ESET 222: Wind & Solar Energy - Power in the Wind Example

What is the formula for calculating the tip-speed-ratio (TSR) of a wind turbine?

TSR = (rpm * D) / v

At what wind speed does a 40-m, three bladed wind turbine produce 600 kW of power?

14 m/s

If the rotor operates with a TSR of 4.0, at what rpm does it turn?

56 rpm

What is the tip speed of the rotor for the given wind turbine?

224 m/s Signup and view all the answers

What gear ratio is needed to match the rotor speed to the generator speed if the generator needs to turn at 1800 rpm?

32:1 Signup and view all the answers

Why does the power output level off at 3,000 kW for a Vesta V90 – 3.0 MW turbine?

The power output levels off due to the turbine reaching its maximum capacity or rated power. Signup and view all the answers

What is tip speed ratio (TSR) and how is it calculated?

Tip speed ratio (TSR) is the speed of the blade at its tip divided by the speed of the wind. It is calculated by dividing the speed of the blade tip by the speed of the wind. Signup and view all the answers

Why does the tip of the turbine blade come under considerable stress?

The tip of the turbine blade comes under considerable stress due to centrifugal force when it is rotating at high speed. Signup and view all the answers

Explain the significance of the tip speed ratio (TSR) of 5 in a wind turbine.

A TSR of 5 means the tip of the blade is traveling five times faster than the speed of the wind. Signup and view all the answers

What is pitch control in the context of wind turbines?

Pitch control refers to changing the pitch of the blade with the changing wind speed to regulate the rotor speed. Signup and view all the answers

How does stall control contribute to speed control in wind turbines?

Stall control involves shifting the blades into a position to stall when the wind speed exceeds the safe limit on the system. Signup and view all the answers

What is the formula for tip speed?

Tip speed = π D N / 60 Signup and view all the answers

How is the tip speed ratio calculated?

The tip speed ratio is calculated by dividing the tip speed by the wind speed upwind of the turbine. Signup and view all the answers

What factors are involved in determining the tip speed ratio?

The rotor speed (N), rotor diameter (D), and wind speed (v) upwind of the turbine are involved in determining the tip speed ratio. Signup and view all the answers

Why is the tip speed ratio important in wind energy?

The tip speed ratio is important in wind energy because it affects the efficiency and power extracted from the wind by the turbine. Signup and view all the answers

What is the significance of the spacing of the towers in relation to the tip speed ratio?

The spacing of the towers affects the efficiency of the turbines by influencing the wind flow and the tip speed ratio. Signup and view all the answers

What is the theoretical maximum rotor efficiency Cp?

59.3% Signup and view all the answers

What is another name for theoretical maximum rotor efficiency Cp?

Betz efficiency or Betz’s law Signup and view all the answers

What percentage of energy can be achieved in converting the power in the wind into the power of a rotating generator shaft under the best operating conditions?

35 to 45 percent Signup and view all the answers

How does the efficiency drop off if the rotor turns too slowly?

Blades are letting too much wind pass by unaffected Signup and view all the answers

How is the usual way to illustrate rotor efficiency?

As a function of its tip-speed ratio (TSR) Signup and view all the answers

What is the tip speed ratio for low solidity turbines typically between?

4 - 8 Signup and view all the answers

Define tip speed ratio for wind turbines.

Ratio of tangential velocity at the tip of the blade to the undisturbed upwind velocity Signup and view all the answers

What defines the maximum operating efficiency of each wind turbine?

Particular tip speed ratio Signup and view all the answers

What happens when the wind turbine blade tip travels at the highest speed?

The tip speed is at its highest Signup and view all the answers

How does turbulence affect the lifting force of the rotor blade?

Prevents the lifting force from acting on the rotor Signup and view all the answers

What is the formula for the tip-speed ratio in wind energy?

(v/vo)^3 = (H/Ho)^α.3 = (H/Ho)^3α Signup and view all the answers

At what height is the wind speed and power density estimated in the first example?

50 m Signup and view all the answers

What is the estimated friction coefficient for ground with hedges and shrubs in the second example?

0.20 Signup and view all the answers

What is the ratio of power at the top of the blade swing to that at the bottom of its swing in the second example?

45% Signup and view all the answers

What important point about the variation in wind speed and power across the face of a spinning rotor is illustrated in the second example?

The power in the wind at the top tip of the rotor is 45% higher than it is when the tip reaches its lowest point. Signup and view all the answers

What is the impact of tower height on wind speed?

Wind speed is greatly affected by the friction that the air experiences as it moves across the earth’s surface. Surface winds are slowed considerably by high irregularities such as forests and buildings. Signup and view all the answers

What is the significance of the roughness length (m) in the formula for wind speed at height H?

The roughness length (m) is a factor that affects the wind speed at a certain height. It is used in the formula to account for the impact of the roughness of the earth’s surface on wind speed. Signup and view all the answers

Under what conditions is the friction coefficient (α) approximately 1/7 or 0.143?

For neutral stability conditions, the friction coefficient (α) is approximately 1/7 or 0.143. Signup and view all the answers

What is the relationship between wind speed at height H and wind speed at height Ho?

The relationship is expressed using the formula v = vo + 0.143 * (z/Ho) * (v - vo), where v is the wind speed at height H, vo is the wind speed at height Ho, α is the friction coefficient, and z is the roughness length (m). Signup and view all the answers

How does the combination of 9 m/s and 3 m/s winds produce more energy compared to winds blowing at a steady 6 m/s?

The combination of 9 m/s and 3 m/s winds produces 75% more energy than winds blowing at a steady 6 m/s, despite having the same average wind speed. Signup and view all the answers

What does the example of energy production at different wind speeds illustrate?

The example illustrates the inaccuracy associated with using average wind speeds to predict energy production. It also shows that under certain common assumptions about wind speed probability distributions, energy in the wind can be almost twice the amount found by using the average wind speed. Signup and view all the answers

How does tower height affect wind speed and energy production?

Tower height affects wind speed by impacting the friction that the air experiences as it moves across the earth’s surface. This, in turn, affects energy production in wind turbines. Signup and view all the answers

What is the significance of using average wind speeds in predicting energy production?

Using average wind speeds can lead to significant inaccuracies in predicting energy production. Under certain common assumptions about wind speed probability distributions, energy in the wind can be almost twice the amount found by using the average wind speed. Signup and view all the answers

How does wind speed variability impact wind energy production?

Wind speed variability significantly impacts wind energy production, as demonstrated by the example of energy production at different wind speeds. Signup and view all the answers

Why is the combination of 9 m/s and 3 m/s winds more effective in energy production than winds blowing at a steady 6 m/s?

The combination of 9 m/s and 3 m/s winds is more effective in energy production due to the impact of wind speed variability, which results in 75% more energy production compared to winds blowing at a steady 6 m/s. Signup and view all the answers

ESET 222: Wind &amp; Solar Energy - Power in the Wind Example

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