DC cable sizing: voltage drop, ampacity and commercial cross-section

What DC cable sizing is

Sizing a DC cable is not reading an ampacity table and stopping there: it is finding the cross-section that simultaneously keeps the voltage drop within budget and respects the current-carrying capacity — and then rounding that up to a section the cable is actually made in. In direct current there is no reactance, no power factor and no skin effect to speak of, so the conductor’s pure resistance is the whole story. That resistance is what bleeds voltage along a long run and what dissipates power as heat.

This makes DC sizing deceptively different from AC. On a 48 V photovoltaic feeder or a 24 V battery link, the voltage available is small, the runs are long, and a drop of even one volt is a meaningful fraction of the system voltage. The result is that voltage drop, not heating, almost always governs the section — frequently demanding a conductor several sizes larger than the current alone would suggest.

The two governing criteria

The method sizes the cable against two independent limits and adopts whichever is larger.

1. Voltage drop. The conductor must not waste more than the allowable drop ΔV_target = (drop% / 100)·V. Since current flows out and back, the resistance spans twice the one-way length, and the minimum section is:

S_vd = 2·ρ(T)·L·I / ΔV_target

2. Ampacity (current density). The conductor must carry the design current without overheating. Using a current-density heuristic J_max:

S_amp = I_proj / J_max, with I_proj = k·I

The design current I_proj applies the application factor k — in photovoltaics, k = 1.25 on the short-circuit current per IEC 60364-7-712; for battery and general DC loads, k = 1.0. The governing minimum is S_min = max(S_vd, S_amp), and the adopted conductor is the next standardized IEC section at or above it.

Why resistivity must be corrected for temperature

The resistance of a metal grows with temperature. A cable does not run at the 20 °C of its catalog table — it runs at the regime temperature set by its insulation: 70 °C for PVC, 90 °C for XLPE/EPR. Over that range copper and aluminium gain roughly 20–30 % resistance. The tool corrects it explicitly:

ρ(T) = ρ₂₀·(1 + α·(T − 20))

with ρ₂₀ = 0.0172 Ω·mm²/m for copper (0.0282 for aluminium) and α ≈ 0.00393 /°C (copper) or 0.00403 /°C (aluminium). Skipping this correction makes the predicted voltage drop optimistic — the cable looks fine on paper and underperforms in the heat.

Copper versus aluminium

Aluminium has about 1.6 times the resistivity of copper, so to hold the same voltage drop it needs roughly 1.6 times the cross-section. That penalty is often worth paying on large feeders, where aluminium is lighter and cheaper per ampere. On small runs, however, copper wins: aluminium terminations are prone to creep and oxidation, and the tool flags any aluminium section below 16 mm² as discouraged.

How the method selects and then verifies the section

The calculation runs in a strict order:

1. Resolve the current — used directly, or derived from power as I = P/V when the load is given in watts.
2. Correct the resistivity to the insulation’s regime temperature.
3. Compute S_vd and S_amp from the two criteria and take S_min = max of them. This also identifies the governing criterion (voltage drop or ampacity).
4. Round up to the commercial section in the IEC series (1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150… mm²).
5. Recompute the real values on the adopted section: R = 2·ρ(T)·L/S, the real drop ΔV = R·I (and ΔV%), and the Joule loss P_J = R·I² — also reported as a percentage of the transmitted power P = V·I.

The verification step matters because the commercial round-up almost always lands above the exact minimum, so the real drop comes out below target. The tool also raises a warning when the Joule loss exceeds about 3 % of the transmitted power, since persistent loss is a recurring energy cost over the life of the installation.

Reading the resistance source

The resistance can come from three places, and the tool labels which it used. By default it is computed from ρ(T)/S. If you select a real cable from a catalog (its Rcc at 20 °C plus its section), it uses the datasheet resistance, corrected to the operating temperature — the most accurate path. If you enter only an Rcc value without a section, it treats it as a manual resistance and still verifies the real drop. Whenever a selected cable falls below the computed minimum section, or its real drop exceeds the target, the result flags it as undersized.

Practical sizing considerations

• Always use 2·L: the return conductor doubles the resistive path; this is the single most common DC sizing error.
• Let the drop drive long runs: on 12/24/48 V systems the voltage-drop section usually dwarfs the ampacity section — size for the drop first, then check ampacity.
• Confirm the real Iz: the J_max density is only a screening value; verify the installed ampacity against the datasheet and the IEC 60364-5-52 installation method, grouping and ambient temperature.
• Mind the PV factor placement: the 1.25 factor sizes ampacity (continuous heating), not the voltage-drop section, which uses the actual operating current.
• Watch the Joule budget: keeping P_J under a few percent of the transmitted power protects efficiency and avoids cumulative energy waste.

Following this chain — current, temperature-corrected resistivity, the larger of the voltage-drop and ampacity sections, a commercial round-up and a real-value verification — yields a DC conductor that holds its voltage budget under load and stands up to the field, not just the catalog.