Worked Example: PV String Sizing and Protection for a 500 kWp Commercial Rooftop — The Walmart Yuba City Fire

In 2019, a 1.2 MW rooftop solar installation at a Walmart distribution centre in Yuba City, California caught fire. The fire originated in a string combiner box where a DC series arc fault developed at a deteriorated MC4 connector. The high-resistance joint generated enough heat to ignite the surrounding wiring and enclosure, spreading fire to the roof membrane and causing approximately US$2.4 million in damage — destroying 30% of the array and requiring extensive structural repairs.

Investigation by the California State Fire Marshal found multiple protection deficiencies. String overcurrent protection fuses were rated below the NEC 690.9 required minimum of 1.56 × I_sc, leaving them susceptible to nuisance tripping during high-irradiance events while still not protecting against sustained arcing faults. String conductors used connectors that had degraded from UV exposure and thermal cycling over several years, creating the high-resistance joints that initiated the arc. Critically, the system predated the NEC 690.11 requirement for DC arc-fault circuit interrupters (AFCI), meaning there was no rapid detection of the series arc fault before it escalated to fire.

This incident — one of several Walmart rooftop solar fires that led the company to temporarily halt new installations — underscores why PV string sizing is not simply a matter of matching module voltages to the inverter. Overcurrent protection, cable sizing, connector integrity, and arc fault detection all form an integrated protection system. A failure in any single element can lead to catastrophic consequences.

Design the PV string configuration, overcurrent protection, and DC cable sizing for a 500 kWp commercial rooftop solar installation.

PV module open-circuit voltage increases as temperature decreases. The maximum system voltage occurs at the coldest expected temperature and determines the maximum number of modules per string, per NEC 690.7(A).

Temperature difference from STC (25°C):

ΔT = T_min − T_STC = −5 − 25 = −30°C

Temperature-corrected V_oc per module:

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

V_oc,max = 49.8 × (1 + (−30 × −0.27 / 100))

V_oc,max = 49.8 × (1 + 0.081)

V_oc,max = 53.83 V per module

Maximum modules per string (limited by inverter maximum voltage 1,100 V):

N_max = floor(V_DC,max / V_oc,max) = floor(1,100 / 53.83) = 20 modules — (Eq. 2)

The minimum string voltage at the hottest cell temperature must remain above the inverter’s MPPT minimum voltage. At maximum cell temperature, V_mpp drops:

ΔT = T_max − T_STC = 75 − 25 = +50°C

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

V_mpp,min = 41.7 × (1 + (50 × −0.27 / 100))

V_mpp,min = 41.7 × (1 − 0.135)

V_mpp,min = 36.07 V per module

Minimum modules per string (to stay above MPPT minimum of 550 V):

N_min = ceil(V_MPPT,min / V_mpp,min) = ceil(550 / 36.07) = 16 modules — (Eq. 4)

With 500 Wp modules and 500 kWp target capacity:

N_modules = 500,000 / 500 = 1,000 modules

N_strings = 1,000 / 18 = 55.6 → 56 strings (rounded up)

Actual system capacity: 56 × 18 × 500 = 504 kWp

String electrical parameters at STC:

NEC 690.9(B) requires that string overcurrent protective devices (OCPDs) be rated at not less than 1.56 × I_sc. This factor combines two requirements: the 1.25 continuous current multiplier and the 1.25 irradiance correction factor (1.25 × 1.25 = 1.5625, rounded to 1.56).

I_OCPD,min = I_sc × 1.56 — (Eq. 5)

I_OCPD,min = 13.15 × 1.56 = 20.5 A

The OCPD must also not exceed the module’s maximum series fuse rating (specified on the module datasheet, typically 20 A or 25 A for modules with I_sc around 13 A). For this module with a 25 A maximum series fuse rating:

20.5 A ≤ I_fuse ≤ 25 A

Selected: 25 A gPV fuse (DC-rated PV fuse per IEC 60269-6), 1,100 V DC rated.

String DC cables must be sized per NEC 690.8(A) for the maximum circuit current, which includes the continuous current and irradiance correction factors:

I_max = I_sc × 1.25 × 1.25 = I_sc × 1.56 — (Eq. 6)

I_max = 13.15 × 1.56 = 20.5 A

The cable ampacity after derating must be at least 20.5 A. Apply derating for rooftop installation (direct sun exposure on dark roof surface):

Temperature correction: Cable on roof surface reaches 75°C ambient. For PV wire (90°C rated), from NEC Table 310.15(B)(1):

C_temp = 0.58 (75°C ambient, 90°C cable)

I_required = 20.5 / 0.58 = 35.3 A — (Eq. 7)

From NEC Table 310.16, for USE-2/PV wire (90°C wet), copper:

Selected string cable: 8 AWG (8.37 mm²) USE-2/PV wire, 1,000 V DC rated.

Calculate voltage drop from the furthest string to the inverter (45 m string cable + 80 m home run = 125 m total, but string and home run are different cable sizes):

String cable voltage drop (8 AWG, 45 m, 12.0 A at MPP):

Resistance of 8 AWG copper at 75°C: 2.551 Ω/km (per NEC Chapter 9, Table 8):

ΔV_string = 2 × I_mpp × R × L / 1000 — (Eq. 8)

ΔV_string = 2 × 12.0 × 2.551 × 45 / 1000 = 2.76 V

Home run cable voltage drop (assume 4 AWG / 25 mm² for combiner-to-inverter, carrying 8 strings × 12.0 A = 96 A, 80 m):

Resistance of 4 AWG copper at 75°C: 1.020 Ω/km:

ΔV_homerun = 2 × 96 × 1.020 × 80 / 1000 = 15.67 V

Total DC voltage drop:

ΔV_total = 2.76 + 15.67 = 18.43 V

ΔV% = 18.43 / 750.6 × 100 = 2.45%

Industry best practice recommends ≤ 2% DC voltage drop for maximum energy harvest. At 2.45%, this design would benefit from upsizing the home run cable to 2 AWG (33.6 mm²), which would reduce the total drop to approximately 1.8%.

String combiner boxes consolidate multiple strings into a single home run cable. For 7 combiner boxes serving 8 strings each (56 strings total):

Combiner box ratings:

Arc fault detection per NEC 690.11:

Since NEC 2011, DC arc-fault circuit interrupters (AFCIs) are required for PV systems on buildings. The AFCI must detect series arcs (high-impedance faults at degraded connectors) and parallel arcs (insulation failure between conductors), and de-energise the faulted string within 2 seconds.

For this 500 kWp system, the string inverters incorporate integrated AFCI per UL 1699B, eliminating the need for external AFCI devices. The inverter monitors each string’s current waveform for the high-frequency noise signature characteristic of DC arcs (typically 1–100 kHz broadband noise superimposed on the DC current).

Design summary: 56 strings of 18 × 500 Wp modules (504 kWp), 25 A gPV fuses, 8 AWG USE-2 string cables, 7 combiner boxes, inverter-integrated AFCI.

The critical design factors are the temperature-corrected voltage window (which limits string length to 16–20 modules) and the NEC 690.9 overcurrent factor of 1.56 (which drives both fuse and cable sizing above naive calculations based on STC current alone).

The Walmart Yuba City fire was caused by a combination of undersized overcurrent protection, degraded connectors, and lack of arc fault detection. The engineering lessons:

• Size string fuses per NEC 690.9 (1.56 × I_sc) — fuses must accommodate the 125% continuous load factor and 125% irradiance correction; undersized fuses lead to nuisance tripping and dangerous field bypassing
• Require DC AFCI per NEC 690.11 — arc-fault circuit interrupters detect the high-frequency signature of series arcs at degraded connectors and de-energise the string within seconds, preventing thermal escalation to fire
• Specify quality MC4 connectors with UV-rated housings — connector degradation from UV exposure and thermal cycling creates the high-resistance joints that initiate arc faults; connectors should be inspected with infrared thermography during annual maintenance
• Apply temperature corrections for both voltage and current — STC ratings at 25°C do not represent field conditions; module cell temperatures of 65–80°C on rooftops significantly affect both string voltage (lower, affecting MPPT tracking) and short-circuit current (slightly higher, affecting fuse sizing)
• Minimise DC voltage drop for energy yield — every 1% voltage drop in the DC system represents approximately 1% energy loss over the system’s 25-year life; investing in slightly larger cables yields significant lifetime return