Solar / Renewable Formulas
Solar and renewable formulas size panels, batteries, and inverters against a daily energy budget. These calculators help you balance generation, storage, and load for reliable off-grid power. They are vital for self-sufficient and backup energy systems.
Solar / Renewable Formula Calculators
- Solar Panel Power Output P = G × η × A Solar Irradiance 10 W/m², Panel Efficiency 2.5 %, Panel Area 10 mm² → Power Output = 2.5 µW
- Solar Array Sizing N = E_daily / (G_peak × η × PSH) Daily Energy Need 1 Wh, Panel Peak Power 10 W/m², System Efficiency 5.5 %, Peak Sun Hours 0.1 h → Number of Panels = 18.18
- Battery Bank Sizing Q = (E_daily × days) / (DOD × V) Daily Energy 1 Wh, Days of Autonomy 0.025, Depth of Discharge 5.5 %, Battery Voltage 0.33 V → Battery Capacity = 1.377 Ah
- MPPT Buck Converter Duty Cycle D = 1 − V_mpp / V_oc Voltage at MPP 0.33 V, Open Circuit Voltage 0.726 V → Duty Cycle = 0.5455
- Wind Turbine Power P = 0.5 × ρ × A × v³ × Cp Swept Area 10 mm², Wind Speed 0.01 m/s, Power Coefficient 2.5 % → Power Output = 1.53 × 10⁻⁷ µW
- European Inverter Efficiency η_EU = weighted average of partial-load efficiencies η at 5% load 5.5 %, η at 10% load 11.8 %, η at 20% load 1.18 %, η at 30% load 25 %, η at 50% load 0.55 %, η at 100% load 0.55 → Euro Efficiency = 14.79 %
Worked result for every Solar / Renewable formula
| Formula | Expression | Worked result |
|---|---|---|
| Solar Panel Power Output | P = G × η × A | Solar Irradiance 10 W/m², Panel Efficiency 2.5 %, Panel Area 10 mm² → Power Output = 2.5 µW |
| Solar Array Sizing | N = E_daily / (G_peak × η × PSH) | Daily Energy Need 1 Wh, Panel Peak Power 10 W/m², System Efficiency 5.5 %, Peak Sun Hours 0.1 h → Number of Panels = 18.18 |
| Battery Bank Sizing | Q = (E_daily × days) / (DOD × V) | Daily Energy 1 Wh, Days of Autonomy 0.025, Depth of Discharge 5.5 %, Battery Voltage 0.33 V → Battery Capacity = 1.377 Ah |
| MPPT Buck Converter Duty Cycle | D = 1 − V_mpp / V_oc | Voltage at MPP 0.33 V, Open Circuit Voltage 0.726 V → Duty Cycle = 0.5455 |
| Wind Turbine Power | P = 0.5 × ρ × A × v³ × Cp | Swept Area 10 mm², Wind Speed 0.01 m/s, Power Coefficient 2.5 % → Power Output = 1.53 × 10⁻⁷ µW |
| European Inverter Efficiency | η_EU = weighted average of partial-load efficiencies | η at 5% load 5.5 %, η at 10% load 11.8 %, η at 20% load 1.18 %, η at 30% load 25 %, η at 50% load 0.55 %, η at 100% load 0.55 → Euro Efficiency = 14.79 % |
Variables used across Solar / Renewable formulas
- P — Electrical power output (W)
- G — Solar irradiance (W/m²)
- η — Panel conversion efficiency (0-1 or %)
- A — Panel area (m²)
- N — Number of solar panels required
- E_daily — Daily energy consumption (Wh)
- P_panel — Peak power rating per panel (W)
- PSH — Peak sun hours for the location (hours)
- Q — Required battery capacity (Ah)
- days — Number of days of backup autonomy
- DOD — Maximum depth of discharge (0-1)
- V — Nominal battery bank voltage (V)
- D — Buck converter duty cycle (0-1)
- V_mpp — Panel voltage at maximum power point (V)
- V_oc — Panel open circuit voltage (V)
- v — Wind speed (m/s)
- Cp — Power coefficient (0-0.593, dimensionless)
- η_EU — Weighted European efficiency (0-1 or %)
- η₅ through η₁₀₀ — Efficiency at 5%, 10%, 20%, 30%, 50%, and 100% of rated power
Questions people ask about Solar / Renewable
- Eu solar inverter weighted efficiency calculation formula — European Inverter Efficiency
- What is eu efficiency solar inverter — European Inverter Efficiency
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