Technology and Engineering · High school

Solar panel

Move the sun and the panel: how do the angle of the light and a single shaded cell change the panel’s power?

In the learning section below the figure, predict, try, complete the tasks and check yourself with short questions.

Fig. 1Solar panel

Move the sun and the panel with the sliders, tap a cell or the junction box

Sun height45°

Panel tilt15°

Every cell carries the same current.

Power output

P = G · A · η · cos θ

219 W

Irradiance facing the Sun867 W/m²
Angle of incidence θ30° · cos θ = 0.87
Angle loss (1 − cos θ)13%
Irradiance on the panel751 W/m²
Voltage29.5 V
Current7.44 A
Loss from shadeno shade

Your own values

You can use a comma or a point. If the irradiance box is empty, it is worked out from the sun height.

Irradiance (facing the Sun) · autoW/m²Cell aream²Efficiency%Sun height°Panel tilt°

What if?

Walk up the scale ladder: each step is ×10. If another star took the Sun’s place, how much light would reach the panel?

Scale ladder: from 10³ km to 10⁹ km, each notch ×10. The Sun and Jupiter, to the same scale

If the Earth were a 1 cm bead, the Sun would be 1.09 m across: about 5 footballs side by side.

Radius: 695,700 km
Times the Earth: ×109
Earths that fit inside: 1.3 × 10⁶
In the Sun’s place: 1,361 W/m²; outside the air, facing the light

The Sun’s radius is 109 times the Earth’s; about 1.3 × 10⁶ Earths would fit inside it. Each square metre of its surface gives out σT⁴ of power; after travelling 1 AU this light has thinned to 1,361 W/m². That is the light the panel in the figure gets above the atmosphere.

In reality: The Sun is on average 149.6 million km (1 AU) from the Earth. Light reaching the ground is weakened by the air: in the figure, with the Sun overhead, about 953 W/m² reaches the panel.

Assumptions: Stars are treated as evenly glowing spheres (σT⁴), with radius and temperature from published measurements; the brightness is worked out from these two, so it can differ a little from published values (about 15% for Arcturus). The panel is the one in the figure, 1.46 m² at 20% efficiency; the light is taken outside the atmosphere, hitting the panel straight on; the panel heating up, its efficiency dropping and the colour of the light are left out. In the comparison the Earth is 1 cm across.

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

The Sun is 30° above the horizon and the panel lies flat. What happens to the power if you tilt the panel to 60°?

Gold dots: photons (packets of light energy)Filled purple dot: electron · hollow ring: hole; in the wires, electrons flow from the (−) end into the outer circuitThe numbers come from a single model: P = G · A · η · cos θ. The default panel has 60 cells (1.46 m² in total, 20% efficiency, 0.5 V per cell); at noon the Sun and the panel both face south, θ = |90° − α − β|. The irradiance facing the Sun, G, is worked out from the thickness of the atmosphere with Meinel’s formula; you can also type your own. Diffuse light, temperature and cable losses are left out. The leaf lets a tenth of the light reach its cell; the bypass diode routes the current around that cell’s 20-cell substring (the diode’s small voltage drop is ignored).

How does a solar panel make electricity? From photon to socketRead the article