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Appendix B: Formula & Constant Quick-Reference

Constants

  • Solar constant (extraterrestrial): ≈1,361 W/m² [Ch 2]
  • Surface peak irradiance / STC: 1,000 W/m² at 25 °C, AM1.5 [Ch 2, 4]
  • Hours per year: 8,760

Electrical fundamentals [Ch 1]

  • Ohm’s law: V = I × R
  • Power: P = V × I = I²R = V²/R
  • Energy: E = P × t (kWh = kW × h)
  • Series: voltages add. Parallel: currents add.

Solar resource [Ch 2]

  • Peak Sun Hours (PSH) = daily insolation (kWh/m²/day)

Array sizing [Ch 14]

  • Daily energy: kWh ≈ Array kW × PSH × Derate
  • Array size: Array kW = Target annual kWh ÷ (PSH × 365 × Derate)
  • Derate: ~0.83 (PVWatts default), 0.77 (conservative), 0.86 (DC-only)
  • Specific yield = annual kWh ÷ kW(DC) (~1,100–1,800 kWh/kWp)
  • Capacity factor = annual kWh ÷ (kW × 8,760)

Module / string [Ch 4, 15]

  • Pmax = Vmp × Imp
  • Cold Voc: Voc(cold) = Voc(STC) × [1 + β(Voc) × (T_min − 25 °C)] (β negative)
  • Hot Vmp: Vmp(hot) = Vmp(STC) × [1 + coeff × (T_cell,max − 25 °C)]
  • Max modules/string = Inverter max DC voltage ÷ Voc(cold) → round down
  • Min modules/string = MPPT minimum voltage ÷ Vmp(hot) → round up

Conductor / OCPD: NEC 690.8/690.9 [Ch 16]

  • Max current: I = Σ Isc × 1.25 (irradiance factor)
  • Min ampacity / OCPD: × 1.25 (continuous) → 1.56 × Isc overall, then apply temperature + conduit-fill derating
  • Interconnection (705.12) 120% rule: Main breaker + PV breaker ≤ 1.20 × busbar rating

Battery [Ch 17]

  • Nameplate kWh = (Critical load kWh × Duration) ÷ (DoD × Round-trip efficiency)
  • Usable kWh = Nameplate × DoD

Commissioning [Ch 33]

  • Expected string Voc = Voc(STC) × [1 + β(T_cell − 25 °C)] × N modules
  • Typical acceptance tolerance: ~±5% Voc, ±10% Isc (irradiance/temp corrected)
  • Performance Ratio = Actual energy ÷ Weather-expected energy