PV system design — modules, strings, NEC 690 / 705 sizing

Reference notes

PV system design integrates module electrical parameters, string sizing constraints, inverter selection, code compliance (NEC Articles 690 and 705), and economic optimization. The central design decisions are string sizing (limited by V_oc at coldest temperature per NEC 690.7) and interconnection (limited by the 120% rule per NEC 705.12).

System architectures

Module electrical parameters (STC)

• STC = Standard Test Conditions: 1000 W/m² irradiance, 25 °C cell temperature, AM 1.5 spectrum.
• V_oc — open-circuit voltage. Typical 35-50 V for 60-cell silicon module.
• I_sc — short-circuit current. Typical 9-11 A.
• V_mpp — voltage at maximum power point. 30-40 V.
• I_mpp — current at MPP. 8-10 A.
• P_mpp = V_mpp × I_mpp = 250-450 W per 60-cell module.
• NOCT — Nominal Operating Cell Temperature, typically 45 °C.

Temperature coefficients

• V_oc T-coefficient: typically −0.30%/°C for silicon. V_oc INCREASES at low temperature, DECREASES at high.
• I_sc T-coefficient: +0.05%/°C. Small effect.
• P_max T-coefficient: −0.35 to −0.45%/°C. Hot panels produce LESS power.
• Operating reality: on a hot summer day, cell temperature reaches 65-75 °C (35-50 °C above ambient); output drops 10-25% from STC.
• Winter morning cold temperature with full sun causes V_oc to rise 10-15% above STC — drives MAX STRING SIZE design.

String sizing — NEC 690.7

• Max string V_oc at coldest expected temperature must NOT exceed inverter / system DC voltage rating.
• Typical max DC: 600 V residential / light commercial; 1000-1500 V utility-scale.
• Coldest temperature per NEC 690.7(B): ASHRAE 2% design low temperature for the site (statistically only 2% of years colder).
• Max modules per string = floor(V_DC_max / V_oc_cold).
• Example: V_oc_STC = 40 V, T_coeff = −0.30%/°C, T_cold = −30 °C → V_oc_cold = 46.6 V. 600 V max → 12 modules max per string.

Minimum string voltage — inverter MPPT range

• String V_mpp at HOTTEST operating temperature must stay within inverter MPPT window.
• If string voltage falls below MPPT minimum, the inverter cannot operate at MPP — energy lost.
• Typical residential string inverter MPPT range: 200-600 V; commercial 250-800 V.
• Min modules per string = ceil(V_MPPT_min / V_mpp_hot).

Current sizing — NEC 690.8

• Conductor: PV-wire (USE-2 / RHW-2), 90 °C wet, sunlight resistant.
• 10 AWG PV-wire ampacity 35 A → handles most module strings (I_sc 10-12 A).
• String OCPD: 15-30 A typical (per 690.9).

Other NEC 690 requirements

AC interconnection — NEC 705.12 120% rule

• Example: 200 A bus + 200 A main → max PV breaker = 0.20 × 200 = 40 A.
• For larger PV: downsize main breaker, load-side tap, or supply-side connection (NEC 230.40).
• Rationale: PV + utility both feed fault current into the busbar; total must not exceed busbar rating with safety margin.

Inverter standards — UL 1741 & IEEE 1547

• Anti-islanding: detect grid de-energization and cease energizing within 2 seconds.
• Voltage ride-through: must remain connected during sags as deep as 0.45 pu for 0.16 s.
• Frequency ride-through: 57.5-61.5 Hz range.
• Smart inverter functions: volt-VAR support, volt-watt curtailment, fixed power factor (IEEE 1547-2018).

Energy yield calculation

• Sun-hours: equivalent hours at STC irradiance per day.
  • Boston: ~4 hr/day
  • Atlanta: ~5 hr/day
  • Phoenix: ~6.5 hr/day
  • Mojave Desert: ~7 hr/day
• Performance Ratio (PR): 75-85% typical. Accounts for soiling, mismatch, temperature, inverter losses, wiring.
• Capacity factor: annual energy / (nameplate × 8760 hr).
  • Northern climates: 12-16%
  • Mid-latitude: 16-20%
  • Southwest US: 20-28%
  • Single-axis tracker in Mojave: up to 32%
• Degradation: 0.5-0.7%/year. After 25 years: 85-90% of initial output.

Economics

• Installed cost (2024):
  • Utility-scale: $1.0-1.5/W DC
  • Commercial: $1.5-2.5/W
  • Residential: $2.5-4.0/W
• Federal Investment Tax Credit (ITC) per IRS Section 48: 30% for solar (extended through 2032 by Inflation Reduction Act 2022). Adders for domestic content (10%), energy-community deployment (10%), low-income (10-20%).
• Net metering rules vary by state; some states moving to value-of-solar or time-of-use export rates.
• Power Purchase Agreement (PPA): developer owns + operates, customer pays per kWh delivered over 20-25 years. Common for commercial and utility-scale.
• LCOE 2024 (Lazard 17.0 estimates):
  • Utility-scale: $30-60/MWh (lowest in southwest US)
  • Commercial rooftop: $60-120/MWh
  • Residential rooftop: $100-200/MWh (effective $70-140 with ITC)
  • Solar + 4-hr storage: adds $15-50/MWh

Module technology trends

• Mono-PERC — passivated emitter rear contact monocrystalline silicon. 20-22% efficiency. Dominant 2018-2023.
• TOPCon — tunnel oxide passivated contact. 22-24% efficiency. Replacing PERC since 2023.
• HJT — heterojunction with intrinsic thin layer. 23-25% efficiency. Higher cost.
• Bifacial modules — capture rear-side irradiance, +5-15% energy yield with ground reflectivity. Common in utility-scale.
• Tandem perovskite-silicon — emerging. Lab efficiency 33%+; commercial 2025-2027 expected.