Question

A generating station has a maximum demand of \(25\text{ MW}\), a load factor of \(60%\), a plant capacity factor of \(50%\). What is the reserve capacity of the plant?

• A. \(25\text{ MW}\)
• B. \(15\text{ MW}\)
• C. \(7.5\text{ MW}\)
• D. \(5\text{ MW}\)

Hint:

An elegant algebraic shortcut relating these variables directly is: \[ \text{Plant Capacity} = \text{Maximum Demand} \times \left( \frac{\text{Load Factor}}{\text{Plant Capacity Factor}} \right) \] Using this here yields $\text{Plant Capacity} = 25 \times \frac{0.6}{0.5} = 30\text{ MW}$.

Answer 1

The Correct Option is D

Concept: In power generation statistics, the margin of generation available to handle contingencies is called the reserve capacity. It is defined as: \[ \text{Reserve Capacity} = \text{Plant Capacity} - \text{Maximum Demand} \] To evaluate this parameter, we utilize the structural operational equations for key system metrics: \[ \text{Load Factor} = \frac{\text{Average Demand}}{\text{Maximum Demand}} \] \[ \text{Plant Capacity Factor} = \frac{\text{Average Demand}}{\text{Plant Capacity}} \]

Step 1: Extract the given constants from the text.
* Maximum Demand = \(25\text{ MW}\) * Load Factor = \(60% = 0.60\) * Plant Capacity Factor = \(50% = 0.50\)

Step 2: Determine the Average Demand of the generating station.
Using the load factor formulation: \[ \text{Average Demand} = \text{Load Factor} \times \text{Maximum Demand} \] \[ \text{Average Demand} = 0.60 \times 25\text{ MW} = 15\text{ MW} \]

Step 3: Deduce the overall physical Plant Capacity.
Using the plant capacity factor equation: \[ \text{Plant Capacity} = \frac{\text{Average Demand}}{\text{Plant Capacity Factor}} \] Substituting the newly derived average demand value: \[ \text{Plant Capacity} = \frac{15\text{ MW}}{0.50} = 30\text{ MW} \]

Step 4: Calculate the final Reserve Capacity.
Subtracting the station's peak historical maximum demand from its full capacity limits: \[ \text{Reserve Capacity} = 30\text{ MW} - 25\text{ MW} = 5\text{ MW} \] This mathematically concludes that the reserve capacity is \(5\text{ MW}\), which is matching Option (D).