# Available energy from wind turbines

As mentioned earlier, wind turbines do not generate electricity all the time, and the wind speed changes from time to time, so it is important to predict how much electricity a wind turbine will generate in a day, week, month, or year.

1. Curve diagram method

The following describes how to calculate the amount of electricity generated by a wind turbine in a year.
Figure 1 shows the average power of wind turbines over a one-year period. These curves in the figure assume that the wind speed spectrum is distributed in a certain way, rather than taking the annual average of wind speed or the average of any number of hours or days. Figure 1 – The estimated output power of wind turbines (Cliff)

If the rated wind speed and cut-out wind speed of the wind turbine are known, the corresponding curve can be selected in Figure 1. When the local average wind speed and the rated wind speed of the wind turbine are known, the ratio of the expected output power of the wind turbine to the rated power can be found on the curve. This ratio is also called the capacity factor, which is a measure of the total utilization of the installed machines. degree indicator. Usually, the capacity coefficient is calculated by the actual annual power generation of the wind turbine, and the maximum value is generally 0.3.

Due to the different frequency distributions of wind, using this method to predict wind turbine output power at a given location may fluctuate by up to 50%. [Example] If the annual average wind speed in a certain place is 7m/s, and the rated power of a wind turbine is 5kW, the rated wind speed is 10m/s, and the cut-out wind speed is 15m/s, calculate the annual power generation of the wind turbine. .

The ratio of cut-out wind speed to rated wind speed is 15/10=1.5, therefore, the corresponding curve can be found in Figure 1. The ratio of average wind speed to rated wind speed is 7/10=0.7. The corresponding value can be determined on the vertical axis, which means that the ratio of the annual average output power of the wind turbine to the rated power is 0.42.
The available annual average output power is 0.42×5=2.1kW.
Then the annual power generation of the wind turbine is 24h×365×2.1kW=18396kW·h.

1. Wind speed average method

Since the power produced by wind turbines is related to the 3rd power of wind speed, the simple assumption that the wind speed is evenly distributed is not suitable for wind power forecasting.
An efficient way to characterize the wind field is to use a parameter called the root mean cube. This parameter first sorts out the upper and lower limits of the wind speed for the wind turbine to work according to the data list other than the working wind speed of most wind turbines (usually 3~16m/s). The monthly average wind speed within the normal operating range of the wind turbine can be calculated by the following formula:

where – the monthly average wind speed, m/s;
vs——cut-in wind speed, m/s;
n — number of days, d;
v—measured wind speed, m/s.

In the 1990s, reports from the then federal Department of Primary Industries and Energy (DPIE) had tabulated or charted data for many locations, covering most of Australia. The average power that a wind turbine can produce is:

where PAv is the average power of the wind turbine;
PR – rated power;
vR——Rated wind speed, m/s.
The amount of electricity that the wind turbine can generate every day can be calculated with E=24PAv.
Using the data mentioned above and the VRMC table, the computer can calculate the estimated monthly production of wind farms or wind turbines at a specific location. Some wind turbine manufacturers also provide power generation forecast data based on this.
The concepts listed above provide a link between wind speed and output power to ensure that performance predictions are not oversimplified in system design and user expectations.

1. Online data collection method

The most accurate method is to take a field measurement at the height of the wind turbine. This method provides hours for each wind speed range. These data make up the wind speed distribution spectrum, that is, can indicate the frequency of occurrence of each wind speed range. The wind speed distribution range mentioned here refers to the range from 0 to the maximum wind speed in the place.
A spectrogram of wind speed is shown in Figure 2. This type of graph is called a histogram. Figure 2 – Histogram of Wind Speed Frequency Distribution

where Nn——wind speed observation hours of the nth grade;
vn—the midpoint of the nth wind speed level, m/s.
Mathematically model this statistical pattern of distribution, and the resulting model is called the Weibull distribution. The shape of the graph of the Weibull distribution is related to a variable called the shape factor, which is denoted by k. Figure 13.7 shows different Weibull distribution curves for k from 1 to 4. The higher the k value, the narrower the corresponding wind speed spectrum. For example, k=4 means that the wind speed is very stable and maintained for a long time, such as trade winds. A lower value of k indicates a wide range of wind speed variation. Note:
(1) Blocking location means that the buildings or trees at the location are in the direction of the local prevailing wind, and the blocking range exceeds 180°.
(2) Unobstructed locations refer to the few or no trees and buildings in the area.

The average wind speed and k value of a place determine the availability of local wind energy. In general, as the average wind speed increases, the height above the ground increases, and k increases accordingly. The most suitable sites for wind farms are those with high average wind speed and low k value.

1. Wind speed correlation

A local wind energy assessment can be carried out through the following steps:
(1) Only the data provided by the nearby weather bureau recording station is used.
(2) Compare the measurement data for a fixed period of time (for example, 3 months) at the site with the data from the nearby meteorological bureau recording stations.
(3) Record data on site for at least 1 year.
Using a nearby weather office requires that the site being assessed and the weather recording station have very similar terrain and are on the path of prevailing winds. The most accurate results are obtained by selecting data from meteorological recording stations within a distance of 40 km from the wind farm on a large area of ​​flat land, but this method has limited operability and accuracy.

Limited site surveys require similar terrain and exposure for optimal results. However, topographic and prevailing wind exposure can be compared by sequentially examining wind speed data, terrain type, surface roughness, inversion effects, and prevailing wind exposure at different locations in all directions. The frequency of some directional winds is small and can be ignored. From this, the relevant proportional coefficients of the downwind speed for different winds can be calculated. This method has limited application scope and accuracy, and it is not easy to take into account the effects of seasonal changes.

Long-term on-site measurements are the most accurate and reliable method. Higher cost due to the need to use a data logging anemometer. The shortest measurement period is 1 year, after which these data can be compared with long-term historical data recorded by the Bureau of Meteorology to confirm whether the data in the measurement year is lower, equal, or higher than previous years.

1. Use the output curve and wind spectrum to estimate the electricity

If the complete wind speed spectrum diagram and the wind power system output-wind speed curve are available, the wind power system output corresponding to each wind speed in the possible wind speed range can be calculated. This process is described in detail below, and an example is given in Table 1. Table 1 – Calculation of wind power output over 1 month using wind speed spectrogram

(1) List the wind speed range and the corresponding occurrence frequency (duration) (columns 1 and 2).
(2) Select the middle point of each wind speed range from the instructions provided by the manufacturer, and read out the corresponding wind power system output, which is listed according to the corresponding frequency (column 3).
(3) The fourth column lists the power generation of the wind turbines in each wind speed range, which is obtained by multiplying the output of the wind power system by the frequency of the wind speed range.