ME 433 Homework 8 solution(1)

ME 433 Homework 8 solution(1) - ME 433 Homework 8 Wind...

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ME 433 Homework 8 - Wind energy 1 1. A Siemens SWT-2.3-82 wind turbine has a rated capacity of 2.3 MW and a rotor diameter of 82.4 meters. The wind turbine has cut-in and cut-out speeds of 5 m/s and 27.5 m/s, respectively and is rated at a wind speed of 17.5 m/s. The table below shows the annual wind data near a potential SWT-2.3-82 installation site. Assume the wind turbine has a gearbox/ generator efficiency of 97% and requires 220 hours of maintenance and service annually. The density of air is 1.225 kg/m 3 . a. What is the root mean cube wind speed (m/s)? b. What is the power coefficient (coefficient of performance) of the wind turbine (%)? Hours Velocity (m/s) 70 22.5-27.5 400 17.5-22.5 1700 12.5-17.5 2400 7.5-12.5 3000 2.5-7.5 1190 0-2.5 V rmc = 1 8760 V i 3 Δ t i 1 i # $ % & ' ( 1 3 V rmc = 25 3 70 ( ) + 20 3 400 ( ) + 15 3 1700 ( ) + 10 3 2400 ( ) + 5 3 3000 ( ) + 0 3 1190 ( ) 8760 ! " # $ % & 1 3 = 11.3 m s ! W rated = 1 2 ρ V rated 3 A swept × C p × η gen+gear C p = ! W rated 1 2 ρ V rated 3 A swept η gen+gear A swept = π 82.4 m ( ) 2 4 = 5330 m 2 C p = 2.3 × 10 6 W 1 × 2 1 × m 3 1.225 kg × s 17.5 m " # $ % & ' 3 × 1 5330 m 2 × 1 0.97 × kg m 2 W s 3 = 13.6% 1 https://www.coursehero.com/file/10395136/Homework-8-solution1/ This study resource was shared via CourseHero.com
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c. What is the expected average electrical power output of the wind turbine at the potential location (MW)? Assume that the maintenance is performed during low wind periods.
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