Solar PV array and storage sizing

Introduction

A stand-alone solar system has to collect each day, in the worst month, at least the energy its loads consume, and store enough to ride through the cloudy days in between. The sizing method used by the IEEE and Sandia guides is an energy balance: daily load divided by the peak sun hours of the design month and by the system losses gives the array power; daily load times days of autonomy divided by the depth of discharge gives the battery; the controller and inverter follow from the currents. This calculator applies it, picks the module count for the chosen string configuration, checks the string voltage in the cold, and tells you how fast the bank recovers after a dark spell.

It is for engineers and technicians specifying off-grid power for navigation aids, remote sensors, small vessels, cabins and telecom sites, and for students of renewable energy.

Formulas

P_array = E_day / (PSH × η_sys) × (1 + margin)
modules = strings × N_series,   strings = ceil(P_array / (N_series P_module))
E_yield = P_installed × PSH × η_sys
V_oc,cold = N_series V_oc (1 + 0.003 (25 − T_min))  ≤ V_controller,max
I_controller = P_installed / V_bat × 1.25   (MPPT)   or   strings × I_sc × 1.25   (PWM)
C_bank = E_day × days / (DoD × η_inverter),   Ah = C_bank / V_bat,   usable = C_bank × DoD
I_charge,avg = E_yield / PSH / V_bat,   recharge days = usable / (E_yield − E_day)
P_inverter = P_peak × 1.25,   I_DC = P_peak / (η_inv V_bat)

Typical values: η_sys 0.70–0.80; DoD 50 % lead-acid, 80 % LiFePO4; autonomy 2–3 days (5+ for critical loads); PSH from the site's irradiation data for the array tilt.

Assumptions and limitations

• One lumped system efficiency covers temperature, soiling, mismatch, wiring, controller, battery round-trip and inverter losses; the battery sizing divides by the inverter efficiency only, and the recharge estimate uses the surplus of yield over load without applying the losses again.
• The design month is the lowest-PSH month for the load; summer surplus is curtailed.
• Battery temperature derating, ageing and Peukert behaviour are not modelled beyond the user's margin; surge loads only through the peak load entered.
• Module data at STC; the V_oc temperature coefficient is a typical −0.3 %/K.

Worked example

A cabin consuming 8.5 kWh/day with a 3 kW peak, design-month irradiation 4.8 kWh/m²/day, system efficiency 75 %, 400 W modules (V_oc 49 V, I_sc 10.5 A) in strings of two, 48 V LiFePO4 bank, 2 days of autonomy, inverter 92 %, controller limit 150 V, coldest module temperature −5 °C.

1. Array: 8 500/(4.8 × 0.75) = 2 361 W (the published example's 2.36 kW); strings of 800 W → 3 strings, 6 modules, 2.4 kW installed; yield 2.4 × 4.8 × 0.75 = 8.64 kWh/day, 102 % of the load.
2. String voltage at −5 °C: 2 × 49 × 1.09 = 107 V, within 150 V.
3. MPPT controller: 2 400/48 × 1.25 = 62.5 A (a PWM controller would need 3 × 10.5 × 1.25 = 39 A but waste the voltage headroom).
4. Battery: 8 500 × 2/(0.8 × 0.92) = 23.1 kWh = 481 Ah at 48 V, 18.5 kWh usable. Average charge current 37.5 A, 0.078 C.
5. Inverter 3.75 kW, 68 A DC at peak. At this 102 % balance only 140 Wh/day is left over after the load, so recharging the bank from 80 % DoD would take about 130 days; a 15 % margin (8 modules, 3.2 kW) brings it to 6 days and 50 % to 3 days, which is why an array margin or a backup generator is the practical choice.

FAQ

Related calculators

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