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Renewable Energy
Published in Chitrarekha Kabre, Synergistic Design of Sustainable Built Environments, 2020
However, a German physicist Albert Betz concluded in 1919 that no wind turbine can convert more than 16/27 (59.3%) of the kinetic energy of the wind into mechanical energy turning a rotor. The theoretical maximum power coefficient of a wind turbine is 0.59, Betz limit or Betz law. Practically, the maximum power coefficient (Cp) may range from 0.25 to 0.45, and the power from a wind turbine can be calculated by Equation 5.8. Pk=Cp½A1.2V3
Wind Turbine Lubrication
Published in Leslie R. Rudnick, Synthetics, Mineral Oils, and Bio-Based Lubricants, 2020
Wind turbines have been used and have been evolving in various forms for the last 7000 years of human civilization. Versions of wind turbine-generated mechanical power helped early Egyptians propel boats along the Nile River as early as 5000 BC. In the fourteenth century, hollow-post mills were used to drive scoop wheels to drain the wetlands in Holland. In the 1700s, American colonists relied on windmills to grind grain, pump water, and cut wood at sawmills. These old-time wind turbines converted kinetic wind energy into mechanical energy and went from using no lubricant very early on to using simple oils such as olive oil [1]. In 1888, the first wind turbine with a rotor diameter of 17 m was used to generate electric power of 12 kilowatts (kW) and battery storage at Brush Windmill in Cleveland, Ohio [2], where it operated for 20 years. Modern wind turbines convert the wind’s kinetic energy, which is proportional to wind turbines’ swept area and the cube of wind speed, into electric power. A wind turbine could not theoretically extract more than 16/27 (59.26%) of the wind’s kinetic energy according to Betz’s law [3]. Wind turbines have grown drastically in output power by increasing the rotor diameter to reduce wind energy cost. In the mid-80s, small turbines with an average capacity of around 30 kW and rotor diameters of below 20 m were turned into giant machines with nominal power of 5 megawatts (MW) or above and rotor diameters of more than 100 m.
Renewable Energy
Published in Efstathios E. Michaelides, Energy, the Environment, and Sustainability, 2018
From Equations 6.8, 6.21, and 6.22, it follows that the maximum efficiency a wind turbine may have is ηmax = 16/27 = 0.593. Therefore, even an ideal wind turbine will convert less than 60% of the available power of the wind to electric power. The maximum wind turbine efficiency (59.3%) is sometimes referred to as the Betz limit or Betz’s law. Actual wind turbines have lesser efficiencies, which depend on the magnitude of the wind velocity.
Dynamic MPPT Controller Using Cascade Neural Network for a Wind Power Conversion System with Energy Management
Published in IETE Journal of Research, 2022
K. Chandrasekaran, Madhusmita Mohanty, Mallikarjuna Golla, A. Venkadesan, Sishaj P. Simon
In an autonomous distributed generation system, the load demand of a region being dynamic does not match with the available wind profile and the wind produced power. Moreover, excess or deficient power cannot be circulated to the grid in an autonomous distributed generation system. In the case of wind turbines, the maximum power that can be extracted from the wind, independent of wind turbine design, is formulated by Betz’s law. According to this law, a wind turbine can capture a maximum of 59.3% of the kinetic energy of wind. Tracking the peak power in varying wind speeds has led to the development of control techniques known as maximum power point tracking (MPPT) algorithms [6]. The common approach to integrate WPCS to the load is by employing power electronics converters. Most of the small WPCSs use a diode bridge rectifier connected to the DC–DC converter for the implementation of the MPPT technique [7,8].
Wake modelling via actuator-line method for exergy analysis in openFOAM
Published in International Journal of Green Energy, 2019
Mohsen Boojari, Esmail Mahmoodi, Ali Khanjari
Exergy analysis is a method that uses the conservation of mass and energy principles together with the second law of thermodynamics for the analysis, design, and improvement of energy and other systems. Exergy consumption during a process is proportional to the entropy generated due to irreversibilities associated with the process. Exergy is a measure of the quality of energy that is not conserved but rather is in part destroyed or lost in any real process. For exergy analysis, the characteristics of a reference environment must be specified. This is commonly done by specifying the temperature, pressure and chemical composition of the reference environment (Humidity has been considered to be negligible in the present work). The results of exergy analysis, consequently, are relative to the specified reference environment, which in most applications are modeled after the actual local environment. It is clear that wind turbines cannot extract the total kinetic energy of the wind (Figure 5). According to Betz’s law, wind turbines can take advantage of up to 59% of the power of the wind. Nevertheless, in practice, their efficiency is about 40% for great wind speeds. The rest of the wind’s energy that is not procurable is exergy loss (Koroneos and Spachos. 2003).
Design modification of three-blade horizontal-axis wind turbine for noise reduction
Published in International Journal of Ambient Energy, 2022
D. Rajesh, P. Anand, Nishant Kumar Nath
The design of the wind turbine blade can be done by using Bernoulli’s principle as well as blade element momentum (BEM) theory, which is first proposed by scientist Betz popularly known as the Betz law. According to the Betz law, the ideal coefficient of power of the wind turbine is 59.25%. According to the world’s largest wind turbine sea titan, 10 MW for a rotor diameter of 190 m, it gives a maximum power output of 10 MW for 10 rotations per minute (RPM). Normally wind speed and direction will not be constant, so the pitch angle in the wind turbine plays a major role in wind turbine power generation through a generator. Horizontal-axis wind turbines (HAWTs) have been used frequently because of its simple design when compared with VAWT turbines as well as the maximum efficiency is generated by the modern wind turbines of HAWT ranging from 20% to 50%. The foil selection is a very important criterion since the investigator needs to assess the values of the L/D ratio (the lift-to-drag ratio) where lift should be higher and drag should be smaller. The selection of foil mainly depends on the chord length, maximum thickness of the foil and camber thickness based on percentage relating to the chord length. The foil thickness will contribute more moments. The chord lengths vary from root to tip of the blade. The forces that act on the foil will vary by section by section of the foil by varying in the lift and drag coefficients. The higher lift coefficient and lower drag coefficient will enhance the rotor swept area (A=ΠR2) which indirectly increases the rotational moment. The tip speed ratios play a crucial role in the safety of wind turbines. Higher tip speeds will affect the wind turbine structure and mainly lead to collapsing of the entire structure.