Turbine power calculator

        Bellow some instructions for using the wind turbine power calculator are given. If you do not want to read all these instructions, please read the additional notes paragraphs in the end, at any case.

Using the power curve and the Weibull distribution to estimate power and energy output
        In order to use the power curve properly, you have to combine your knowledge of the Weibull distribution with the power curve. For each tiny 0.1 m interval of wind speeds we multiply the probability of that wind speed interval (from the Weibull curve) with the value from the power curve of the wind turbine. We then take the sum of all these multiplications to get the mean, or average, power output. If the power is multiplied by 365.25 by 24, which is the number of hours in a year, then the total energy output for an average year comes.

Site data
        The pop up menu can be used to fill out European wind distribution data automatically. The data calculated for roughness classes 0, 1, 2 and 3 was taken from the European wind atlas. For roughness class like 1.5, interpolation is used to find the data.

Air density data
        The energy in the wind varies in proportion to the density of air. Try changing the air temperature from, say 40 degrees Celsius, to -20 degrees Celsius. There are almost 25% more air molecules in a cubic metre of the cold air than in a cubic metre of the warm air, so the energy output changes also. For changing the altitude above sea level, start setting the temperature at sea level first. The programme will then automatically compute the likely temperature and pressure at the altitude that is set. The air density can also be directly changed directly. The program then computes a likely set of data for the other variables.

Wind distribution data
        The Weibull shape parameter is generally around 2 in Northern Europe, but situations vary, so maybe a wind atlas is needed to set this more accurately. You can either enter the mean wind speed, or the Weibull scale parameter. The programme then automatically computes the other.
        The measurement height for the wind speed is very important, because wind speeds increase with heights above ground level, because of the wind shear. Meteorology observations are generally made at 10 m height, but anemometer studies are often made at hub height of the wind turbine, in our example 50 m.
        The average roughness of the surrounding terrain is important to determine the wind speed at turbine hub height, if it differs from the height at which wind speed measurements were made. You may either set the roughness length or the roughness class, depending on the local landscape type.

Wind turbine data
        This section of the calculator lets you specify the rated power of the main generator, the rotor diameter, the cut in wind speed and the cut out wind speed, and the hub height of your machine. At the bottom of the page you may then specify the power curve of your machine. It is much easier, however, to use the first pop up menu which allows you to set all turbine specifications using a built-in table of data for typical Danish wind turbines. We have already put data for a typical 600 kW machine in the form for you, but you may experiment by looking at other machines.
        The second pop up menu will allow you to choose from the available hub heights for the machine you have chosen. You may also enter a hub height of your own, if you wish. Try experimenting a bit with different hub heights, and see how energy output varies. The effect is particularly noticeable if the machine is located in terrain with a high roughness class. You can modify the roughness class in the wind distribution data to see for yourself.
        If you modify the standard machine specifications, the text on the first pop up menu changes to User example, to show that you are not dealing with a standard machine. It is safe to play with all of the variables, but it does not make much sense to change the generator size or rotor diameter for a standard machine, unless you also change the power curve. We only use the rotor diameter to show the power input and to compute the efficiency of the machine in terms of the power coefficient. We only use the rated power of the generator to compute the capacity factor.

Wind turbine power curve
        For practical reasons (keeping your input data and your results in view at the same time) the listing of the turbine power curve is placed at the bottom of the page. You can use this area to specify a turbine which is not listed in the built-in table. The only requirement is that wind speeds be ordered sequentially in increasing order. The program approximates the power curve with a straight line between each two successive points which have non zero values for the power output. Note that the programme only uses wind speeds up to 40 m/s in its calculations of the wind climate, so do not bother about fantasy machines that work beyond 30 m/s.

Control buttons
        The following control buttons apply:
- Calculate: recalculates the results on the form. You may also click anywhere else or use the tab key after you have entered data to activate the calculator. Note that if you change the power curve, the machine will not recalculate your data until you click calculate, or change other data.
- Reset Data: sets the data back to the user example you first encountered on your screen.
- Power Density: plots the power density graph for this site and machine in a separate window.
- Power Curve: plots the power curve for the machine you have selected in a separate window.
- Power Coefficient: plots the power coefficient, i.e. the efficiency of the machine at different wind speeds.

Site power input results
        The following site power results apply:
-Power input per square metre rotor area: shows the amount of energy in the wind which theoretically would flow through the circle containing the rotor area, if the rotor were not present. Iin reality, part of the airflow will be diverted outside the rotor area due to the high pressure area in front of the rotor.
- Maximum power input at x m/s: shows at what wind speed we achieve the highest contribution to total power output. The figure is usually much higher than average wind speed, cf. the page on the power density function.
- Mean hub height wind speed: shows how the programme recalculates your wind data to the proper hub height. If you have specified a hub height which is different from the height at which wind measurements were taken, the program automatically recalculates all wind speeds in the Weibull distribution in accordance with the roughness class, or roughness length, you have specified.

Turbine power output results
        The following turbine power output results may be derived from the calculator:
- Power output per square metre of rotor area: tells how much of the power input per square metre the machine will convert to electricity. Generally, you will find that it is cost effective to build the machine to use about 30% of the power available. Please note, that the figure for site power input includes the power for wind speeds outside the cut in/cut out wind speed range, so you cannot divide by that figure to obtain the average power coefficient.
- Energy output per square metre rotor area per year: is simply the mean power output per square metre rotor area multiplied by the number of hours in a year.
- Energy output in kWh per year: tells how much electrical energy the wind turbine will produce in an average year. That is probably the figure the owner cares more about than the rest. However, when the owner considers that figure he will also have to take the price of the machine, its reliability and the cost of operation and maintenance. The annual energy output calculated here may be slightly different from the real figures from the manufacturer. This is particularly the case if you vary the density of air. In that case the manufacturer will calculate different power curves for each density of air. The reason is, that with a pitch controlled turbine the pitching mechanism will automatically change the pitch angle of the blade with the change of air density, while for a stall controlled turbine, the manufacturer will set the angle of the blade slightly differently depending on the local average air density. This programme may be up to 3.6% below the correct figure from the manufacturer for low air densities and up to 1.6% above the manufacturers' figures for high air densities.
- Capacity factor: tells how much the turbine uses the rated capacity of its (main) generator. You may read more on the page on annual energy output from a wind turbine.

Additional notes
        Put attention in the following subjects:
- Note 1: Make sure that you use the same hub height for comparing how two machines with the same rotor diameter perform.
- Note 2: For comparing machines with different rotor diameters you should look at the energy output per square metre of rotor area instead (you should still use the same hub height).
- Note 3: Low wind machines (large rotor diameter relative to generator size) will generally perform badly at high wind sites and vice versa. Most low wind machines are not designed for use in high wind areas with strong gusts.

Turbine power calculator