Lecture 30 November 4, 2013 ECEN 2060 Lecture 30 Fall 2013.

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

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Rapid Grow of Wind Capacity

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World Wide Growth of Wind Energy

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Fraction of Total Generation by Wind

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Data on Wind

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Types of Wind Turbines

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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.

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Schematic for Horizontal Wind

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Wind Turbine Gear Box

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Area of Capture

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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.

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Pitch Angle Controls Lift, Speed and Power

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High Pitch Can Lead to Stall

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Wind is Slowed by Blades

• 1

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Wind Power

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Wind Power

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Area of Darrieus

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Lecture 31 November 6, 2013

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Temperature Correction for Air Density

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The molecular weight of air is approximately 28.97 and the density at 15o C is 1.225 kg/m3

Dry Air Pressure at 1Atmosphere

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Altitude Correction

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Table of Air Pressure with Corrections for Temperature and Altitude.

• .

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Effects of Tower Height

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Z is the roughness length

Surface Friction

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Roughness

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Effects of Height with Different Roughness

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Effects of Variation of Wind Speed with Height on Stress

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This leads to vibrations, noise, blade flexing and fatigue. Factors to 1.45 more power at top to bottom in example.

Maximum Rotor Efficiency

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Betz limit 1/3 initial velocity

Blade Efficiency

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Assume uniform velocity over the blade

To find the maximum power efficiency

Real Turbines

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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 Efficiency

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Efficiency for Different Blade Systems

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Idealized Operating Power Curve

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Matching Generator Size to Rotor Diameter with Wind Speed

• 1

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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%

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Some Real Turbines

• 1

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Efficiency and Power for Some Turbines

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Average Wind Speed Classifications

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Wind Speed Measurements

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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.

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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

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dt

ddst

B

Types of Systems

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Synchronous Generator

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A Direct Drive Permeate Magnetic Machine

• 1

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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.

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Forces with a Rotating Magnetic Field

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Squirrel Cage Rotor

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Note 3 phase driving current gives a rotating field when the currents are120 degrees out of phase

Synchronous speed Ns = 120 f/p where f is the frequency and pIs the number of poles.

Squirrel Cage Rotor

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Rotating Magnetic Fields

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Induction Motor Torque –Slip Curve

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Example of Induction Motor.

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Inductance Machine as Generator

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1. The wind starts the machine as a motor until it gets above synchronous speed2. Can be connected to the grid or self excited with a capacitor and remnant

magnetic field. Set it to resonate with the Stator Inductance

Need for Speed Control

• 1. Want to operate with a tip speed ratio of 4-6 for maximum power and blade efficiency Cp

• 2. If direct connection to the grid need a fixed blade speed for phase and frequency control to match frequency on the grid if you have a fixed turbine to generator connection.

• 3. Need to shed power in high winds.

4. Use a gear box. • 5. Use pitch control of the blades • 6. Control of slip which in turn controls power.• 7. Doubly wound rotor.

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Inductance Generator Speed Control

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Examples of Speed Adjustments.

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Control of the Number of Poles in the Stator

• 1. This can be done by changing the connections on the windings. For example two poles adjacent to each other can be connected to look like one. This is 1/2 the frequency for a fixed speed.

• 2. Change gear ratio.• 3. Varying the resistance seen by the rotor winding

varies the slip.• 4. Use an indirect connection to the grid by way of

an inverter AC to DC to AC(60hz.) This allows for variable frequency into the inverter and variable turbine speed.

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Variable Speed Turbine and Indirect Connection to the Grid

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Doubly Wound Induction Machine

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Gearless Drive

• 1

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Average Wind Power

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This is the wind turbine owners get paid.

Note there is a big difference between V average and V3average

A wind speed histogram

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A Probability Density Function

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Weibull and Rayleigh Functions

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Weibull Density Functions

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The Rayleigh Probability Density Function

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Rayleigh Distribution

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Some Real Data

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Midwest Wind

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Wind Turbine Gear Box

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