Solar insolation in Switzerland

Solar insolation at any point of the Earth’s surface has a maximum of about 1025 W/m², measured on one square metre perpendicular to sunrays. Since the Earth’s surface is curved, the further a location is from the equator, the more surface area is required to achieve this irradiation – to be more precise, 1025 W is received by a surface area 1m x 1/(cosine of the latitude). The geometry of a curved surface is more complicated, but for the purposes of our calculation this is accurate enough. Switzerland lies at between 45.8° and 47.7°, or on average 46.75° (approximately at the level of Berne, which is at 46.5° North).

The surface area equivalent (SAeq) is on average for Switzerland: 1.0m x 1/(cos46.75) = 1.46m2, meaning that each 1.46m2 surface area parallel to the ground in full sunlight receives 1025 W/m² as a yearly average. Throughout the year, any point on the Earth’s surface changes its orientation towards the sun, which gives rise to the seasons. Since the Earth’s axial tilt is 23.4°, Berne’s angle of inclination to incoming sunrays varies from 23.1° to 69.9°. This then suggests that Berne’s SAeq varies from 1.09m2 in mid-summer to 2.9m2 in mid-winter. In Palermo (38° north), the average SAeq = 1.27m2. In Berlin (52.3° north), SAeq = 1.64m2.

Given that Switzerland has a surface area of 41,285km2 (41.29 x 109m2), the total average irradiation is (41.29 x 109) x cos(46.75°) x 1025 W/m² = 29.0 x 1012 Watts = 29.0 TW. This means that the average total solar irradiation at noon on a cloudless day is 29 million megawatts. But how does this translate into total energy that is available over a year?

Intensity of solar radiation varies by season, cloud cover, and time of day. We can ignore the seasonal variation, because 29.14 TW is the average over the year. The number of hours of sunlight over Berne is around 42% of the 4380 daylight hours, or 1840 hours of sunshine per year (long-term average). Since the Sun moves across the sky during the day, its intensity on any surface area ranges from zero to full, or a rough average of about 50% of the maximum daily average. This means that we can count 920 full-insolation equivalent hours over a year.

Assuming Berne’s insolation is the average for Switzerland, and a full-insolation hour in Switzerland provides 29.0 x 1012 Wh over the whole country, then 920 hours provides 920 x 29.0 x 1012 = 2.7 x 1016Wh in a year, or 27,000 TWh. By comparison, Switzerland consumed 58.24 TWh of electricity from all sources in 2016 (total generation was 61.6 TWh, and the excess was grid losses and trade imbalance). Solar insolation is 460 times electricity consumption. Obviously, not all of solar insolation can be converted to electricity, but if Switzerland can tap and effectively convert 0.22% of it, it would not need any other power source, and just 0.08% would replace all nuclear power.

The efficiency of the newest generation of silicon-crystalline solar cells is about 18%. This means that 18% of radiation is converted to electricity by a new, clean solar panel. Panels typically lose 20% of their efficiency over their 20 year lifespan, and are not always maintained optimally, so we can use 15% as an approximate average efficiency. This means that 27,000 TWh of solar insolation could be converted to about 4000 TWh of electricity, which is 69 times consumption. Incidently, this ignores that fact that there are more efficient ways of utilising solar energy, such as solar thermal (using the thermal energy directly for heating), and fuel generation.