Calculate the generation cost of a hydro-power station in two parts: fixed charges and running charges based on provided parameters.

Steps to Solve

1. Calculate Units Generated Annually To find the total units generated per year, use the formula: [ \text{Units generated per annum} = \text{Maximum demand} \times \text{Load factor} \times \text{Total hours in a year} ] Applying the values: [ (40 \times 10^3) \times 0.6 \times 8760 = 210.24 \times 10^6 \text{ kWh} ]

2. Determine Capital Cost of the Plant The capital cost can be calculated as follows: [ \text{Capital cost of the plant} = \text{Capacity} \times \text{Cost per kW} ] Substituting the values: [ 50 \times 10^6 = 50 \times 10^3 \times 1000 = 50 \times 10^6 \text{ Rs} ]

3. Calculate Annual Depreciation Charges The depreciation is 10% of the capital cost: [ \text{Depreciation} = 0.1 \times \text{Capital cost} = 0.1 \times 50 \times 10^6 = 5 \times 10^6 \text{ Rs} ]

4. Calculate Salaries and Maintenance Costs Given that the total expense for salaries and maintenance is Rs 7,00,000, we find: [ \text{Salaries and maintenance} = 2 \times 7,00,000 = 1.4 \times 10^6 \text{ Rs} ]

5. Calculate Total Annual Fixed Charges Total fixed charges include depreciation and salaries: [ \text{Total annual fixed charges} = \text{Depreciation} + \text{Salaries and maintenance} = 5 \times 10^6 + 1.4 \times 10^6 = 6.4 \times 10^6 \text{ Rs} ]

6. Compute Cost per kW for Fixed Charges The fixed cost per kW is calculated as: [ \text{Cost per kW} = \frac{\text{Total annual fixed charges}}{\text{Maximum demand}} = \frac{6.4 \times 10^6}{40 \times 10^3} = 160 \text{ Rs} ]

7. Calculate Annual Running Charges The annual running charges can be calculated as: [ \text{Running charges} = 0.8 \times 7,00,000 = 5.6 \times 10^6 \text{ Rs} ]

8. Compute Cost per kWh for Running Charges To find the cost for running charges per kWh generated: [ \text{Cost per kWh} = \frac{\text{Running charges}}{\text{Units generated}} + \text{Royalty} ] Royalty is given as Re. 1 per kWh, so: [ \text{Total Cost per kWh} = \frac{5.6 \times 10^6}{210.24 \times 10^6} + 1 ]

9. Calculate Final Costs Final calculations:

• Run the fractions to determine the cost in Rs.
• Combine both fixed and running charges for total generation cost.