Photovoltaic Arrays, Inverters and Low-Voltage Runs

Ohm's law, and the load that draws more when you starve it

Everything here rests on two relationships: power is voltage times current, and for a resistance, voltage is current times that resistance. Between them they answer almost every low-voltage question, and the arithmetic is trivial.

The trap is which kind of load is on the end. A RESISTIVE load obeys the second relationship directly — drop the voltage and the current falls with it, and the power falls with the square. That is the intuition most people carry.

A CONSTANT-POWER load does the opposite. An inverter, a switch-mode supply or an electronic driver delivers the output it was asked for and takes whatever input current that requires, so lowering the supply voltage RAISES the current it draws. A sagging supply therefore increases the load on the very conductors that were sagging, which heats them, which drops the voltage further. It is a positive feedback rather than a self-limiting one, and it is why undersized conductors to electronic loads fail in a way undersized conductors to heaters do not.

The string limit is the coldest morning of the year

A photovoltaic cell's open-circuit voltage carries a negative temperature coefficient: it RISES as the cell gets colder. A module therefore produces its highest voltage on a bright freezing morning, before the sun has warmed it, and its lowest on a hot afternoon.

So the maximum number of modules in a series string is set by the coldest expected temperature at the site, not by any operating average. The check is against the inverter's absolute maximum DC input voltage, and the rounding is DOWN, because exceeding that voltage is not a performance shortfall — it is an over-voltage event that destroys the inverter, and it is not covered by any warranty.

The lower bound is set by the other end of the same curve. A string that is too SHORT can fall below the inverter's minimum tracking voltage on a hot day, at which point the inverter simply stops, and the array produces nothing at the time of year it should be producing most. String length is therefore a window rather than a maximum.

The design temperature is a record-based figure for the location, not a seasonal average, and that is the input most often taken casually. A string sized on a mild assumption works for years and then meets one genuinely cold clear morning.

Rated output is a laboratory condition the roof rarely reaches

A module's nameplate is quoted at standard test conditions: a stated irradiance, a stated spectrum, and a CELL temperature of twenty-five degrees. Those conditions almost never occur together in service.

Cell temperature is the reason. A module in full sun runs well above the air around it — commonly twenty-five to thirty degrees above ambient on an unventilated roof — and output falls by a few tenths of a per cent for every degree above twenty-five. On the hottest, sunniest day, a module can be delivering fifteen to twenty per cent below its nameplate, which is when the array looks most disappointing and is behaving exactly as specified.

Several further derates stack on top: soiling, module mismatch, wiring and connector losses, inverter conversion efficiency, and any shading. Each is a modest percentage and they multiply, which is why a realistic system-level derate is substantially larger than any single term suggests.

This is also why the DC array is deliberately larger than the inverter's AC rating. Because the array so rarely reaches its nameplate, an inverter sized to the DC peak would spend its life far below its efficient range; oversizing the array means the inverter runs nearer its best point for far more hours, and CLIPS the few hours a year when the array genuinely exceeds it. A ratio above one is the design rather than a mistake, and the clipped energy is cheaper to lose than the inverter capacity would be to buy.

Shade is not proportional to its area

Modules in a series string carry the same current, and that current is limited by the WORST-PERFORMING cell in the chain. A shadow across a small part of one module can therefore suppress the output of every module in that string — far out of proportion to the area covered.

BYPASS DIODES limit the damage. Each module is divided into sub-strings with a diode across each, so a shaded sub-string is short-circuited out rather than throttling the rest. That turns a catastrophic loss into a partial one, and it is why the orientation of a shadow matters: a shadow lying across the sub-strings hurts far more than one lying along them.

The consequence for layout is that small obstructions matter enormously. A flue, an aerial, a parapet or a neighbouring tree casts a narrow moving shadow that can cross a string every day, and its energy cost is nothing like its footprint. Module-level power electronics — optimisers or micro-inverters — exist mainly to contain that, by letting each module operate at its own maximum point.

A shading assessment is therefore a geometry exercise over the whole year rather than a look at the roof at noon. The sun's path changes with the season, so an obstruction that clears the array in June can cross it for hours in December, which is when the system can least afford it.

Ballasted mounts: the load is uplift, and the roof carries the answer

A ballasted array on a flat roof is held down by weight rather than by fixings, so the design case is WIND UPLIFT and the check is a moment balance rather than a strength one.

The load is not uniform across the array. Wind separating at the roof's edges and corners produces much higher suction there than over the field — the same zoning that governs roof coverings and fastener schedules — so ballast is concentrated at the perimeter and corners, and an evenly distributed ballast layout is simultaneously over-provided in the middle and under-provided where it matters.

Interior modules are also shielded by the rows around them, which is why a large array needs proportionally less ballast per module than a small one and why removing a perimeter row changes the loading on everything behind it.

The quantity that has to be checked elsewhere is the roof. Ballast can weigh several times the array itself, applied as concentrated loads at the support points, and a roof that comfortably carries a fixed array may not carry a ballasted one. It is a structural question that belongs to the building rather than to the solar design, and the calculators here return a required mass rather than a verdict on whether the roof can take it.

Low-voltage runs: the drop that matters and the strip that fades

Voltage drop is a percentage of the supply voltage, so at twelve volts a three per cent budget is about a third of a volt — an amount a few metres of thin cable will consume on its own. Low-voltage distribution is therefore dominated by conductor size and run length in a way mains distribution is not, and the usual remedies are larger conductors, shorter runs, or a higher distribution voltage with local conversion.

A constant-voltage LED strip shows the problem visibly. Fed from one end, the far end sees a lower voltage than the near end and runs dimmer, and on a long run the gradient is plainly noticeable. The remedies are to feed from both ends, to inject power at intervals along the run, or to break the installation into shorter segments — none of which is a product choice, all of which are layout decisions made before anything is cut.

Supply sizing needs the strip's ACTUAL consumption per metre, which varies with colour temperature, density and drive level rather than being a single figure per product family, and it needs headroom above the computed total — both because a supply run continuously at its limit runs hot and shortens its life, and because inrush at switch-on exceeds the steady draw.

Outdoor lighting adds two constraints that are not electrical. Fittings and connections need an ingress rating appropriate to where they sit, because the failures are water rather than overload; and cable routes need burial depth and mechanical protection. The calculators here size conductors and supplies, and those requirements come from the installation rules rather than from the arithmetic.