Math Problem Statement

Vi installerar ett solcellskraftverk (PV-system) om 30x40 m. Den genomsnittliga totala strålningen i denna region är 1 200 kWh/m²/år. Energiproduktionseffektiviteten för detta PV-system är 21 procent. Hur mycket el genererar vårt system årligen? Svara i kWh.

Solution

The problem in the image asks to calculate the annual electricity generation of a solar power system (PV system) installed on an area of 30 m × 40 m, given the following information:

  • The total average solar radiation in the region is 1,200 kWh/m²/year.
  • The energy production efficiency of the PV system is 21%.
  • We are asked to calculate the electricity generated by the system annually in kWh.

Step-by-Step Calculation:

  1. Calculate the total area of the PV system: Area=30m×40m=1200m2\text{Area} = 30 \, \text{m} \times 40 \, \text{m} = 1200 \, \text{m}^2

  2. Determine the total solar energy received by this area per year: Total solar energy=Area×Solar radiation per m2\text{Total solar energy} = \text{Area} \times \text{Solar radiation per m}^2 =1200m2×1200kWhm2year=1,440,000kWh/year= 1200 \, \text{m}^2 \times 1200 \, \frac{\text{kWh}}{\text{m}^2 \cdot \text{year}} = 1,440,000 \, \text{kWh/year}

  3. Apply the system efficiency to calculate the actual electricity generated: Electricity generated=Total solar energy×Efficiency\text{Electricity generated} = \text{Total solar energy} \times \text{Efficiency} =1,440,000kWh/year×0.21=302,400kWh/year= 1,440,000 \, \text{kWh/year} \times 0.21 = 302,400 \, \text{kWh/year}

Final Answer:

The solar PV system will generate 302,400 kWh per year.


Do you have any questions or would you like a more detailed explanation?

Here are 5 related questions:

  1. How is solar radiation typically measured in different regions?
  2. How does the efficiency of a PV system affect energy production over time?
  3. What factors could influence the real-world efficiency of a solar panel system?
  4. How would a change in the size of the PV system affect the annual electricity generation?
  5. What are the benefits of using solar energy compared to other renewable energy sources?

Tip: Solar panel efficiency can decrease over time due to factors like dirt accumulation, degradation, and temperature changes. Regular maintenance can help sustain performance.

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Math Problem Analysis

Mathematical Concepts

Area Calculation
Energy Conversion
Efficiency

Formulas

Area = Length × Width
Total Solar Energy = Area × Solar Radiation per m²
Electricity Generated = Total Solar Energy × Efficiency

Theorems

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Suitable Grade Level

High School