A shadow on one corner costs far more than one corner

Cells in series must share a current

A solar cell behaves, in the range that matters here, as a current source rather than a voltage source. The current it can push is roughly proportional to the light falling on it, while its voltage barely moves across a wide span of illumination. Wire a set of cells in series, as every panel does internally and as most systems then do again at panel level, and one consequence follows immediately.

The same current has to pass through every element in the chain. That means the least illuminated cell decides the current for all of them. A cell in shadow cannot pass what its neighbours want to push, so it acts as a restriction, and the whole string collapses towards whatever the worst member can carry.

This is why the arithmetic of shading looks nothing like the arithmetic of area. Shade one cell out of sixty and you have not lost one-sixtieth of the panel. Without protection you would lose most of it.

Bypass diodes limit the damage rather than repair it

Every modern panel contains bypass diodes, usually three, each spanning a group of cells. When a group is dragged down far enough, its diode conducts and current routes around the group entirely. The panel goes on working at reduced output instead of choking, and — the more important function — the shaded cell stops being forced to dissipate the rest of the string’s power as heat.

That second job is a safety matter rather than an efficiency one. A reverse-biased cell sitting in a high-current string turns into a resistor, and the resulting hot spot can crack the cell, discolour the encapsulant around it, or in a bad case damage the backsheet. Bypass diodes exist as much to prevent that as to save energy.

But look at what the diode actually does. It removes a third of the panel from the circuit. A shadow the size of a hand, falling across a single cell, costs you the output of twenty cells. The loss is far smaller than it would be without the diode and still far larger than the shadow.

A string repeats the problem one level up

Panels wired in series into a string reproduce the same pattern at a larger scale. String current is limited by the weakest panel, so one partly shaded module can drag down every module wired with it. A chimney shadow crossing three panels in a twelve-panel string does not cost a quarter of the string; it costs considerably more.

A conventional string inverter can make this worse before it makes it better. It runs maximum power point tracking across the whole string, hunting for the combination of voltage and current that yields the most power. With an unevenly lit string, the power curve develops several local peaks, and a tracker can settle on the wrong one and sit there for some time before it rescans.

This is why installers care so much about which panels share a string. Grouping the shaded modules together, ideally on their own tracker input where the inverter offers more than one, contains the damage instead of letting it spread across the clear part of the roof.

Small nearby shadows are worse than big distant ones

A counterintuitive result falls out of all this. A thin object close to the array does more harm over a year than a large object further away. A vent pipe, an aerial, a satellite dish or a single overhead cable casts a narrow shadow, but that shadow sweeps across cell after cell through the day, and at every moment it is taking out a whole diode group.

A distant tree that shades the array for the first hour after sunrise costs an hour of a period that was producing very little in any case. A soil pipe standing two metres from the panels costs a slice out of the middle of the day, every day, for the working life of the system.

Snow, fallen leaves and lichen behave the same way. So does the streak of dirt that builds along the bottom edge of a panel where rainwater collects and evaporates, because that streak reliably crosses the lowest row of cells in every panel it forms on, and the lowest row is a whole diode group.

What to do about it, cheapest first

The cheapest remedy is simply deciding where the panels go. Moving an array a metre sideways, dropping the bottom row, or leaving a section of roof empty because a flue occupies it costs nothing once the system is up, and it beats every electronic fix available. Shade avoidance is worth more than shade tolerance.

Next cheapest is string layout, which is free at design time and awkward afterwards. After that come module-level electronics, optimisers or microinverters, which do recover a worthwhile share of the loss but add cost and put components on the roof.

It is entirely reasonable to conclude that a shaded roof should not be fitted at all. If a chimney and a neighbour’s tree between them take a third of the array through the middle of the day, no amount of electronics turns that into a good installation. A smaller array confined to the clear part of the roof is often the better system, and occasionally the honest answer is that this particular roof does not suit solar.