# Calculating Electric Power from Wind Turbines

• Bizkit
In summary, siliconchip.com reports that semiconductor manufacturers are now producing chips that will generate a constant voltage from a source that has varying voltage or current capacity. This will help eliminate some of the calculation problems.
Bizkit

## Homework Statement

Consider a wind turbine farm that uses turbines with a blade span diameter of 80 m at a site subjected to wind speeds over the range of 4 to 32 m/s. Taking the overall efficiency of each turbine to be 25% and the air density to be 1.112 kg/m3, determine the electric power generated by a single turbine.

## Homework Equations

I know that, for an average wind speed, the equation I need is: W = m(V2/2)*η (the bold variables are per unit time), but I'm not sure exactly how to modify this equation for a range of velocities. I at first thought that I could take the integral of the equation with respect to velocity, but then I end up with the wrong units.

W = m(V2/2)*η = ρVA(V2/2)*η = ρπr2(V3/2)*η = ρπ(d/2)2(V3/2)*η = ρπ(d2/4)(V3/2)*η = ρπ(d2/8)V3

## The Attempt at a Solution

Since I'm not sure what equation to use, I can't attempt to find the solution.If someone could help me, I would really appreciate it. Thanks.

I think they just want the power as a function of v. You already gave this in your last equation.
You might think that you could find the average power by integrating, but this only works if
- the wind is always between 4 and 32 m/s
- all wind speeds between 4 and 32 m/s are equally likely.
Only if these two are valid you could find the avergage power by integrating from v_min to v_max and then dividing by the range of v_max - v_min.

Thanks for the help. I still have a question, though. How does leaving the power as the function of V I gave above (W = ρπ(d2/8)V3*η) show that V has a range of values, rather than just being an average? I mean, shouldn't there be like a Vlow and Vhigh or something like that to show that V has a range values, or is that not how it works? Hopefully this question doesn't confuse you. Sorry if it does.

Bizkit said:
Thanks for the help. I still have a question, though. How does leaving the power as the function of V I gave above (W = ρπ(d2/8)V3*η) show that V has a range of values, rather than just being an average? I mean, shouldn't there be like a Vlow and Vhigh or something like that to show that V has a range values, or is that not how it works? Hopefully this question doesn't confuse you. Sorry if it does.

You kinda answered your own question there. By defining the power as a function of V it follows that V can take a range of values and not just one set value.

Ok, I understand what you are saying, but I just thought of something else. If the people who wrote the problem wanted me to just define the power as a function of V, then why didn't they just ask me to find the power over a range of wind speeds, without giving any specific values. Since they gave specific values, that makes me think that I need to integrate and divide. What do you think?

Mark: Semiconductor manufacturers are now producing chips that will generate a constant voltage from a source that has varying voltage or current capacity. Some even match their input impedance to maximize total power, rather than just current.

Although you may still wish to explore the mathematical theory regarding such things, these new chips will help eliminate some of those calculation problems.

## What is the formula for calculating electric power from wind turbines?

The formula for calculating electric power from wind turbines is P = 0.5 x ρ x A x V^3 x Cp, where P is power, ρ is air density, A is the swept area of the turbine blades, V is the wind speed, and Cp is the power coefficient of the turbine.

## What is the importance of calculating electric power from wind turbines?

Calculating electric power from wind turbines is important because it allows us to determine the efficiency and potential energy generation of a turbine. This information is crucial for designing and optimizing wind energy systems for maximum output.

## How does air density affect the calculation of electric power from wind turbines?

Air density is a crucial factor in the formula for calculating electric power from wind turbines. Higher air density means there is more mass for the turbine blades to interact with, resulting in higher power generation. Similarly, lower air density will result in lower power generation.

## What is the significance of the swept area in the formula for calculating electric power from wind turbines?

The swept area, or the area covered by the turbine blades as they rotate, is an important factor in determining the amount of power a wind turbine can generate. Larger swept area means more interaction with the wind and more potential for energy generation.

## How does the power coefficient impact the calculation of electric power from wind turbines?

The power coefficient, or the ratio of actual power output to the maximum possible power output, is a key factor in the formula for calculating electric power from wind turbines. It takes into account the efficiency of the turbine and can greatly affect the final calculation of power output.

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