Lecture 24 Wind : Part 4

Wind-Speed Data Analysis

Measured wind-speed data can be represented using three curves: a speed-frequency distribution curve, a speed-duration curve, and a power-density curve. Each presents a different view of a site’s wind resource. Together, they help assess a location and guide wind-turbine design.

1. Speed-Frequency Distribution Curve

A speed-frequency distribution curve shows how often wind occurs within each speed range, expressed as hours per year or as a percentage of the year.

It is commonly modeled using the Weibull probability density function:

[ f(V)=\frac{k}{c}\left(\frac{V}{c}\right)^{k-1}e^{-(V/c)^k} ]

where:

• (V) is wind speed in m/s.
• (c) is the scale parameter, measured in units of speed. A larger (c) generally indicates a windier site.
• (k) is the dimensionless shape parameter. In the lecture’s explanation, lower values (around 1.5) indicate more variable, gusty wind, while higher values (around 3) indicate steadier wind.

To construct the curve from hourly data:

1. Group measured speeds into ranges, such as 0–2, 2–4, and 4–6 m/s.
2. Count the hours in each range. For a full year, the counts should total 8,760.
3. If desired, convert each count to a percentage by dividing by 8,760 and multiplying by 100.
4. Plot the speed ranges or their midpoints against the hours or percentages.

In the lecture’s example, the most frequent range is 6–8 m/s, at about 25% of the year. The ranges from roughly 4–10 m/s together account for about 63% of annual hours. Speeds above 14 m/s occur infrequently.

This curve is useful for an initial assessment of the wind resource and for identifying the most commonly occurring speeds. On its own, however, it does not show which speeds contribute the most energy.

2. Speed-Duration Curve

A speed-duration curve shows the cumulative number of hours per year for which wind speed equals or exceeds a specified speed.

Unlike the frequency curve, which shows time spent in each individual range, the duration curve accumulates hours across speed ranges.

To construct the curve:

1. Start with the frequency hours for each speed range.
2. Accumulate the hours from the highest speed range downward, so each value represents the hours at or above that speed.
3. Continue until the cumulative total reaches 8,760 hours at the lowest speed threshold.
4. If desired, convert cumulative hours to a percentage of the year by dividing by 8,760 and multiplying by 100.
5. Plot wind speed against cumulative time exceeded.

In the lecture’s example, wind speeds above about 3 m/s occur for approximately 8,360 hours per year, while speeds above about 15 m/s occur for only about 260 hours per year (around 3% of the year).

This curve helps estimate how long a turbine can operate at or above particular speeds. The width of a step in the plotted curve corresponds to the duration of a speed range.

3. Power-Density Curve

A power-density curve shows how the wind resource’s power potential is distributed across wind speeds. It is more directly relevant to energy capture than frequency alone.

Wind power density is power per unit swept area:

[ P_D=\frac{P}{A}=\frac{1}{2}\rho V^3 ]

where (P_D) is in W/m², (\rho) is air density (often taken as about 1.225 kg/m³), and (V) is wind speed in m/s.

Because power density is proportional to the cube of wind speed, a modest increase in speed can produce a large increase in available power.

To estimate each speed range’s contribution:

1. Use the midpoint speed of each range to calculate its power density.
2. Weight that value by the percentage of time the wind occurs in that range.
3. Add the weighted values to obtain the total contribution. Then divide each range’s contribution by the total and multiply by 100 to find its share.
4. Plot the contribution by speed range, in absolute terms or as a percentage.

In the example, ranges around 8–14 m/s provide roughly 65% of the power-density contribution. The 10–12 m/s range contributes the most, at about 24.13%.

This contrasts with the frequency curve: 6–8 m/s is the most common range, but it is not the largest contributor to energy potential.

Implications for Turbine Design

The lecture distinguishes three important operating speeds:

• Cut-in speed (called “cutting speed” in the subtitles) is the minimum wind speed at which the turbine begins producing useful electrical power. Below it, the turbine may rotate but cannot overcome system losses to generate useful electricity.
• Rated speed is the speed at which the turbine first reaches its designed maximum power output. Between cut-in and rated speed, output rises rapidly as wind speed increases.
• Cut-out speed is the maximum speed at which the turbine can operate safely. Above it, the turbine shuts down to protect its blades, gearbox, generator, and tower. Between rated and cut-out speed, controls limit or regulate the turbine so it does not exceed its rated output.

For the example site, the lecture gives approximate values of 4–5 m/s for cut-in, 11 m/s for rated speed, and 17 m/s for cut-out. The precise choices depend on the site and turbine.

The key design lesson is to base decisions on energy contribution and safety, not simply on the most frequent wind speed. Choose a cut-in speed that captures useful energy, a rated speed near the peak energy contribution, and a cut-out speed that protects the machine during very high winds.

Speakers and Sources

• Speaker: An unnamed lecturer presenting the wind-energy material.
• Sources and concepts mentioned: The Weibull distribution and an illustrative hourly wind-speed dataset for a hypothetical site. No other speakers are identifiable in the subtitles.