Wind Resources

LINK TO SLIDES USED IN CLASS PRESENTATION

This section discusses wind resources in the United States and world.

# Wind Power Technologies

## Conventional Wind Turbines

Conventional wind turbines are the most prevalent means of generating electricity from wind throughout the world. In general, a wind turbine is a mechanical device that converts the energy produced by the wind into mechanical energy. The mechanical energy is then converted into electricity and then delivered to end users via the power grid. The sections below will further detail how wind turbines are used to produce electricity.

Picture of a Conventional Wind Turbine

### Design

Rotor blades, a shaft, and a generator are the three major components of a wind turbine. The rotor blades are designed such that wind perpendicular to the blades causes them to move in a circular motion. Rotor blades are usually made of fiberglass-reinforced epoxy or wood epoxy and they typically range from 160 feet to 300 feet in diameter. The shaft acts as the coupling to transfer the mechanical energy from the rotor blades to the generator. Through a series of gearboxes, the generator uses electromagnetic induction to create electricity.

### Wind Speeds and Frequency

Wind speeds and the frequency of those wind speeds are the major determinant in how much energy a wind turbine can produce. It is intuitive that wind does not blow at a constant speed throughout the day and certainly not throughout the year. Generally, higher velocity wind produces more energy, however high velocity wind occurs less frequently than low velocity wind. Due to this, the majority of energy is produced during the infrequent, high velocity periods. Since this is true, a wind farm cannot work at full capacity for any sustainable period. Therefore, a wind turbine is assigned a capacity factor based on its location. If a turbine had a capacity factor of 0.25 then it would produce 25% of its maximum energy each year. Capacity factors typically range from 20% to 40%.

Power versus Wind Velocity

Wind Velocities and Frequencies

### Electricity Production

Most individual wind turbines rated in the range of 0.25 MW to 5 MW. So a turbine with a power rating of 2MW and a capacity factor of 0.25 could produce 10,950,000 kWh/year.

2 MW(1000 MW/kW) X (365 days)(24 hours) X 0.25 = 10,950,000 kWh/year

### Geographical Locations

There are currently 37 states in the US that use wind turbines to generate electricity. Texas is by far the biggest wind energy state with over 9,700 wind turbines installed. The table below shows the top 10 states in terms of installed wind turbines.

Texas 202 9708
California 17 2739
Washington 6 1914
Minnesota 1 1796
North Dakota 20 1222
Indiana 92 1127
Missouri 149 457
West Virginia 84 414
South Dakota 99 412

## Offshore Wind

Offshore wind turbines follow the same principles as onshore wind turbines. The main difference is that offshore wind velocities are higher than onshore wind velocities. Also, the rotors blades are much larger due to that fact that they do not have to be shipped via roadways. Therefore offshore wind has higher capacity factors and can produce more energy per year, thereby decreasing the payback period for a wind farm installation.

## High Altitude Wind

Because wind power increases with the cube of velocity, one way to increase the available power is by finding higher speed winds. These are available at higher altitudes, up to about 10 km.

In addition, while ground and sea based wind turbines must be spread out over a two dimensional space, altitude adds a third dimension to the available space that can be used.

### Design

High altitude wind generators take a variety of forms, but are usually a tethered glider, balloon, kite, or blimp which has propellers or blades to catch the wind. Designs are more varied than ground and sea based turbines as the technology is less mature.

### Challenges

There are several challenges associated with high altitude wind turbines including the weight of the tether cable, lightning, air traffic interference, and loss of altitude (crashing). These are problems for which technical solutions can probably be found and many companies are searching.

## Solar Wind

While atmospheric wind is composed of air, solar wind is a stream of charged particles generated by the sun.

Solar wind technology is still in the theoretical stage, however one proposal would use a magnetic field to generate power from solar wind and beam it to earth using an infrared laser. Current optics are not sufficient to beam power over the distances required.

# Physical Limits of Wind Power

## Wind

Wind is caused by pressure differentials which accelerate air from high pressure areas to lower pressure areas. The two largest driving factors wind are the difference in solar heating between the equator and the poles and planetary rotation. Near the Earth's surface, friction slows the wind from the higher speeds found at elevation.

## Energy in Wind

The kinetic energy contained in the wind can be determined by the following equation

(1)
\begin{align} P = {1 \over 2} \rho A v^3 \end{align}

where
$\rho$ is the air density
A is the cross-sectional area
v is the wind velocity

Of course, not all energy in the wind can be extracted. The actual power output of a wind turbine is subject to several inefficiencies.

(2)
\begin{align} P = {1 \over 2} \rho A v^3 C_p E_g E_b \end{align}

where
A is the turbine swept area, $A = {\pi \over 4} d^2$
$C_p$ is the coefficient of performance (less than Betz limit of 0.593)
$E_g$ is the generator efficiency
$E_b$ is the gear box efficiency

From this we can see that power from a turbine increases with the square of turbine diameter and with the cube of wind speed.

Wind turbines can not be spaced tip to tip due to turbulence robbing power from adjacent turbines. Minimum spacing to avoid significant power loss is estimated at 3 diameters across and 6 diameters down wind.

The power that wind turbines can generate per unit land area is:

(3)
\begin{align} {\text{power per wind turbine} \over \text{land area per wind turbine}} = {{1 \over 2} \rho {\pi \over 4} d^2 v^3 C_p E_g E_b \over 6d~3d \end{align}

Or, to simplify:

(4)
\begin{align} {\text{power per wind turbine} \over \text{land area per wind turbine}} = {\rho \pi v^3 C_p E_g E_b \over 144} \end{align}

From this we can see that total power from a wind farm is not dependent on turbine diameter. The driver for larger turbine diameters must then be economy of scale or to reach the higher wind speeds at higher altitudes.

The density of air ($\rho$) is approximately 1.2 $\mathrm{kg/m^3}$. If the efficiency factors and coefficient of performance reduce to about 0.5, and wind speed is assumed to be 6 m/s this results in power generation of 2.8W per square meter of land area. Actual wind farms typically produce 1 to 5W per square meter of land.

## Wind Classification

The amount of wind received at different locations varies, so a classification system based on wind power density (WPD) was developed. Generally classes 3 and greater are considered suitable locations for land-based wind turbines.

## Wind Potential

Global wind power potential for the year 2000 was estimated to be about 72 TW, five times world energy use. US wind potential was recently estimated to be about 10.5 TW, compared to total current electricity generating capacity of 1 TW and average annual use of about half that.

To supply all of the US electricity demand from land-based wind turbines using today's technology would thus take 250 billion square meters or 250,000 square kilometers assuming that wind turbines can produce 2 W per square meter. Wind turbines have a capacity factor of roughly 0.2 to 0.3 to account for time when the turbine is not generating at full capacity, however. Offshore capacity factors may reach 0.4 and high altitude capacity factors can double that. Assuming a capacity factor of 0.25 for land-based turbines, the land area must be quadruped to 1,000,000 square kilometers. This is roughly the land area of North and South Dakota, Nebraska, Kansas, Oklahoma, Iowa, and Illinois combined.

# The Economics of Wind Power

In order for wind power to be a viable alternative energy solution, it must be economically competitive with traditional forms of electricity generation. There are four main cost components associated with the generation of traditional electricity: fuel cost, cost of CO2 emissions, operations and maintenance costs, and capital costs. Obviously, wind power does not have to deal with raw fuel costs and CO2 emissions. However, wind power is very capital intensive. The European Wind Energy Association put out an excellent report in March of 2009 detailing the economics of wind energy. The EWEA looks at two scenarios, a low fuel cost scenario and a high fuel cost scenario. As you can see wind energy is very competitive with traditional means of electricity generation when coal and natural gas prices are high. Figure 2.5 is based on a crude oil price of $59/barrel and Figure 2.6 is base on a crude oil price of$119/barrel.

### Talk

page revision: 75, last edited: 10 Dec 2010 01:31