Instructions: Please write your answers clearly, explain each step, and use proper mathematical notation. You can use Microsoft Excel, or any other software or online graphing tool to plot the graphs. Make sure to label your axes. Problem (Wind Energy Production) Authors: S. Smith and W. Song Edited by: M. Tanzy and 0. Yavuz Wind power is defined as the use of air flow through wind turbines to provide the mechanical force to generate electricity. Wind power is an alternative to burning fossil fuels, and is renewable and produces no greenhouse gas emissions during operation. Modern horizontal-axis wind turbines often use three blades. Theoretically, the maximum power P (unit: watts) that a three-blade wind turbine can extract from the wind power can be calculated as: Blade length 1 = P=pAv3Cp (Equation 1) where p is the air density (kg/m), A is the sweep area of the turbine (m) and can be calculated from the length of the turbine blades, and v is the wind speed (m/s). Cp is the power coefficient that is unique to each turbine type. This coefficient represents the amount of kinetic energy from the wind that is captured by the turbine. From the Betz's limit law we know that the best power conversion possible is Cp,max = 0.59. Part 1 Given the following data: Blade length 1 = 50 m Air density p=1.5 kg/m3 Power coefficient Cp= Cp,max = 0.6 Plot the power output P as a function of wind speed v on the interval [0 m/s, 30 m/s]. = Part 2 Many factors impact the final output of wind power. The rotor-blade friction and drag, gearbox losses, generator and converter losses, all reduce the power delivered by a wind turbine. In 2001, commercial utility-connected turbines deliver 75% to 80% of the Betz limit Cp,max of power extractable from the wind, at rated operating speed, that is, Cp = 0.40. Create a second plot of power output as a function of windspeed using the original value of Cp,max = 0.6 and the value of Cp = 0.40 (80% of the previous value) together over the interval of velocities [0 m/s, 30 m/s]. Instructions: Please write your answers clearly, explain each step, and use proper mathematical notation. You can use Microsoft Excel, or any other software or online graphing tool to plot the graphs. Make sure to label your axes. Problem (Wind Energy Production) Authors: S. Smith and W. Song Edited by: M. Tanzy and 0. Yavuz Wind power is defined as the use of air flow through wind turbines to provide the mechanical force to generate electricity. Wind power is an alternative to burning fossil fuels, and is renewable and produces no greenhouse gas emissions during operation. Modern horizontal-axis wind turbines often use three blades. Theoretically, the maximum power P (unit: watts) that a three-blade wind turbine can extract from the wind power can be calculated as: Blade length 1 = P=pAv3Cp (Equation 1) where p is the air density (kg/m), A is the sweep area of the turbine (m) and can be calculated from the length of the turbine blades, and v is the wind speed (m/s). Cp is the power coefficient that is unique to each turbine type. This coefficient represents the amount of kinetic energy from the wind that is captured by the turbine. From the Betz's limit law we know that the best power conversion possible is Cp,max = 0.59. Part 1 Given the following data: Blade length 1 = 50 m Air density p=1.5 kg/m3 Power coefficient Cp= Cp,max = 0.6 Plot the power output P as a function of wind speed v on the interval [0 m/s, 30 m/s]. = Part 2 Many factors impact the final output of wind power. The rotor-blade friction and drag, gearbox losses, generator and converter losses, all reduce the power delivered by a wind turbine. In 2001, commercial utility-connected turbines deliver 75% to 80% of the Betz limit Cp,max of power extractable from the wind, at rated operating speed, that is, Cp = 0.40. Create a second plot of power output as a function of windspeed using the original value of Cp,max = 0.6 and the value of Cp = 0.40 (80% of the previous value) together over the interval of velocities [0 m/s, 30 m/s]
