SECTION B (Q4-Q6) Q5(a) Compare between distributed and centralised grids. [5] Q5(b) A homeowner is considering a rooftop installation of a solar PV system to offset a part of his grid energy cost. The total surface area of the rooftop is \( 400 \mathrm{~m}^{2} \). (i) Determine the system maximum installed capacity in kW if the only available [6] solar PV modules are 100W with dimensions of ( \( 1.3 \mathrm{~m} \times 2.1 \mathrm{~m} \) ). (ii) If the daily total solar irradiation for the site where the homeowner plans to [5] set up a solar PV system is \( 4.5 \mathrm{kWh} / \mathbf{m}^{2} \). Using this information and considering a conversion efficiency of \( 21 \% \), calculate the expected annual energy from the projected solar PV system. Q5(c) For a typical wind turbine: (i) What does the power coefficient, \( C_{p} \), indicate and what is its theoretical [5] maximum value? (ii) Explain why \( C_{p} \) is zero when \( \lambda=0 \) and \( \lambda=12 \) ? [4] Total [25]

### QUESTION 5(a) **Compare between Distributed and Centralized Grids.** *[5 Marks]* **Distributed Grids:** 1. **Generation Location:** Electricity is generated close to the point of consumption using multiple small-scale sources (e.g., rooftop solar panels, small wind turbines). 2. **Scalability:** Easily scalable by adding more local generation units as demand increases. 3. **Reliability:** Enhanced reliability and resilience since the failure of one source has minimal impact on the overall system. 4. **Transmission Losses:** Reduced transmission losses due to shorter distances between generation and consumption points. 5. **Environmental Impact:** Often utilizes renewable energy sources, leading to lower environmental footprints. **Centralized Grids:** 1. **Generation Location:** Electricity is produced at large, centralized power plants (e.g., coal, nuclear, large hydroelectric) and transmitted over long distances to consumers. 2. **Economies of Scale:** Beneficial from economies of scale, typically resulting in lower cost per unit of electricity generated. 3. **Infrastructure:** Requires extensive transmission and distribution infrastructure to deliver electricity from central plants to end-users. 4. **Reliability:** Vulnerable to large-scale outages; a failure at a central plant can disrupt supply to a wide area. 5. **Environmental Impact:** Centralized plants, especially those using fossil fuels, can have significant environmental impacts, including higher greenhouse gas emissions. **Comparison Summary:** - **Flexibility:** Distributed grids offer greater flexibility and adaptability compared to centralized grids. - **Cost:** Centralized grids may have lower generation costs due to scale but higher transmission costs, whereas distributed grids can reduce transmission losses but may have higher per-unit generation costs. - **Resilience:** Distributed grids are generally more resilient to disruptions than centralized systems. --- ### QUESTION 5(b) **A homeowner is considering a rooftop installation of a solar PV system to offset a part of his grid energy cost. The total surface area of the rooftop is \( 400 \mathrm{~m}^{2} \).** #### (i) Determine the system maximum installed capacity in kW if the only available solar PV modules are 100 W with dimensions of \( 1.3 \mathrm{~m} \times 2.1 \mathrm{~m} \). *[6 Marks]* **Given:** - **Total Rooftop Area:** 400 m² - **Solar PV Module Rating:** 100 W - **Module Dimensions:** 1.3 m × 2.1 m = 2.73 m² per module **Calculation Steps:** 1. **Determine the number of modules that can fit on the rooftop:** \[ \text{Number of Modules} = \frac{\text{Total Rooftop Area}}{\text{Area per Module}} = \frac{400\, \text{m}²}{2.73\, \text{m}²/\text{module}} \approx 146.45 \] Since partial modules aren't feasible, the maximum number is **146 modules**. 2. **Calculate the total installed capacity:** \[ \text{Total Capacity} = \text{Number of Modules} \times \text{Power per Module} = 146 \times 100\, \text{W} = 14,600\, \text{W} = 14.6\, \text{kW} \] **Answer:** The maximum installed capacity is **14.6 kW**, achieved by installing 146 modules on the 400 m² rooftop. #### (ii) If the daily total solar irradiation for the site where the homeowner plans to set up a solar PV system is \( 4.5 \mathrm{kWh} / \mathrm{m}^{2} \). Using this information and considering a conversion efficiency of \( 21\% \), calculate the expected annual energy from the projected solar PV system. *[5 Marks]* **Given:** - **Daily Solar Irradiation:** 4.5 kWh/m²/day - **Conversion Efficiency:** 21% - **Total Rooftop Area:** 400 m² - **Installed Capacity:** 14.6 kW (from part i) **Approach:** Calculate the energy produced by the entire rooftop area considering the solar irradiation and efficiency. **Calculation Steps:** 1. **Total Daily Solar Energy Incident:** \[ \text{Daily Solar Energy} = \text{Solar Irradiation} \times \text{Total Area} = 4.5\, \text{kWh/m}²/\text{day} \times 400\, \text{m}² = 1,800\, \text{kWh/day} \] 2. **Effective Energy Converted by PV System:** \[ \text{Effective Daily Energy} = \text{Daily Solar Energy} \times \text{Efficiency} = 1,800\, \text{kWh/day} \times 0.21 = 378\, \text{kWh/day} \] 3. **Annual Energy Production:** \[ \text{Annual Energy} = \text{Effective Daily Energy} \times 365\, \text{days} = 378\, \text{kWh/day} \times 365 = 137,970\, \text{kWh/year} \] **Answer:** The expected annual energy from the solar PV system is **137,970 kWh**. --- ### QUESTION 5(c) **For a typical wind turbine:** #### (i) What does the power coefficient, \( C_p \), indicate and what is its theoretical maximum value? *[5 Marks]* **Power Coefficient (\( C_p \)):** - **Definition:** The power coefficient \( C_p \) represents the fraction of the kinetic energy in the wind that is converted into mechanical energy by the wind turbine. - **Formula:** \[ P = C_p \cdot \frac{1}{2} \rho A v^3 \] where: - \( P \) = Power extracted - \( \rho \) = Air density - \( A \) = Swept area - \( v \) = Wind velocity **Theoretical Maximum Value:** - **Betz's Law:** Establishes that no wind turbine can capture more than 59.3% of the kinetic energy in wind. - **Maximum \( C_p \):** \( \frac{16}{27} \approx 0.593 \) or **59.3%** **Answer:** \( C_p \) indicates the efficiency with which a wind turbine converts the wind's kinetic energy into mechanical energy. Its theoretical maximum value, as defined by Betz's Law, is **59.3%**. #### (ii) Explain why \( C_p \) is zero when \( \lambda = 0 \) and \( \lambda = 12 \). *[4 Marks]* **Definitions:** - **Tip Speed Ratio (\( \lambda \)):** The ratio of the tangential speed of the turbine blade tip to the wind speed. \[ \lambda = \frac{\omega R}{v} \] where: - \( \omega \) = Angular velocity - \( R \) = Rotor radius - \( v \) = Wind speed **Explanation:** 1. **When \( \lambda = 0 \):** - **Interpretation:** This implies that the rotor is not rotating (\( \omega = 0 \)). - **Effect on \( C_p \):** Without rotation, the turbine does not extract any energy from the wind. - **Result:** \( C_p = 0 \) 2. **When \( \lambda = 12 \):** - **Interpretation:** The rotor is rotating too fast relative to the wind speed. - **Effect on \( C_p \):** At very high tip speed ratios, the turbine blades cannot effectively capture the wind energy as the angle of attack becomes inefficient, leading to minimal energy extraction. - **Result:** \( C_p = 0 \) **Answer:** When \( \lambda = 0 \), the turbine is stationary and does not rotate, resulting in no energy extraction (\( C_p = 0 \)). Conversely, when \( \lambda = 12 \), the turbine spins too rapidly relative to the wind speed, making energy capture inefficient, which also causes \( C_p \) to be zero.