Lecture 30 November 4, 2013 ECEN 2060 Lecture 30 Fall 2013
Wind Power Systems • 1. Windmills go back a long time. A key money maker for milling grain. • 2. First use for electrical generation in 1891 by Poul la Cour used generate hydrogen. • 3. Used shortly afterward in the rural US. • 4. 1941 Grand Paw’s Knob Vermont 1250 kW,175ft two blade system. Failed in 1945 • 5. 1970’s to mid 1980’s in California and then to Europe
Characteristics of Some Wind Turbines • 1. Horizontal Axis Wind turbine Up wind and Down wind. • A. Down wind has advantage of self aligning (yaw) • B. Disadvantages Shadowing by tower that increases flexing of the blades which, decrease power, increases fatigue and noise. • C. Up wind Advantage More power, Smoother • D. Disadvantages more complicated control • 2. Vertical Axis, Darrieus • Advantage Heavy equipment on the ground. Lighter tower. • Disadvantage Blades close to the ground where the wind is slower. Low starting torques. Hard to feather in high winds.
Wind Turbines • Most wind turbines are up wind horizontal. • Many blades high torque and works well at low wind speeds. • Two blades turn faster than 3 blades, less turbulence. 3 blades smoother and installed the most. 3 blade weights more.
Temperature Correction for Air Density The molecular weight of air is approximately 28.97 and the density at 15o C is 1.225 kg/m3
Effects of Tower Height Z is the roughness length
Effects of Variation of Wind Speed with Height on Stress This leads to vibrations, noise, blade flexing and fatigue. Factors to 1.45 more power at top to bottom in example.
Maximum Rotor Efficiency Betz limit 1/3 initial velocity
Blade Efficiency Assume uniform velocity over the blade To find the maximum power efficiency
Real Turbines 1 Best 80% of Betz limit more often 40% to 50% 2. Depends on ratio of rotor speed to wind speed. Often defined in terms of Tip speed.
Blade Speed Limits • 1. Want to operate in the TSR of 4-6 • 2. Example 40m blades 600kW ,14m/s, This leads to 26 revolutions per minute and tip speed of 56m/s • 3. Required gear ratio to get to 1800rpm of 67.4 • 4. Wind Power of 2,112 kW to get 600kW or an efficiency of 28%
Types of Generators • 1. Synchronous Generators • A. Fixed Speed • Rotational speed N(rpm) = p = number of poles • f = frequency for a three phase winding. 2. Induction Generators These generators have slip between the rotor speed and the speed of the rotating field in the stator.
Generators for Wind Turbines • 1. A key issue is the variable of the wind speed and a need for nearly constant speed to achieve 50 or 60hz. • 2. Basic equations • F= q(E + vxB) = qE + I xB and Vinduced = - = - ~ I 3. Note the current I is proportional to the rate of change of the magnetic field B and the force is proportional to the product B ∂B/∂t 3. Synchronous Generators A. Need for constant speed to keep output at 60hz. 4. Induction Generators
Induction Generator • 1.Fixed windings on the rotor and does not require brushes or electrical contact with the rotor. • 2. The rotor runs a little slower than the rotating field when operating as a motor and faster when it is working as a generator. • 3. The induced current in the rotor conductors generate the magnetic fields that lead to the torques.
Squirrel Cage Rotor Note 3 phase driving current gives a rotating field when the currents are 120 degrees out of phase Synchronous speed Ns = 120 f/p where f is the frequency and p Is the number of poles.