The question asks about the factors influencing the choice between a base-load station and a peak-load station, given an annual cost expression for a generating station. The annual cost is expressed as:

\(\text{Annual Cost (Rs)} = \text{A} + \text{B} \cdot \text{kW} + \text{C} \cdot \text{kWh}\)

Let's break down the components of this cost equation:

• A: This represents the fixed annual costs that do not depend on the station's size or how much energy it produces. These could include administrative expenses, property taxes, etc.
• B \(\cdot\) kW: This part of the cost depends on the maximum capacity of the station (in kW). Factor B is often called the capacity cost factor or fixed cost per kW of installed capacity. It covers expenses like interest on the capital investment, depreciation of equipment, and insurance, which are related to the station's size regardless of how much it operates.
• C \(\cdot\) kWh: This part of the cost depends on the total energy generated per year (in kWh). Factor C is often called the energy cost factor or running cost per kWh. It covers variable expenses like fuel cost, lubricating oil, maintenance that increases with operation, and the wages of operating staff.

Base-Load Station Considerations

A base-load station is designed to run almost continuously throughout the year to meet the minimum, constant demand of the electrical grid. These stations are characterized by:

• High Energy Output: They generate a very large amount of energy (kWh) annually because they operate for many hours.
• High Utilization: Their equipment is used for a significant portion of the year.

For a base-load station, since it produces a massive amount of kWh, even a small cost per unit of energy can add up significantly. Therefore, to keep the overall annual cost low and be economically viable, the energy cost factor (C) must be as low as possible. This means focusing on highly efficient technologies with low fuel consumption. While the initial capital cost (which influences factor B) might be higher, it gets spread over a very large amount of energy produced, making the cost per kWh competitive.

Peak-Load Station Considerations

A peak-load station is designed to operate only during periods of high demand (peak hours), which occur for limited durations. These stations are characterized by:

• Low Energy Output: They generate relatively less energy (kWh) annually because they operate for only a few hours per day or week.
• Low Utilization: Their equipment is idle for most of the time.

For a peak-load station, since it runs for short periods and its total energy generated (kWh) is relatively low, the fixed costs associated with its capacity (kW) become very important. If the initial capital cost or fixed operating cost (represented by factor B) is high, it will significantly increase the overall annual cost despite low energy generation. Therefore, for a peak-load station, it is crucial that the capacity cost factor (B) is low. The energy cost factor (C) might be higher than that of a base-load station, but its impact on the total annual cost is less pronounced because the total kWh generated is small.

Comparing Cost Factors for Generating Stations

The optimal choice between these station types hinges on minimizing their respective dominant cost components:

To summarize, for a base-load station that runs continuously and produces a lot of energy, the per-unit energy cost is critical, so factor C should be lower. For a peak-load station that runs only occasionally to meet sudden demand, the fixed cost of having the capacity available is more important than the per-unit running cost, so factor B should be lower.

Therefore, the choice depends on the fact that factor B should be less for the peak load station and factor C should be less for the base load station.