull Distribution for Fault Analysis

The developing process of the aggregated dynamic equivalent model (DEM) for doubly-fed induction generator (DFIG) wind farms could be less computational and more efficient compared with the multimachine DEM, but less accurate when wind speed differences exist inside the wind farm. In addition, the wind speed differences contribute to the different activation patterns of the crowbar systems of DFIGs. Therefore, a dynamic weighted aggregation modeling approach is proposed in this paper to improve the applicability of the aggregated DEM for DFIG wind farm. First, the Gaussian density distance clustering algorithm is applied to segment the wind speed power curve into different zones such that each segmented zone is corresponded to one equivalent aggregated machine. Then the dynamic weighted aggregation equivalent model could be developed based on the conventional aggregated DEM, where the weighting factors for each generator are calculated according to the Weibull distribution of wind speeds. Different scenarios are simulated in MATLAB/Simulink environment to analyze the applicability of the proposed dynamic weighting equivalent model. The simulation results show the effectiveness of the proposed method.

Wind turbine power curve modeling using maximum likelihood estimation method

Modeling of wind turbine power curve which shows the relationship between wind speed and its power output can be used as an important tool in monitoring and forecasting wind energy. A data-driven approach to find most probable probability distribution function (PDF) for wind speed and turbine power is presented in this study. Equations for the scale and shape parameters in the Weibull wind speed distribution and equations for the four parameters in the logistic function were obtained explicitly by maximum likelihood estimation (MLE) method. With help of a selected data set from the wind speed and the corresponding power output data which was collected over a period of a year, the values of the parameters were obtained by solving the equations by iteration procedures. The predicted powers by the obtained logistic function closely follow the measured turbine powers averaged at 5-min or 10-min. Monitoring turbine power output by the logistic function was also tested for the measured powers in other time duration.

Optimal design of wind farm layout using a biogeographical based optimization algorithm

Promoting renewable energy utilization is treated as a must in current energy market worldwide. This paper studies the layout optimization process for wind farms with more realistic mathematical models. It uses a recent evolutionary algorithm known as BBO (biogeographical based optimization), which produces better results for various benchmarks, especially in continuous problems. Single and multiple wake models are adopted from latest work, which gives the best approximation according to real-world experiments and exact computer-aided simulations. Cost function models have been designed to best simulate a detailed practical farm during its lifetime. Weibull distribution for wind speed over a year period with arbitrary factors is considered for the site under study; this model is applied to the farm with the uniformly distributed wind to be able to compare turbine micro sitting results. Utilization of the realistic and detailed models provides different results compared to those of generic models. The practicality of the obtained results forms the distinction between the present work and previous studies. Various tests are performed using the aforementioned wake model on the former results for wind farm layout optimization problem (WFLOP). In addition to the suggested layouts for different land types and wind models, the sensitivity analysis of financial parameters is also conducted in this work.