Ohm’s Law for Solar PV: The Arithmetic Behind Strings, Cables and Losses

The Three Relationships Every PV Designer Uses

Ohm’s law, V = I x R, says that the voltage across a conductor equals the current through it multiplied by its resistance. Two companion formulas follow from it and the definition of power:

• Power: P = V x I. The output of a string is its voltage multiplied by its current.
• Resistive loss: P = I x I x R. The heat lost in a cable grows with the square of the current.
• Voltage drop: V = I x R, applied to the resistance of the cable run.

USP&E’s walk-through of the formula across every kind of power station covers the theory for all plant types. This page applies it to solar arrays, where long DC cable runs and many parallel strings make the arithmetic especially important.

Series Strings Add Voltage

Connecting modules in series adds their voltages while the current stays that of a single module. A string of twenty modules, each producing about forty volts at its maximum power point, delivers roughly eight hundred volts. Higher string voltage means lower current for the same power, and lower current means smaller voltage drop and lower losses in the cables.

That is why utility arrays push string voltage as high as equipment ratings allow. The limit is set by the maximum system voltage of the modules, inverters and cables, and by safety rules for DC systems.

Cold Mornings Raise Voltage

Module voltage rises as temperature falls. On a clear, cold morning the open-circuit voltage of a string can exceed its rated figure by a noticeable margin. If the string is too long, that cold-weather voltage can exceed the inverter’s maximum input or the module’s system rating and damage equipment.

Designers therefore calculate string length using the lowest expected site temperature and the module’s temperature coefficient of voltage. Hot afternoons do the opposite, lowering voltage, so the string must also stay above the inverter’s minimum tracking voltage on the hottest day.

Parallel Strings Add Current

Strings connected in parallel add their currents while the voltage stays the same. Combiner boxes gather many strings onto larger cables leading to the inverter. Every step up in current makes cable resistance more important, because losses rise with the square of the current.

Parallel connection also raises a protection question. If one string develops a fault, the others can feed current back into it. String fuses, sized from the module’s short-circuit current with a safety margin, prevent that reverse current from causing damage. Our page on protection coordination in solar EPC covers how DC and AC protection work together.

A Worked Voltage Drop Example

Take a single string carrying thirteen amps through copper cable with a resistance of about four and a half ohms per kilometre. If the string sits one hundred metres from the combiner box, the current travels two hundred metres in total, out and back.

1. Cable resistance: 0.2 km x 4.6 ohm per km = about 0.92 ohm.
2. Voltage drop: 13 A x 0.92 ohm = about 12 V.
3. Against an eight-hundred-volt string, that is roughly one and a half percent of the voltage.
4. Power lost as heat: 13 A x 13 A x 0.92 ohm = about 155 W.

Doubling the cable cross-section roughly halves the resistance and the loss. Whether that is worth the extra copper depends on the energy value over the plant’s life, which is why cable sizing is an economic as well as a technical decision.

DC Cable Sizing in Practice

Cable size is set by three checks. The cable must carry the maximum current without overheating, taking into account burial depth, grouping and ambient temperature. It must keep voltage drop within the design target. And it must withstand the fault current until protection operates.

On the AC side, the same logic applies to inverter output cables, transformer connections and the export line. Losses everywhere eat into the energy the plant sells. Our article on the performance ratio in solar EPC shows how cable losses add to the gap between theoretical and delivered energy, and our guide to energy yield assessment explains how designers estimate them before construction.

Inverter Windows and the MPPT Range

Every inverter has a voltage window within which its maximum power point tracker works. String design must keep the array inside that window across the full range of site temperatures and irradiance. Too few modules per string and hot afternoons drop the voltage below the window; too many and cold mornings push it above the limit.

Current limits matter as well. Inverters can clip power when the array produces more than their rated input, which designers sometimes accept by design when the DC array is deliberately oversized to boost morning and evening output.

Mismatch, Shading and Ohm’s Law

In a series string, every module carries the same current. If one module is shaded, soiled or damaged, it limits the current of the whole string. Bypass diodes inside each module let current flow around a shaded section, but the string still loses the voltage of the bypassed cells. Ohm’s law and the power formula explain why one dirty module can reduce a string’s output far more than its share of the array.

Mismatch also occurs between strings connected in parallel. If one string has fewer modules or a different orientation, its voltage differs from the others and the inverter tracker must find a compromise. Good design keeps strings on the same tracker identical in length, orientation and tilt, and cleaning schedules keep soiling even across the array.

Earthing, Insulation and Safe DC Work

High DC voltages bring particular hazards. Unlike AC, direct current does not pass through zero, so arcs are harder to extinguish. Insulation resistance between conductors and earth must stay high; a fall indicates damaged cables or connectors and can lead to dangerous faults. Inverters measure insulation resistance before connecting each morning and raise an alarm if it is low.

• Use DC-rated isolators, fuses and connectors from matched manufacturers.
• Check insulation resistance during commissioning and periodically after.
• Inspect connectors for heat damage with thermal imaging.
• Isolate and verify before working on any string, since panels generate whenever light falls on them.

These checks protect both people and plant, and they are simple applications of the same electrical principles used to size the cables.

Using the Formulas in Design Reviews

During design review, a few quick calculations test whether a layout is sound. Check the cold-weather open-circuit voltage of the longest string against the inverter limit. Check the hot-weather operating voltage of the shortest string against the tracking minimum. Calculate the voltage drop and resistive loss on the longest DC run and the main AC feeders. Confirm fuse ratings against module short-circuit current. These checks take minutes with the formulas above and catch most of the errors that would otherwise surface during commissioning.

Hybrid Plants and the AC Side

Many solar plants in Africa and other emerging markets run alongside generators or batteries. There, Ohm’s law reaches into the AC network: cable runs between the solar inverters, generator sets and loads must be sized so that voltage stays within limits as power flows shift through the day. Fault levels also change when generators start or stop.

USP&E designs hybrid power systems that combine solar, storage and generation, and delivers them through its power plant EPC projects. Our solar EPC overview explains how electrical design fits into the full scope.