Tree shade on solar panels: how much yield does it really cost?
A tree to the south looks threatening, but the numbers are usually smaller than the feeling. Here is the calculation for an 8 kWp system in Vienna, with spruces and broadleaf trees at various heights and distances, month by month.
The rule of thumb that usually holds
What matters is not the height of the tree but the angle at which it appears from the centre of the roof, and the direction. At noon in summer the sun in Vienna stands about 65° high, in winter only 19°. A tree that appears below 20° only interferes in winter, when there is little yield anyway. A tree that looks 45° high also takes hours in spring and autumn.
Spruce to the south: yield loss by height and distance
System: 8 kWp, 30° tilt, facing south, roof centre 7 m above ground, Vienna. Without a tree PVGIS gives 9 332 kWh per year. The tree is a cone (spruce) with crown base 1.5 m, directly south of the roof centre.
| Spruce, height | distance 6 m | 10 m | 15 m | 20 m |
|---|---|---|---|---|
| 8 m | 0 kWh (0.0 %) | 0 kWh (0.0 %) | 0 kWh (0.0 %) | 0 kWh (0.0 %) |
| 12 m | 169 kWh (1.8 %) | 38 kWh (0.4 %) | 0 kWh (0.0 %) | 0 kWh (0.0 %) |
| 18 m | 916 kWh (9.8 %) | 305 kWh (3.3 %) | 139 kWh (1.5 %) | 67 kWh (0.7 %) |
| 25 m | 2301 kWh (24.7 %) | 858 kWh (9.2 %) | 358 kWh (3.8 %) | 180 kWh (1.9 %) |
Reading: a 12 m spruce at 10 m costs about 40 kWh a year, roughly 6 € at 15 ct. A 25 m spruce at 6 m costs a quarter of the system. Everything you see in daily life lies in between.
Direction: south is not west
The same 18 m spruce at 10 m, moved around the house:
| Tree stands to the … | loss per year | share |
|---|---|---|
| south | 305 kWh | 3.3 % |
| south-west | 372 kWh | 4.0 % |
| south-east | 297 kWh | 3.2 % |
| west | 175 kWh | 1.9 % |
| east | 142 kWh | 1.5 % |
| north | 0 kWh | 0.0 % |
West costs a little more than east because afternoon sun in Vienna is on average slightly stronger than morning sun (fog, cloud patterns). To the north a tree is irrelevant for yield.
Month by month: when the tree strikes
Spruce 18 m, 10 m south, angle 48°:
| Month | no tree kWh | with tree kWh | loss kWh | % |
|---|---|---|---|---|
| Jan | 365 | 319 | 46 | 13 % |
| Feb | 533 | 471 | 62 | 12 % |
| Mar | 831 | 780 | 51 | 6 % |
| Apr | 1 030 | 1 030 | 0 | 0 % |
| May | 1 066 | 1 066 | 0 | 0 % |
| Jun | 1 101 | 1 101 | 0 | 0 % |
| Jul | 1 138 | 1 138 | 0 | 0 % |
| Aug | 1 047 | 1 047 | 0 | 0 % |
| Sep | 890 | 890 | 0 | 0 % |
| Oct | 644 | 639 | 5 | 1 % |
| Nov | 369 | 296 | 73 | 20 % |
| Dec | 317 | 250 | 67 | 21 % |
In December and January 30 to 40 % of an already small yield is missing, in summer almost nothing. That is typical for trees to the south: they hit the months in which the system produces little. A tree to the west hits the summer afternoon instead.
Broadleaf versus spruce
A broadleaf tree of the same height has a wider crown and therefore costs more: 12 m broadleaf at 10 m 263 kWh instead of 38 kWh for the spruce, 18 m broadleaf 1655 kWh instead of 305 kWh. In winter a broadleaf tree is bare and lets part of the light through, which the calculation ignores, so the winter loss of a broadleaf tree is somewhat overestimated.
The tree grows
A spruce adds 25 to 40 cm a year until mature. The 12 m spruce above, which costs 38 kWh today, is 15 m in ten years and costs 159 kWh, 18 m in twenty years and 305 kWh. Over the life of the system the tree is a growing item. PV-Schatten has a slider for this: “Tree growth: years into the future”.
What the figures do not include
- String losses. PVGIS removes the direct irradiance behind the tree but not the electrical effect: a partly shaded module can drag down the whole string without optimisers. See partial shading and bypass diodes.
- Diffuse light. The tree also takes part of the sky light, which is not subtracted here. With dense crowns close to the roof the real loss is somewhat higher.
- Leaves in winter. Bare broadleaf trees let 30 to 60 % through.
Fell it or not?
Calculation: annual loss in kWh × electricity price × remaining life of the system, against the cost of felling (300 to 1,500 €) and the value of the tree for cooling, privacy and neighbourly peace. The 25 m spruce at 6 m with 2301 kWh loss a year is about 9 204 € at 20 ct over 20 years, worth a conversation. The 12 m spruce at 15 m costs nothing measurable; it stays.