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which is too big to present here. But it is clear from Figure 5 
that if the yellow line represents sun's ray then the pink area 
will be in shadow caused by the building in front. 
Then the method was applied for actual city models. In Figure 6 
most of the roofs are shadowed marked by green because it was 
early in the morning and the yellow line is direction the sun. 
  
Figure 6. Shadow area in the morning 
Figure 7 show the result of afternoon when more roofs marked 
in red gets sunlight. 
  
Figure 7. Shadow area in the morning 
The information of shadow is obtained for the whole model 
where the surface is potential for energy production. As energy 
production of a photovoltaic module is determined by the 
weekest link, the position of shadow will affect the result. In 
Figure 8 shadow caused by the linear object partially blocks 4 
cells in module A and 5 cells in module B which will cause 
significant difference in energy production than unshadowed 
module at same condition. The linear objects might be electric 
or telephone wire, or antenna, which are only present in detail 
city models. An example has been presented in Figure 9 for 
existing photovoltaic modules. 
  
Figure 9. Shadow from a temporary objects like antenna and 
signboard on photovoltaic module 
In the right side of Figure 9 a rectangular object is blocking the 
photovoltaic module. This is a temporary object and might not 
always be present within the city model. But it has also 
significant impact on energy production. 
A B 
  
Figure 10. Shadow on photovoltaic module of same size and 
shape but in different location. 
In figure 10 shadows of same size but on different position will 
cause different shadow effect. Because for module A 12 cells 
are completely shaded and for module B 6 are completely 
shaded and 12 are partially shaded, which means 18 cells are 
affected in module B. 
Terrain has also big impact on shadow calculation. In Figure 11 
an example has been presented where photovoltaic modules has 
been installed beside a hill which causes daily reduction of sun 
hour. But if the terrain is not included in the city model then the 
result will be very different from the reality. 
    
Figure 11. Shadow area in the mornin