Solar PV Cable Sizing: String Current, Volt Drop and Temperature Derating

The two currents in one string

Every solar module datasheet gives two currents and it is worth being clear which one does what. Isc is the short-circuit current, the current the module delivers into a short, and it is the highest current the string can produce under any load condition. Imp is the current at maximum power, typically about 92 to 96 % of Isc, and it is the current the string actually delivers to the inverter in normal operation.

Cable sizing uses Isc, because a cable has to survive the worst case, and the worst case includes a fault. But volt drop uses Imp, because that is the current flowing in normal operation and the drop has to be evaluated under the conditions the plant operates in, not under a short circuit. Sizing and volt drop are therefore two different calculations on the same string, and mixing the two currents up is the most common arithmetic error in a PV design.

• Isc: the short-circuit current; use it for cable rating and protection
• Imp: the current at maximum power; use it for voltage drop and for energy estimates
• Imp is typically 92 to 96 % of Isc on a crystalline module
• Both are specified at STC: 1000 W/m² irradiance and 25 °C cell temperature

The 1.25 and 1.56 rules, and where they come from

The two factors in EN 50618 and IEC 62548 are often quoted as if they were alternative rules of thumb. They are not: they are the same chain applied at two different points. The first 1.25 accounts for enhanced irradiance, since a module under a cloud edge or with reflection from water, sand or snow can see more than the 1000 W/m² of standard test conditions, and the standard accounts for up to 1250 W/m². The second 1.25 is the safety and ageing margin on the cable itself. Multiply them and you have 1.56.

The practical result is two different requirements. A string cable protected by an overcurrent device, or a string that cannot receive reverse current from more than two others, is rated at 1.25 × Isc. A cable in an unprotected parallel group, which can carry reverse current from its neighbours as well as its own, is rated at 1.56 × Isc. Where an overcurrent device is fitted, it is selected at no more than 2 × Isc and no more than the maximum series fuse rating the module manufacturer publishes.

Why the cold morning sets the string length

Crystalline silicon modules have a negative temperature coefficient of voltage: the colder the cell, the higher its open-circuit voltage. A typical coefficient for Voc is about −0.28 % per kelvin, which sounds small until it is multiplied by thirty or forty degrees and by twenty modules in series. The array voltage on a clear cold morning, before the current has warmed anything, is the highest voltage the string will ever produce, and it decides how many modules can go in series.

Work it for a 550 W module with Voc of 49.8 V at standard test conditions and a coefficient of −0.28 %/K, at a site minimum temperature of −10 °C. That is 35 K below the 25 °C reference, so the voltage rises by 0.28 % × 35 = 9.8 %, and each module becomes 49.8 × 1.098 = 54.7 V. In a 1000 V DC system the string voltage must stay under 1000 V, so the maximum is 1000 / 54.7 = 18.3 modules, which is 18. In a 1500 V DC system the same calculation gives 1500 / 54.7 = 27.4 modules, which is 27. Half as many strings, half the cable runs, half the combiner inputs, and a lower current for the same power: that is the whole economic case for 1500 V.

• Use the lowest expected ambient temperature at the site, not the average
• If no local record is available, a −10 °C assumption is a common conservative default
• The cable voltage rating must be at least the maximum system voltage: 1.0 kV or 1.5 kV DC
• The inverter's maximum DC input voltage is the other limit on string length, and it often governs before the cable does

Volt drop on the DC side

On the DC side there is no √3 and no reactance to consider, because the cable carries direct current. The drop is simply the resistance of the two conductors, out and back: ΔU = 2 × L × I × R, with L the one-way run length in metres, I the current in amperes and R the resistance in ohms per kilometre. The factor of 2 appears because the current travels the distance twice.

The arithmetic has to be done at the resistance the conductor actually has when it is working, which is not the 20 °C value in the standard. A PV cable operating at 70 °C has a resistance about 20 % higher than at 20 °C, because copper's temperature coefficient is 0.00393 per kelvin and the conductor is 50 K above the reference. Using the 20 °C figure will underestimate the drop by roughly a fifth, which is enough to make a marginal design look acceptable.

Worked example: a 20-module string at 60 m and at 150 m

Take a string of 20 modules, each 550 W with Isc 14.0 A and Imp 13.2 A. The string voltage at maximum power is 20 × 41.8 = 836 V, and the string power is 11 kW. The array is 60 m from the inverter in the first case and 150 m in the second.

Start with the current rating. 1.56 × Isc = 1.56 × 14.0 = 21.8 A. A 4 mm² cable in free air at 60 °C ambient is rated 44 A on these reference figures, so it clears the requirement comfortably. Now the voltage drop at 60 m, using the 70 °C resistance of 6.09 Ω/km: ΔU = 2 × 60 × 13.2 × 6.09 / 1000 = 9.65 V. As a proportion of 836 V that is 1.15 %, so 4 mm² is acceptable on both counts at this length, and the design would normally use 6 mm² for mechanical strength and for the voltage margin on a hot day.

Move the inverter to 150 m and rerun it. With 4 mm²: ΔU = 2 × 150 × 13.2 × 6.09 / 1000 = 24.1 V, which is 2.89 % of 836 V. If the project target is 1.5 % on the DC side, that fails. With 6 mm² the resistance is 4.06 Ω/km and ΔU = 2 × 150 × 13.2 × 4.06 / 1000 = 16.1 V, which is 1.92 %, still above 1.5 %, so it also fails. With 10 mm² the resistance is 2.33 Ω/km and ΔU = 2 × 150 × 13.2 × 2.33 / 1000 = 9.2 V, which is 1.10 %, and that passes. The selected size for the 150 m run is 10 mm², even though the current it carries is only 13.2 A.

• The 150 m string needs 300 m of 10 mm² conductor, which is about 26.7 kg of copper per string
• Raising the number of modules per string reduces the current and the cable size, which is the 1500 V argument again
• A string-level microinverter or optimiser system has a different voltage and current, and the arithmetic changes with it
• The inverter's MPPT voltage range sets the actual voltage the percentage is taken of; use Vmp, not Voc

Temperature and grouping derating on a hot roof

PV cable lives in the worst ambient of any cable in a building: on a dark roof in full sun, in a metal conduit, or under the modules where there is no air movement. The reference ratings below are for a 60 °C ambient, and the on-surface column is for a cable lying on the roof rather than in free air, which is a materially worse heat path. A further factor applies where several strings are bundled together, and inside a conduit on a roof the ambient is higher than the outside air again.

Rerun the 60 m case with the on-surface figures instead. Four string cables grouped and lying on the roof: 4 mm² is rated 30 A on the surface, and with a grouping factor of 0.70 for four touching single-core cables that becomes 21.0 A. The requirement is 21.8 A, so 4 mm² fails, narrowly, and it fails only because the 1.56 rule applies: with the 1.25 × Isc = 17.5 A requirement it would have passed. A 6 mm² cable rated 39 A on the surface gives 39 × 0.70 = 27.3 A and passes. This is the case that shows the two factors doing different work, and it is worth checking both rather than assuming one follows from the other.

Sizing the array cable to the inverter

The array cable from the combiner box to the inverter carries the sum of the strings it collects, and it is sized the same way. Four strings of 13.2 A gives 52.8 A, and with the 1.25 factor the requirement is 66 A. On the reference figures above, a 16 mm² cable in free air at 60 °C is rated 106 A and passes; if it is lying on the roof surface it is 72 A and also passes, but with little margin for a hotter site.

The reason this cable is usually larger than the string cables is not the current alone. The DC side of a PV plant is normally designed for a total voltage drop, DC plus AC, of no more than about 3 %, and the array cable carries all the current of its group over the length that matters. Where the distance from the combiner to the inverter is significant, this single run often decides the whole DC cable cost of the project, and it is the run where moving the inverter closer pays the most.

Cable type, marking and what to check on the drum

The cable for this duty is a single-core, halogen-free, cross-linked cable to EN 50618, designated H1Z2Z2-K, and designated PV1-F under the older TÜV 2 PfG 1169 specification. It is rated for a continuous conductor temperature of 90 °C with a maximum of 120 °C, it is tested for UV and ozone resistance and for water immersion, and the standard sets an expected service life of 25 years. Voltcore's PV cable carries TÜV Rheinland certification, which covers exactly this product range.

On delivery, three checks are quick and worth doing. The marking on the sheath should give the designation, the voltage rating as 1.0 or 1.5 kV DC, the size, the standard and the manufacturer, and it should be legible after handling. The insulation and sheath should be a cross-linked material, which can be verified by the hot set test on a sample if there is any doubt. And the conductor should be tinned: tinned copper is the requirement for this duty, because the cable spends its life hot, damp and in ultraviolet light, and a bare copper conductor in a damp termination will not last as long as the rest of the plant.

• Look for the EN 50618 designation and the H1Z2Z2-K marking on the sheath
• Check the voltage rating: 1.0/1.0 kV DC or 1.5/1.5 kV DC, to match the system
• Confirm tinned copper, Class 5 stranding
• Ask for the UV, ozone and hot set test results with the shipment
• Use stainless steel or UV-resistant cable ties, and do not overtighten them on a hot cable