Tools › Building Systems › Energy › Solar PV and Battery Sizing › Example
7.2 kW grid-tied solar array at latitude 35° N with a 13.5 kWh backup battery: tilted irradiation, module count, strings, production, payback and LCOE
| Tool | Solar PV and Battery Sizing |
| Source | Dobos, A. P. (2014). PVWatts Version 5 Manual. NREL/TP-6A20-62641, National Renewable Energy Laboratory, Golden, CO (Table 6 and eq. 9, system losses; eq. 8, module model); Sandia National Laboratories (1995). Stand-Alone Photovoltaic Systems: A Handbook of Recommended Design Practices. SAND87-7023, Albuquerque, NM (Point Design No. 8, pp. 200-205, for the stand-alone option); Short, W., Packey, D. J., and Holt, T. (1995). A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies. NREL/TP-462-5173 (levelized cost of energy). |
| Level | Professional |
Problem
An illustrative house at latitude 35° N uses 12,450 kWh a year. Monthly horizontal irradiation runs from 2.9 kWh/m²/day in December to 8.1 in June. Size a south-facing array at a 30° tilt of 400 W modules to produce the whole load, arrange it in strings on a 600 V inverter with two tracker inputs, check a 13.5 kWh battery for a 24-hour outage of a 9 kWh/day critical load, and find the payback, net present value, internal rate of return and levelized cost at 3.00 per watt with a 30 % incentive.
Inputs to Enter
- Latitude 35°, tilt 30°, azimuth 180°; horizontal irradiation 3.2 4.2 5.4 6.8 7.7 8.1 7.5 6.9 5.9 4.7 3.5 2.9 kWh/m²/day; Erbs diffuse share; ground reflectance 0.2; solar constant 1,367 W/m²
- Monthly ambient 2 5 9 13 18 24 26 25 21 14 7 2 °C, record low -15 °C, design high 38 °C, NOCT 45 °C
- Module 400 W, V_oc 37.1 V, V_mp 31.0 V, I_sc 13.8 A, I_mp 12.9 A, -0.27 %/°C on voltage, -0.35 %/°C on power, 1.72 × 1.13 m
- PVWatts default losses (2, 3, 0, 2, 2, 0.5, 1.5, 1, 0, 3 %), inverter efficiency 0.96, DC to AC ratio 1.1; load 1150 980 900 820 900 1150 1350 1300 1050 850 900 1100 kWh, share 100 %
- Inverter: 600 V maximum, tracker window 100 to 550 V, 20 A per input, 2 inputs; battery 13.5 kWh, depth of discharge 0.9, ageing 0.9, round trip 0.9, 5 kW; critical load 3.5 kW peak, 9 kWh/day, 24 h
- 3.00 per W, battery 12,000, incentive 30 %, 0.16 per kWh rising 2.5 %/yr, degradation 0.5 %/yr, O&M 20 per kW-yr rising 2 %/yr, net metering, export 0.05, discount 5 %, 25 years, replacement 2,000 in year 13
Answers
- Irradiation on the array 4.78 (December) to 7.17 (June) kWh/m²/day, 2,285 kWh/m² a year against 2,034 horizontal; best fixed tilt 31° for the year, 52° for the poorest month
- System loss 14.08 % (the PVWatts 14 %); specific yield 1,798.3 kWh/kW; required 6.923 kW, 18 modules, 7.200 kW DC, 6.545 kW AC inverter, 34.98 m²
- Production 12,948 kWh/yr (104.0 % of the load), performance ratio 0.7868, capacity factor 20.53 % on the DC rating
- Strings: V_oc 41.11 V at -15 °C, longest 14; V_mp 27.30 V at the 69.25 °C hot cell, shortest 4; 2 strings of 9 modules; string current 17.25 A, conductor ampacity 21.56 A
- Battery delivers 10.37 kWh against 9.00 needed (27.66 h); 5 kW against the 3.5 kW peak
- Installed cost 33,600.00, after the incentive 23,520.00; year-1 saving 1,872.88; simple payback 12.6 years; NPV 8,280.81; IRR 7.976 %; LCOE 0.1554 per kWh (simple form 0.1400)
Notes
The tool's default inputs are this case; press Submit. The site, module, battery and costs are illustrative (stated on the method page), not a published example. The method is checked by test_solar_pv_battery_sizing.php (4,461 checks) against the Sandia handbook's residential and beacon worksheets, the PVWatts loss table, the NREL Solar Position Algorithm example, the NREL levelized-cost examples and an independent numpy / scipy implementation (References/Solar-PV/checks/). Choosing the stand-alone system with the handbook's module (3.0 A, 15.9 V, 14.4 V hot) reproduces Point Design No. 8: 72.9 and 82.7 Ah/day, 17.5 A, 709 Ah, 8 batteries, 12 modules.