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ECE 333 Green Electric Energy

ECE 333 Green Electric Energy. Lecture 23 Betz Efficiency, Tip Speed Ratio, Power Curves Professor Tim O’Connell Department of Electrical and Computer Engineering. Betz efficiency. Plot Cp vs. λ. λ = 1/3 Cp =16/27 ≈ 0.593. = λ. Tip Speed Ratio (TSR).

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ECE 333 Green Electric Energy

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  1. ECE 333 Green Electric Energy Lecture 23 Betz Efficiency, Tip Speed Ratio, Power Curves Professor Tim O’Connell Department of Electrical andComputer Engineering

  2. Betz efficiency • Plot Cp vs. λ λ = 1/3 Cp =16/27 ≈ 0.593 = λ

  3. Tip Speed Ratio (TSR) • Actual rotor efficiency will be less than the Betz limit • For a given wind speed, efficiency is a function of the rotor rotational speed • Spin too slowly, wind passes by without being “captured” • Spin too quickly, blades cause wind turbulence which reduces the efficiency of the blades. • Efficiency can be expressed in terms of the Tip Speed Ratio: [m] (7.30) [m/s]

  4. Tip Speed Ratio • Optimal TSR for 2- and 3-blade modern turbines is in the 4-6 range.

  5. Tip Speed Ratio • A typical large (0.5-2 MW) wind turbine will spin at about 20-30 rpm • Gear box will speed that up by a factor of 50-70 • Overall efficiency is around 25-35% (lower than the Betz limit)

  6. Variable Rotor Speed • Because TSR affects efficiency, and TSR depends on the wind speed, the rotor efficiency varies with the wind speed • There is a benefit to increasing the rotor speed as the wind speed increases to stay as close as possible to the optimal TSR 3 discrete rotor speeds

  7. Variable Rotor Speed • A few discrete speeds can greatly improve power output 20 rpm 40 rpm 30 rpm

  8. Idealized Power Curve Electric machines are limited by their power rating. v^3 relationship Figure 6.32

  9. Idealized Power Curve Before the cut-in wind speed, no net power is generated Then, power rises like the cube of wind speed After the rated wind speed is reached, the wind turbine operates at rated power (sheds excess wind) Three common approaches to shed excess wind Pitch control – physically adjust blade pitch to reduce angle of attack Stall control (passive) – blades are designed to automatically reduce efficiency in high winds Active stall control – physically adjust blade pitch to create stall

  10. Idealized Power Curve Above cut-out or furling wind speed, the wind is too strong to operate the turbine safely, machine is shut down, output power is zero “Furling” –refers to folding up the sails when winds are too strong in sailing Rotor can be stopped by rotating the blades to purposely create a stall Once the rotor is stopped, a mechanical brake locks the rotor shaft in place

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