Wind speed modelling using Weierstrass function fitted by a genetic algorithm

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

Researching on interaction between wind farm and power system, it usually uses simple model to describe the wind farm. The wind turbines in a wind farm always suppose as a coherent generator group, every wind turbines have identical wind speed. As wind turbine locates in the different site in the wind farm, the wind speed at each wind turbines will not change simultaneously. Wake effect is another factor that should take into consideration. So, it needs to get wind speed equivalent model. The equivalent model of wind speed in the wind farm is based on output of power. Gust wind and ramp wind are discussed. Wind farm will change gust wind into step varying wind and make ramp wind into different type wind. The arrangement of wind turbines will also affect equivalent model of wind speed. The result show that the length of wind farm will smooth the power output. It explains why the power output fluctuation of wind farm is smaller than single wind turbine. The onshore wind farm located in Dongtai Jiangsu province is proposed as an example. The equivalent wind speed model and equivalent impedance connected to grid are calculated. The results illustrate the impact of wind speed model on wind farm output.

This paper represents a platform for steady-state analysis of permanent Magnet Synchronous Generator (PMSG) based on uncertain wind speed. To evaluate the system performance such as torque, speed, current, voltage, and power of PMSG with considering the uncertain wind speed. This system consists of a wind speed model, wind turbine model, and PMSG model. The proposed wind speed model is put forward that could reflect the natural wind speed characteristics. The wind speed for wind turbine is used as an input, so that it captures the optimal power of wind and generates mechanical torque for PMSG. Mathematical analysis is used to demonstrate the efficacy of the model in dq-synchronous rotating reference frame of the generator. The steady-state analysis of the proposed PMSG uncertain wind speed model is evaluated with MATLAB/Simulink software.

First-order Markov chain approach to wind speed modelling

Appropriate wind speed modeling for generating synthetic wind speed data is crucial in microgrid reliability evaluation studies. This paper proposes a 2-D wind speed statistical model based on historical wind speed data. The first dimension of the proposed wind model focuses on the probability distribution on the time duration of different wind speed scales, while the second dimension focuses on the probability distribution of wind speed in each wind speed scale. Unlike traditional wind speed models, the proposed model can simultaneously deal with the probabilistic characteristics of wind speed and wind time duration. This paper also presents a 2-D wind model-based data sampling method, and incorporates it into the microgrid reliability assessment algorithm. Using historical wind speed data in Tianjin, China, it shows that the proposed 2-D wind speed statistical model helps to fully simulate the volatility of wind energy. Furthermore, the proposed wind speed model is applied on the microgrid reliability evaluation study, which shows that the proposed model can be effectively utilized by planners to conduct reliability evaluation for microgrid.

Large scale wind power penetration has a significant impact on the reliability of the electric generation systems. A wind farm consists of a large number of wind turbine generators (WTGs). A major difficulty in modeling wind farms is that the WTG not have an independent capacity distribution due to the dependence of the individual turbine output on the same energy source, the wind. In this paper, a model of the wind farm output power considering multi-wake effects is established according to the probability distribution of the wind speed and the characteristic of the wind generator output power: based on the simple Jenson wake effect model, the wake effect with wind speed sheer model and the detail wake effect model with the detail shade areas of the upstream wind turbines are discussed respectively. Compared to the individual wake effect model, this model takes the wind farm as a whole and considers the multi-wakes effect on the same unit. As a result the loss of the velocity inside the wind farm is considered more exactly. Furthermore, considering the features of sequentially and self-correlation of wind speed, an auto-regressive and moving average (ARMA) model for wind speed is built up. Also the reliability model of wind farm is built when the output characteristics of wind power generation units, correlation of wind speeds among different wind farms, outage model of wind power generation units, wake effect of wind farm and air temperature are considered. Simulation results validate the effectiveness of the proposed models. These models can be used to research the reliability of power grid containing wind farms, wind farm capacity credit as well as the interconnection among wind farms

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension (), structure fractal dimension () and total fractal dimension (D).

Advanced control of large-scale wind turbines: Structural load reduction and lifetime control

Sensitivity analysis of the system of wind speed distributions

Influence of the input layer signals of ANNs on wind power estimation for a target site: A case study

The effective exploitation of renewable energy sources is one of the most effective solutions to counter the energy, environmental and economic problems associated with the use of fossil fuels. Small-scale wind turbines (converting wind energy into electric energy with a power output lower than 50 kW) have received tremendous attention over the past few decades thanks to their reduced environmental impact, high efficiency, low maintenance cost, high reliability, wide wind operation range, self-starting capability at low wind speed, limited installation space, reduced dependence on grid-connected power and long transmission lines, low capital costs, as well as the possibility to be installed in some urban settings. However, there are significant challenges and drawbacks associated with this technology from many different perspectives, including the significant discrepancy between theoretical performance data provided by the manufacturers and real field operation, that need to be investigated in greater depth in order to enable a more widespread deployment of small-scale wind turbines. In this review, a complete and updated list of more than 200 commercially available small-scale horizontal and vertical wind turbine models is provided and analysed, detailing the corresponding characteristics in terms of the number and material of blades, start-up wind speed, cut-in wind speed, cut-out wind speed, survival wind speed, maximum power, noise level, rotor diameter, turbine length, tower height, and specific capital cost. In addition, several scientific papers focusing on the experimental assessment of field performance of commercially available small-scale horizontal and vertical wind turbines have been reviewed and the corresponding measured data have been compared with the rated performance derived from the manufacturers’ datasheets in order to underline the discrepancies. This review represents an opportunity for the scientific community to have a clear and up-to-date picture of small-scale horizontal as well as vertical wind turbines on the market today, with a precise summary of their geometric, performance, and economic characteristics, which can enable a more accurate and informed choice of the wind turbine to be used depending on the application. It also describes the differences between theoretical and in-situ performance, emphasizing the need for further experimental research and highlighting the direction in which future studies should be directed for more efficient design and use of building-integrated small-scale wind turbines.

The adequacy assessment of generation system including wind farm is a complicated process due to the inherent uncertainty of wind power generation. To evaluate the reliability benefit of the integration of wind power properly, it is critical to model the stochastic characteristics of wind power generation accurately. Considering that wind power output highly depends on wind speed, several methods to simulate wind speed have been studied. However, some statistical indices that obtained from the wind speeds simulated by the existing methods and the historical wind data do not match exactly. In this paper, a novel model, where time-sequential transition matrices of wind speed are established based on historical hourly data, is proposed to simulate the wind speed series. The proposed model is compared with probability sampling, time series analysis in terms of several statistical indices, and it is observed that the proposed method has an advantage over other methods. Through the wind integrated IEEE-RTS test system, the ability of different wind speed models to reflect the macroscopic statistical properties of actual wind speed data is compared. Besides, the impact of different wind speed models on the adequacy assessment of generation system is analyzed.

This study evaluated three surface meteorology variables from in-situ/observation data and compared it with WRF-PBL model and ERA5 reanalysis datasets during the two prevailing seasons of wet and dry over Ile-Ife study location. The aim was to determine which of the two datasets was capable of reproducing the diurnal variation of the selected datasets to serve as an alternative data source over the study area. Time series, quantitative statistics, Taylor Diagram (TD) and Taylor Skill Scores (TSS) were used to evaluate the capacity of the dataset against the in-situ data. Time series analysis results showed that model data followed the same diurnal pattern but overestimated 2 m air temperature (T2M), and 2 m relative humidity (RH2M) while ERA5 had better alignment with observation for the two seasons. The model wind speed (WS10M) showed overestimation for both seasons. ERA5 temperature data had the lowest values for MBE, MAE and RMSE, while relative humidity and wind speed from model data got the lowest values for all three statistics used. Pattern matching results for T2M and RH2M from Taylor Diagram placed ERA5 above model data with higher values of R mostly (>= 0.88) except for wind speed. Taylor Skill Score ranked ERA5 better for T2M, MYNN2 for RH2M while YSU and MYJ ranked better for WS10M for this study. Overall, ERA5 have better aggregate performance for temperature and relative humidity and not for wind speed. Results from this study will be useful in sourcing datasets for micrometeorological applications over the study area.

Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm

In this paper how to generate respiratory flow that has fractal signal feature is introduced. Physiological signal have fractal feature have been verified by many researchers, such as heart beat rate, interbreath interval. Mechanical ventilators are used to provide life support for patients with respiratory failure. But these machines can damage the lung, causing them to collapse. On the other hand, fractal feature can be used as an indication of health situation; as a result in patient simulation the physiological signal should also have fractal features. The fractal feature is generated by fractional Brownian motion simulation. The fractal dimension is decided by Hurst exponent in routine. The algorithm is realized by R language and result is input into LabVIEW which have friendly interface and easy for simulation control usage. The method can be used in design of mechanical ventilator and medical patient simulator.