The sizing math

Every number in your build comes from this deterministic chain (docs/03 Part A). Same inputs → same build.

1. Loads → daily energy

E_day_AC = your preset + the delta of each load you add. Peak = the largest motor surge plus everything else running at that moment.

2. Battery bank

E_bank = E_day_DC × autonomy days ÷ (80% depth × 95% round-trip). We design LiFePO4 to 80% depth to protect cycle life (3,000–6,000 cycles), then snap to whole modules.

3. Solar array

Array W = E_day_DC ÷ (design sun-hours × 0.75 system losses). Year-round off-grid designs on your December worst-month; grid-tied hybrids on the annual average because the grid tops up winter.

4. Charge controller — the cold-Voc check

Panel voltage rises in the cold. We keep the cold-corrected string voltage under your controller’s limit, per NEC 690.7 — the #1 way DIYers fry an MPPT. String length is designed against your actual inverter’s MPPT window and your ZIP’s record low.

5. Wire & fuse

Cable gauge and fuse size use the NEC 125% continuous-duty factors; LiFePO4 banks get a Class-T main fuse for their high short-circuit current.