Worked Example: Solar PV String Cable — 10 kW Rooftop Inverter

This example reveals a surprising asymmetry: on the DC side, the concern is voltage RISE at low temperature (which can destroy the inverter), while on the AC side, the concern is voltage RISE at the point of supply connection (which can push the grid voltage above statutory limits). Different standards set different limits and measure in different directions.

Maximum string length (cold temperature limit):

At minimum ambient temperature, module V_oc increases. The temperature correction must use ambient temperature minus a small offset because V_oc is measured at cell temperature, but at minimum temperature and no irradiance, cell temperature approximately equals ambient temperature.

ΔT = T_min − T_STC = −2 − 25 = −27°C

V_oc,max = V_oc,STC × (1 + (ΔT × TK_Voc / 100)) — (Eq. 1)

V_oc,max = 37.2 × (1 + (−27 × −0.25 / 100))

V_oc,max = 37.2 × (1 + 0.0675)

V_oc,max = 39.71 V per module

Maximum modules per string (AS/NZS 5033, Cl. 4.3.3.3, max system voltage 600 V for residential):

N_max = floor(600 / 39.71) = 15 modules — (Eq. 2)

ΔT = 0 − 25 = −25°C

V_oc,max = 37.2 × (1 + (−25 × −0.25 / 100))

V_oc,max = 37.2 × 1.0625

V_oc,max = 39.53 V per module

NEC 690.7(A) maximum system voltage for residential = 600 V:

N_max = floor(600 / 39.53) = 15 modules

At maximum cell temperature, V_mpp drops. The string must stay above the inverter’s MPPT minimum.

ΔT = T_cell,max − T_STC = 75 − 25 = +50°C

V_mpp,min = V_mpp,STC × (1 + (ΔT × TK_Voc / 100)) — (Eq. 3)

V_mpp,min = 31.4 × (1 + (50 × −0.25 / 100))

V_mpp,min = 31.4 × 0.875

V_mpp,min = 27.48 V per module

Minimum modules per string (MPPT minimum = 150 V):

N_min = ceil(150 / 27.48) = 6 modules — (Eq. 4)

With 400 Wp modules and 10 kWp target: 10,000 / 400 = 25 modules total.

Select 2 strings of 13 modules (total 26 modules = 10.4 kWp).

Voltage checks:

AS/NZS 5033:2021 (Clause 3.3.4):

AS/NZS 5033 requires cable ampacity to be at least 1.25 × I_sc for the string:

I_cable,min = 1.25 × I_sc = 1.25 × 13.96 = 17.45 A — (Eq. 5a)

Temperature derating for cable on roof surface (AS/NZS 5033 Table 3.2, cable in contact with roof, 75°C ambient, 90°C rated cable):

C_temp = 0.58

Required tabulated ampacity:

I_z = 17.45 / 0.58 = 30.1 A — (Eq. 6a)

From AS/NZS 5033 Table 3.3 (solar DC cable, 90°C, copper, single-core on roof):

Selected: 4 mm² DC solar cable (TUV-certified, double-insulated, per AS/NZS 5033 Cl. 3.3.3).

NEC requires the maximum circuit current to include both the continuous load factor (1.25) and the irradiance correction (1.25):

I_cable,min = I_sc × 1.25 × 1.25 = I_sc × 1.56 = 13.96 × 1.56 = 21.78 A — (Eq. 5b)

Temperature correction from NEC Table 310.15(B)(1), 75°C ambient, 90°C cable:

C_temp = 0.58

Required ampacity:

I_z = 21.78 / 0.58 = 37.6 A — (Eq. 6b)

From NEC Table 310.16, 90°C column:

Selected: 8 AWG (8.37 mm²) USE-2/PV wire.

IEC 62548 requires cable ampacity to be at least 1.25 × I_sc (similar to AS/NZS):

I_cable,min = 1.25 × 13.96 = 17.45 A — (Eq. 5c)

With same derating:

I_z = 17.45 / 0.58 = 30.1 A — (Eq. 6c)

Selected: 4 mm² DC solar cable (same as AS/NZS).

In a PV system, current flows FROM the array TO the inverter. Voltage is highest at the array and drops toward the inverter. This is technically a voltage DROP from source to load. However, the key performance metric is energy harvest: every volt lost in the cable reduces the power delivered to the inverter.

ΔV_DC = 2 × I_mpp × R × L / 1000 — (Eq. 7)

Where the factor of 2 accounts for positive and negative conductors, and R is resistance per km at operating temperature.

4 mm², 25 m, 12.74 A (AS/NZS and IEC):

Resistance of 4 mm² copper at 70°C: 5.36 Ω/km (from AS/NZS 5033, Table 3.4):

ΔV_DC = 2 × 12.74 × 5.36 × 25 / 1000 = 3.41 V

ΔV_DC% = 3.41 / 408.2 × 100 = 0.84%

8 AWG (8.37 mm²), 25 m, 12.74 A (NEC):

Resistance of 8 AWG at 70°C: 2.551 Ω/km:

ΔV_DC = 2 × 12.74 × 2.551 × 25 / 1000 = 1.63 V

ΔV_DC% = 1.63 / 408.2 × 100 = 0.40%

The inverter feeds power back to the grid through the main switchboard. On the AC side, the direction of power flow reverses the voltage gradient: the inverter terminal voltage is HIGHER than the grid voltage at the MSB during export. This creates a voltage rise at the inverter terminals relative to the point of supply.

Calculate AC output current:

I_AC = P_inverter / (V × PF) = 10,000 / (230 × 1.0) = 43.5 A — (Eq. 8)

(Grid-tied inverters operate at unity power factor by default.)

AS/NZS 4777.1, Clause 3.3.4 specifies that the voltage rise from the inverter to the point of supply connection must not exceed 2% of nominal voltage (230 V). This is a stringent limit designed to prevent the supply voltage from exceeding the +10% statutory maximum of 253 V.

For a 30 m AC cable run at 43.5 A (single-phase), the cable must limit voltage rise to:

ΔV_max = 0.02 × 230 = 4.60 V — (Eq. 9)

Required maximum cable impedance:

Z_max = ΔV_max / (2 × I_AC) = 4.60 / (2 × 43.5) = 0.0529 Ω — (Eq. 10)

Required maximum resistance per metre:

r_max = Z_max / L = 0.0529 / 30 = 1.763 mΩ/m

From AS/NZS 3008 Table 35, the cable size where r ≤ 1.763 mΩ/m:

Selected: 16 mm² (voltage rise governs).

But check current capacity: the 50 A MCB protecting this circuit requires the cable to carry at least 50 A after derating. For 16 mm² TPS on tray at 35°C ambient:

From AS/NZS 3008 Table 13, 16 mm² on tray: 76 A. Derating for 35°C ambient: k₁ = 1.04 (below 40°C reference). Derated capacity: 76 × 1.04 = 79 A. Exceeds 50 A. PASS.

BS 7671 and IEC 60364-7-712 do not specify a dedicated voltage rise limit for PV inverters. Instead, the general voltage drop limit of 3–5% applies, interpreted as voltage rise for generation sources. The Engineering Recommendation G98 (UK) limits voltage rise to 1% at the connection point for systems up to 16 A/phase, but for a 43.5 A inverter, the designer typically uses the 2% rise limit from G99.

With a 2% limit (same as AS/NZS): 16 mm² selected (same result).

With a relaxed 3% limit (if applying IEC general limit):

ΔV_max = 0.03 × 230 = 6.90 V

r_max = 6.90 / (2 × 43.5 × 30) = 2.644 mΩ/m

10 mm² cable (r = 2.19 mΩ/m) would pass: 10 mm² selected.

NEC does not specify an explicit voltage rise limit for grid-connected inverters. NEC 210.19 and 215.2 provide informational notes suggesting 3% for branch circuits and 5% total. For PV AC output cables, the standard practice is to limit voltage rise to 2% per NEC 690 best practice (not a code requirement but an engineering recommendation from IEEE 1547).

With 2% limit: same calculation as above, 16 mm² equivalent = 6 AWG (13.3 mm²) selected.

However, NEC 690.8(A)(1)(2) requires the AC cable ampacity to be at least 1.25 × maximum inverter output current (continuous load rule):

I_cable = 1.25 × 43.5 = 54.4 A

From NEC Table 310.16, 90°C column:

NEC selected: 4 AWG (21.2 mm²) for AC output cable.

Here is the critical insight that confuses many solar installers:

The AC voltage rise limit is the more consequential constraint because exceeding it triggers the inverter’s anti-islanding protection. When the grid voltage at the inverter connection point rises above the statutory maximum (typically 253–264 V depending on jurisdiction), the inverter must disconnect within 1–2 seconds per AS/NZS 4777.2 Table 2 / IEEE 1547 Table 4. In areas with already-high grid voltage (common in rural Australia where long distribution feeders have rising voltage profiles), even a 2% rise can push the supply above 253 V, causing nuisance tripping and lost generation.

The key finding in solar PV cable sizing is that voltage rise on the AC side, not voltage drop on the DC side, is the governing constraint for most residential installations — and the standards disagree on how strict this limit should be.

Under AS/NZS 4777.1, the 2% mandatory voltage rise limit on the AC side forces a 16 mm² cable for a mere 30 m run, even though the 43.5 A current could be carried by 6 mm² on thermal grounds alone. The cable is nearly three times the size that current capacity alone would require.

Meanwhile, on the DC side, the NEC 1.56 factor forces 8 AWG (8.37 mm²) where AS/NZS and IEC allow 4 mm² — more than double the copper. But the irony is that the NEC’s larger DC cable has lower voltage drop (0.40% vs 0.84%), which means marginally more energy harvested over the system’s 25-year life. Whether this extra copper pays for itself through increased energy yield depends on the local electricity price and solar irradiance — in most cases, the payback on the extra DC copper under NEC is approximately 8–12 years.

The deepest surprise is directional: solar engineers trained on load circuits think “voltage drop” but must think “voltage rise” on the AC side. A cable that is perfectly adequate for carrying current can cause the inverter to trip repeatedly if the resulting voltage rise pushes the grid connection above statutory limits. This is not a theoretical problem — it is the single most common cause of solar inverter nuisance tripping in Australian residential installations, particularly in rural areas with already-elevated grid voltage.