# Calculation Formula of Photovoltaic Power Generation System

## Calculation Formula of Photovoltaic Power Generation System

1. Conversion efficiency

η= Pm (peak power of cell)/A (area of cell)×Pin (incident light power per unit area)

Where: Pin=1KW/㎡=100mW/cm².

2. Charging voltage

Vmax=V amount×1.43 times

3. Battery modules connected in series and parallel

3.1 The number of battery modules connected in parallel = the average daily power consumption of the load (Ah) / the average daily power generation of the modules (Ah)

3.2 Number of battery components in series = system operating voltage (V) × coefficient 1.43/component peak operating voltage (V)

4. Battery capacity

Battery capacity = load daily average power consumption (Ah) × number of consecutive rainy days / maximum discharge depth

5. Average discharge rate

Average discharge rate (h) = number of consecutive rainy days × load working time / maximum discharge depth

6. Load working time

Load working time (h) = ∑ load power × load working time / ∑ load power

7. Battery

7.1 Battery capacity = load average power consumption (Ah) × number of consecutive rainy days × discharge correction factor / maximum discharge depth × low temperature correction factor

7.2 Number of batteries connected in series = system operating voltage / battery nominal voltage

7.3 Number of batteries connected in parallel = total capacity of batteries / nominal capacity of batteries

8. Simple calculation based on peak sunshine hours

8.1 Component power = (power consumption of electrical appliances × power consumption time / local peak sunshine hours) × loss factor

Loss coefficient: take 1.6~2.0 according to the local pollution degree, line length, installation angle, etc.

8.2 Battery capacity = (power of electrical appliances × power consumption time / system voltage) × number of consecutive rainy days × system safety factor

System safety factor: take 1.6~2.0, according to battery discharge depth, winter temperature, inverter conversion efficiency, etc.

9. The calculation method based on the total annual radiation

Components (square matrix) = K × (operating voltage of electrical appliances × operating current of electrical appliances × power consumption time) / total annual local radiation

When someone maintains + general use, K takes 230; when no one maintains + reliable use, K takes 251: when no one maintains + harsh environment + requires very reliable, K takes 276

10. Calculation based on annual total radiation and slope correction factor

10.1 Square array power = factor 5618 × safety factor × total load power consumption / slope correction factor × annual average radiation on the horizontal plane

Coefficient 5618: according to the charge and discharge efficiency coefficient, component attenuation coefficient, etc.; safety factor: according to the use environment, whether there is a backup power supply, whether there is someone on duty, etc., take 1.1 to 1.3

10.2 Battery capacity = 10 × total load power consumption / system operating voltage: 10: no sunshine coefficient (applicable to continuous rainy days not exceeding 5 days)

11. Multi-channel load calculation based on peak sunshine hours

11.1 Current

Component current = load daily power consumption (Wh) / system DC voltage (V) × peak sunshine hours (h) × system efficiency coefficient

System efficiency coefficient: including battery charging efficiency 0.9, inverter conversion efficiency 0.85, component power attenuation + line loss + dust, etc. 0.9, which should be adjusted according to the actual situation.

11.2 Power

Total power of components = component power generation current × system DC voltage × coefficient 1.43

Coefficient 1.43: The ratio of component peak operating voltage to system operating voltage.

11.3 Battery pack capacity

Battery pack capacity = [load daily power consumption Wh/system DC voltage V] × [number of consecutive rainy days/inverter efficiency × battery discharge depth]

Inverter efficiency: about 80% to 93% according to equipment selection; battery discharge depth: choose between 50% and 75% according to its performance parameters and reliability requirements.

12. Calculation method based on the peak sunshine hours and the interval between two rainy days

12.1 Calculation of system battery pack capacity

Battery pack capacity (Ah) = safety frequency × load daily average power consumption (Ah) × maximum number of continuous rainy days × low temperature correction coefficient / battery maximum discharge depth coefficient

Safety factor: Between 1.1 and 1.4: Low temperature correction factor: 1.0 for above 0°C, 1.1 for above -10°C, 1.2 for above -20°C: battery maximum discharge depth coefficient: 0.5 for shallow cycle, 0.75 for deep cycle, Alkaline nickel-cadmium batteries take 0.85.

12.2 Number of components connected in series

Number of components in series = system operating voltage (V) × coefficient 1.43/peak operating voltage of selected components (V)

12.3 Calculation of average daily power generation of modules

Daily average power generation of modules = (Ah) = peak operating current of selected modules (A) x peak sunshine hours (h) x slope correction factor x module attenuation loss coefficient

The peak sunshine hours and the slope correction factor are the actual data of the system installation site: the component attenuation loss correction factor mainly refers to the loss due to component combination, component power attenuation, component dust cover, charging efficiency, etc., generally take 0.8:

12.4 Calculation of the battery capacity that needs to be supplemented for the shortest interval between two consecutive rainy days

Supplementary battery capacity (Ah) = safety factor × load daily average power consumption (Ah) × maximum number of consecutive rainy days

Calculation of the number of components connected in parallel:

The number of modules connected in parallel = [supplementary battery capacity + daily average power consumption of loads × minimum interval days] / average daily power generation of components × minimum interval days

Load daily average power consumption = load power / load operating voltage × working hours per day

13. Calculation of power generation of photovoltaic array

Annual power generation = (kWh) = local annual total radiant energy (KWH/㎡) × area of photovoltaic square (㎡) × module conversion efficiency × correction factor. P=H·A·η·K

Correction coefficient K=K1·K2·K3·K4·K5

The attenuation coefficient of K1 module for long-term operation, take 0.8: take 0.82: K3 is the line correction, take 0.95: K4 is the inverter efficiency, take 0.85 or according to the manufacturer’s data: K5 is the correction factor for the orientation and inclination angle of the photovoltaic array, which is about 0.9.

14. Calculate the area of the photovoltaic array according to the power consumption of the load

Photovoltaic module square array area = annual power consumption / local annual total radiant energy × module conversion efficiency × correction factor

A=P/H·η·K

15. Conversion of solar radiation energy

1 card (cal) = 4.1868 joules (J) = 1.16278 milliwatt hours (mWh)

1 kilowatt-hour (kWh) = 3.6 megajoules (MJ)

1 kWh/㎡(KWh/㎡)=3.6 MJ/㎡(MJ/㎡)=0.36 kJ/cm?(KJ/cm?)

100 mWh/cm? (mWh/cm?) = 85.98 cal/cm? (cal/cm?)

1 MJ/m? (MJ/m?) = 23.889 cal/cm? (cal/cm?) = 27.8 mWh/cm? (mWh/cm?)

When the unit of radiation is cal/cm?: annual peak sunshine hours = radiation x 0.0116 (conversion factor)

When the unit of radiation is MJ/m?: annual peak sunshine hours = radiation ÷ 3.6 (conversion factor)

When the unit of radiation is kWh/m?: Peak sunshine hours = radiation ÷ 365 days

When the unit of radiation is kJ/cm², peak sunshine hours = radiation ÷ 0.36 (conversion factor)

16. Battery selection

Battery capacity≥5h×inverter power/battery rated voltage

17. Electricity price calculation formula

Power generation cost price = total cost ÷ total power generation

Power station profit = (power purchase price – power generation cost price) × working hours within the life span of the power station

Power generation cost price = (total cost – total subsidy) ÷ total power generation

Power station profit = (power purchase price – power generation cost price 2) × working hours within the life span of the power station

Power station profit = (power purchase price – power generation cost price 2) × working time within the life of the power station + non-market factor income

18. ROI Calculation

No subsidy: annual power generation x electricity price ÷ total investment cost x 100% = annual rate of return

With power station subsidies: annual power generation x electricity price ÷ (total investment cost – total subsidy) x 100% = annual rate of return

There are electricity price subsidies and power station subsidies: annual power generation x (electricity price + subsidized electricity price) ÷ (total investment cost – total subsidy) x 100% = annual rate of return

19. Photovoltaic square array inclination angle and azimuth angle

19.1 Tilt angle

Latitude component horizontal inclination

0°-25° inclination = latitude

26°-40° inclination = latitude +5°-10° (+7° in most areas of our country)

41°-55° inclination=latitude+10°-15°

Latitude > 55° Inclination = Latitude + 15°-20°

19.2 Azimuth

Azimuth = [peak time of load in a day (24h system)-12]×15+(longitude-116)

20. Spacing between front and rear rows of photovoltaic array:

D = 0 . 7 0 7 H / t a n [ a c r s i n ( 0 . 6 4 8 c o sΦ- 0 . 3 9 9 s i nΦ) ]

D: front and rear spacing of component square array

Φ: latitude of photovoltaic system (positive in the northern hemisphere, negative in the southern hemisphere)

H: the vertical height from the bottom edge of the rear row of photovoltaic modules to the upper edge of the front row of shelters