Useful Formulas for Off-Grid PV Systems with Practical Examples

Описание: 1. Solar Panel Output Power (P = V × I)
Formula: P=V×I
Where:
P = Power output (Watts)
V = Voltage (Volts)
I = Current (Amperes)

Example: A solar panel operates at 18 V and produces 8 A of current.
The output power is: P=18 V×8 A=144 WP

2. Energy Consumption Estimation (E = P × t)
Formula: E=P×tE
Where:
E = Energy consumption (Wh)
P = Power (Watts)
t = Time of usage (hours)

Example: A 100 W light bulb is used for 5 hours. The energy consumed is:
E=100 W×5 h=500 Wh

3. Battery Capacity (C = E / V)
Formula: C=E/V
Where:
C = Battery capacity (Ah)
E = Energy storage required (Wh)
V = Battery voltage (Volts)

Example: To store 5000 Wh with a 12 V battery, the capacity needed is:
C = 5000 Wh/12 V = 416.67 Ah

4. Daily Solar Energy Production (E = P × H × η)
Formula: E=P×H×η
Where:
E = Energy produced (Wh)
P = Panel power (Watts)
H = Solar hours per day (hours)
η = System efficiency (decimal)

Example: A 300 W panel operates for 5 solar hours per day at 85% efficiency:
E=300 W×5 h×0.85 = 1275 Wh/day

5. Number of Panels Needed (N = E / (P × H × η))
Formula: N=(E)/(P×H×η)

Where:
N = Number of panels
E = Total energy demand (Wh)

Example: For a 5000 Wh daily demand with 300 W panels, 5 solar hours, and 85% efficiency: N=5000/(300×5×0.85)= 4 panels

6. Inverter Sizing (P_inv = P_load × SF)
Formula: P(inv)=P(load)×SF
Where:
P(inv) = Inverter power (Watts)
P(load) = Total load power (Watts)
SF= Safety factor (typically 1.25)

Example: For a load of 2000 W: P(inv)=2000 W×1.25 = 2500 WP

7. Charge Controller Current (I_cc = P / V)
Formula: I(cc) = P/V
Where: Icc​ = Charge controller current (Amps)

Example: A 500 W panel system with 12 V batteries requires:
Icc=500/12=41.67 A / A 60 A controller is recommended.

8. System Efficiency (η = E_out / E_in × 100)
Formula: η=[E(out)/E(in)]×100
Where:
E(out) = Useful energy output (Wh)
E(in)= Total energy input (Wh)

Example: If the system receives 1500 Wh but outputs 1275 Wh:
η=(1275/1500)×100 = 85%

9. Peak Sun Hours (H = E / P)
Formula: H=E/P
Where: H = Peak sun hours (hours)

Example: If a 200 W panel produces 1000 Wh in a day:
H=1000/200=5 hours

10. Total System Cost (Cost = (P × Price_per_W) + Battery_Cost + Inverter_Cost)
Formula: Break the costs into components.

Example: For a 5 kW system:
Panel cost: 5000 W×0.5 USD/W=2500 USD
Battery cost: 3000 USD
Inverter cost: 1500 USD
Total: 2500+3000+1500=7000 USD

These formulas and examples provide a practical toolkit for designing and analyzing off-grid PV systems. Let me know if you’d like further clarification on any of these!

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