Refining Shadow Calculations for Wind Turbines

Refining Shadow Calculations for Wind Turbines

Random Rotor Direction (Random Azimuth)
It is very unlikely that the wind and thus the rotor will track the sun in practice. We may therefore get a more realistic result if we Two shadows modify our calculations by assuming that the rotor can assume any position at any time. In the small picture to the far right you can see a situation where the rotor is directly facing the sun. The tiny white dot near the bottom right is the centre of the wind turbine tower.
Now, let us assume that we yaw the rotor out of its position by one degree, take a snapshot of the shadow image, then yaw it by another degree, take another snapshot etc., until we have done a full 360 degree turn. Then we overlay all our 360 snapshots, and what we end up with will look similar to the small image to the left: The centre will get the most of the shadow, but as we move towards the outer edge (where the vertical edges of the rotor disc cast their shadows) the overall shadow intensity will decrease.
Shadow casting is on average reduced to 63% of the worst case results, if you assume a random rotor direction. Ideally, we should have a wind rose, (preferably hourly for each day or month) to do an exact calculation.

Fixed Rotor Direction (Fixed Azimuth)
Fixed azimuth image In practice the wind turbine rotor will follow the wind direction (if the wind speed is above the cut in speed). This image shows the shape of an area (in red) which gives 10 hours or more of shadows per year at 55° Northern latitude with the rotor yaw (azimuth) fixed at an angle of -45 degrees (i.e. with the wind permanently coming from the Southwest or Northeast). As you can see, there will be almost no shadows at an angle of +45 degrees, i.e. in the direction parallel to the rotor plane.
Shadow casting is typically reduced to around 62% of the worst case results, if we assume a fixed rotor direction.

Actual Rotor Direction (Wind Rose)
Usually we will already have a wind rose with a frequency distribution of the wind in the different directions of the compass when we are planning a wind turbine site. Using that information, we may calculate a more exact shadow picture. In the case of our test example, Copenhagen, shadows are reduced to some 64 per cent of the comparable worst case value.

Turbine Operating Hours
The rotor will not be running all the time, so we may multiply the number of minutes of shadow flicker by a factor of typically 0.75, depending on the local wind climate, (and ideally using the correct factor for daytime during each month).

Actual Sunshine Hours
When studying shadows, we should only count the fraction of the time when the sun is actually shining brightly, ideally using the correct fraction for each hour of the day during the year. In 1853 the first reliable sunshine recording device was invented (and improved in 1879), which means that in many parts of the world the meteorological institutes have very accurate long term statistics on the number of hours of bright sunshine during the year.
The number of bright sunshine hours varies with the geographical location and the season (summer or winter). We have included data for three Danish sites (Christiansø, Copenhagen, and Viborg) where the number of sunshine hours vary from 44 to 40, and 36 per cent of the time.

Combining Turbine operating hours, Actual Rotor Direction, and Actual Sunshine Hours
If we use both turbine operating hours, the actual rotor direction, and the actual bright sunshine hours we get a result (in the case of Denmark) which is some 18 per cent of the worst case assumption, using 75% operating hours in both cases. (The percentages given above are the results of simulations for Copenhagen on a 720 by 720 metre square with a turbine in the centre with 43 m rotor diameter and 50 m hub height).
The two images below compare a worst case simulation (with 75% operating hours) with an actual simulation for Copenhagen (also 75% operating hours) using both sunshine and wind statistics. The red area is the zone with 30 hours of shadow or more per year. Each map represents 720 by 720 metres.
The important conclusion of this simulation is that actual sunshine hours play a very important role in diminishing the amount of shadows north of the turbine (in the Northern hemisphere). The reason why this is important is that there are very few hours of sunshine when the sun is low in the sky to the south during winter.

Worst 30 hour zone Actual shadow simulation

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© Copyright 1998 Soren Krohn. All rights reserved.
Updated 26 September 2000
http://www.windpower.org/tour/env/shadow/shadowr.htm


		Refining Shadow Calculations for Wind Turbines Random Rotor Direction (Random Azimuth) It is very unlikely that the wind and thus the rotor will track the sun in practice. We may therefore get a more realistic result if we modify our calculations by assuming that the rotor can assume any position at any time. In the small picture to the far right you can see a situation where the rotor is directly facing the sun. The tiny white dot near the bottom right is the centre of the wind turbine tower. Now, let us assume that we yaw the rotor out of its position by one degree, take a snapshot of the shadow image, then yaw it by another degree, take another snapshot etc., until we have done a full 360 degree turn. Then we overlay all our 360 snapshots, and what we end up with will look similar to the small image to the left: The centre will get the most of the shadow, but as we move towards the outer edge (where the vertical edges of the rotor disc cast their shadows) the overall shadow intensity will decrease. Shadow casting is on average reduced to 63% of the worst case results, if you assume a random rotor direction. Ideally, we should have a wind rose, (preferably hourly for each day or month) to do an exact calculation. Fixed Rotor Direction (Fixed Azimuth) In practice the wind turbine rotor will follow the wind direction (if the wind speed is above the cut in speed). This image shows the shape of an area (in red) which gives 10 hours or more of shadows per year at 55° Northern latitude with the rotor yaw (azimuth) fixed at an angle of -45 degrees (i.e. with the wind permanently coming from the Southwest or Northeast). As you can see, there will be almost no shadows at an angle of +45 degrees, i.e. in the direction parallel to the rotor plane. Shadow casting is typically reduced to around 62% of the worst case results, if we assume a fixed rotor direction. Actual Rotor Direction (Wind Rose) Usually we will already have a wind rose with a frequency distribution of the wind in the different directions of the compass when we are planning a wind turbine site. Using that information, we may calculate a more exact shadow picture. In the case of our test example, Copenhagen, shadows are reduced to some 64 per cent of the comparable worst case value. Turbine Operating Hours The rotor will not be running all the time, so we may multiply the number of minutes of shadow flicker by a factor of typically 0.75, depending on the local wind climate, (and ideally using the correct factor for daytime during each month). Actual Sunshine Hours When studying shadows, we should only count the fraction of the time when the sun is actually shining brightly, ideally using the correct fraction for each hour of the day during the year. In 1853 the first reliable sunshine recording device was invented (and improved in 1879), which means that in many parts of the world the meteorological institutes have very accurate long term statistics on the number of hours of bright sunshine during the year. The number of bright sunshine hours varies with the geographical location and the season (summer or winter). We have included data for three Danish sites (Christiansø, Copenhagen, and Viborg) where the number of sunshine hours vary from 44 to 40, and 36 per cent of the time. Combining Turbine operating hours, Actual Rotor Direction, and Actual Sunshine Hours If we use both turbine operating hours, the actual rotor direction, and the actual bright sunshine hours we get a result (in the case of Denmark) which is some 18 per cent of the worst case assumption, using 75% operating hours in both cases. (The percentages given above are the results of simulations for Copenhagen on a 720 by 720 metre square with a turbine in the centre with 43 m rotor diameter and 50 m hub height). The two images below compare a worst case simulation (with 75% operating hours) with an actual simulation for Copenhagen (also 75% operating hours) using both sunshine and wind statistics. The red area is the zone with 30 hours of shadow or more per year. Each map represents 720 by 720 metres. The important conclusion of this simulation is that actual sunshine hours play a very important role in diminishing the amount of shadows north of the turbine (in the Northern hemisphere). The reason why this is important is that there are very few hours of sunshine when the sun is low in the sky to the south during winter.

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