To calculate the requested parameters related to the solar plant with a PV (photovoltaic) system, we can use the following information:
- Average solar irradiance: \( G = 1 , \text{kW/m}^2 \)
- Operation time per day: \( t_{\text{day}} = 16 , \text{hours} \)
- Days of operation per year: \( d_{\text{year}} = 300 \)
- Efficiency of the PV system: \( \eta = 40% = 0.40 \)
- Usable annual AC electricity generated: \( E_{\text{AC}} = 3 , \text{GWh} = 3 \times 10^9 , \text{Wh} \)
- Solar energy generated by the panels: \( E_{\text{PV}} = 2.4 , \text{GWh} = 2.4 \times 10^9 , \text{Wh} \)
9.1 Performance Ratio (PR) of the Plant
The Performance Ratio (PR) is defined as the ratio of the actual output of a solar plant to the expected output from the system at standard test conditions, taking into account losses due to inefficiencies, temperature, and other factors.
\[ \text{PR} = \frac{\text{Actual Output}}{\text{Expected Output}} \]
Where:
- Actual Output is the usable AC electricity generated (\( E_{\text{AC}} \)).
- Expected Output is the energy that should be generated by the solar panels based on the solar irradiance, area, and efficiency.
First, we need to calculate the expected output:
\[ E_{\text{expected}} = G \times A \times t_{\text{year}} \times \eta \]
Where:
- \( t_{\text{year}} \) = \( t_{\text{day}} \times d_{\text{year}} = 16 , \text{hours/day} \times 300 , \text{days} = 4800 , \text{hours} \)
To find \( A \) (the area), we can rearrange the formula to calculate energy generated, using the energy generated by solar panels:
\[ E_{\text{PV}} = G \times A \times t_{\text{year}} \times \eta \]
Solving for area \( A \):
\[ A = \frac{E_{\text{PV}}}{G \times t_{\text{year}} \times \eta} \]
Then, we can calculate the Performance Ratio (PR):
- Calculate \( t_{\text{year}} \):
\[ t_{\text{year}} = 16 \times 300 = 4800 , \text{hours} \]
- Calculate \( A \):
\[ A = \frac{2.4 \times 10^9 , \text{Wh}}{1 , \text{kW/m}^2 \times 4800 , \text{hours} \times 0.40} \]
\[ A = \frac{2.4 \times 10^9 , \text{Wh}}{1 \times 4800 \times 0.40 , \text{Wh/m}^2} = \frac{2.4 \times 10^9}{1920} \approx 1,250,000 , \text{m}^2 \]
- Calculate the expected output:
\[ E_{\text{expected}} = G \times A \times t_{\text{year}} \times \eta \] \[ E_{\text{expected}} = 1 , \text{kW/m}^2 \times 1,250,000 , \text{m}^2 \times 4800 , \text{hours} \times 0.40 \]
\[ = 1 , \text{kW/m}^2 \times 1,250,000 \times 4800 \times 0.40 \] \[ = 1,200,000,000 , \text{Wh} = 1200 , \text{GWh} \]
- Calculate PR:
\[ \text{PR} = \frac{E_{\text{AC}}}{E_{\text{expected}}} \] \[ \text{PR} = \frac{3 \times 10^9}{1,200 \times 10^9} = \frac{3}{1200} = 0.0025 , or , 0.25% \]
9.2 Solar Power Generated
The total solar power generated can be summarized as:
\[ E_{\text{PV}} = 2.4 , \text{GWh} \]
9.3 Surface Area of the Collectors
From our earlier calculations, we can conclude:
\[ A \approx 1,250,000 , \text{m}^2 \]
Summary
- Performance Ratio (PR): 0.25%
- Solar Power Generated: 2.4 GWh
- Surface Area of Collectors: Approximately 1,250,000 m²
Please note that the low PR indicates that there is a significant loss in performance (potentially due to factors indicated in the equations).