Shading losses: why a little shade costs a lot.

The cells in a panel are connected in series and share the same current. A shaded cell produces less current than the others, and without protection it is forced to carry the current in reverse. It then becomes a load that heats up – a so-called hot spot.

The bypass diode sits in parallel with a group of cells. When the group is reverse-biased, the diode carries the current past it, and the voltage across the shaded group is limited to roughly one diode drop. PVEducation gives about 15 silicon cells as an upper limit per diode, which is why a panel is divided into several substrings, each with its own diode.

The price is that the whole substring is bypassed. In a panel with three substrings, a shadow over just a few cells can take a third of the power, and a shadow across all three can take almost all of it.

In a string without optimisers, all panels share the same current. The inverter looks for the operating point that gives the most power for the whole string: either the string carries the weaker panel’s current, or that panel’s substrings are bypassed and the string voltage drops. The power curve gets several peaks, and the difference from the sum of the panels’ own maximum power is the mismatch loss.

In a typical panel with three substrings, they run along the long side. A shadow along the bottom edge of the panel – from the row in front on a flat roof, or from snow that stays put – therefore reaches all three substrings in a portrait panel but only the bottom one in a landscape panel. That is one reason to lay panels in landscape in rows. Check the number of bypass diodes and how the cells are connected in the panel datasheet.

Sweden: in Stockholm the sun stands just over 7° above the horizon at midday in December, so a one-metre chimney casts a shadow almost eight metres long. November–January gives only about 5 % of the annual yield, so the long winter shadows cost little energy. What decides the annual total is shading from March to October.

Germany: in Munich the solar elevation is 18° and November–January gives just over 13 % of the year. A shadow that reaches the panels only in winter shows up in the annual total.

Spain: in Madrid the sun stands 26° above the horizon and winter gives close to a fifth of the yield. Winter shading counts for more than in the north, while a row spacing calculated for the winter sun costs less roof area, because the shadow per metre is shorter.

Italy: in Rome the solar elevation is 25° and winter gives 17 %. The picture is similar to Madrid. In valleys and near mountains, the horizon often matters more than the solar elevation.

The calculation follows the sun through the year. For each moment it determines whether direct light reaches a point on the panel or is blocked, and the loss is weighted by how much sunlight falls at that moment. A shadow on a December morning therefore counts for little, a shadow at midday in June for a lot.

Diffuse light comes from the whole sky. The sky view factor is the share of the sky that a point on the panel sees, weighted by the panel’s tilt. A dormer or an adjacent wall takes a piece of the sky even when it does not block the sun, and so also reduces the diffuse light.

The horizon is added as a profile around the site: when the sun is below the profile, direct light counts as blocked. PVGIS, the European Commission’s calculation tool, derives such a profile from a terrain model.

Finally, the string is calculated electrically. The shading on each substring gives the panel’s curve, and the string’s operating point decides how much is lost. That is the difference between a geometric shaded fraction and the real power loss.

With an optimiser or a microinverter on each panel, every panel works at its own maximum power point. Mismatch between panels in a string is then reduced, but substrings within a shaded panel are still bypassed by the bypass diodes. The components have their own losses and their own cost, and the benefit depends on how often and how unevenly the panels are shaded. Calculate the yield with and without, and compare the difference with the extra cost.