Correct Answer - Option 3 : 8 MW

Plant capacity factor: It is the ratio of actual energy produced to the maximum possible energy that could have been produced during a given period.

\(Plant\;capacity\;factor = \frac{{{\rm{Actual\;energy\;produced}}}}{{Maximum\;energy\;that\;could\;have\;been\;produced}}\)

Plant capacity factor \( = \frac{{Average\;demand × T}}{{Plant\;capacity × 100}}\)

Plant capacity factor \(= \frac{{Average\;demand}}{{Plant\;capacity}}\)

\(Annual\;plant\;capacity\;factor = \frac{{{\rm{Annual\;kWh\;output}}}}{{Plant\;capacity × 8760}}\)

The plant capacity factor is an indication of the reverse capacity of the plant. A power station is so designed that it has some reserve capacity for meeting the increased load demand in the future. Therefore, the installed capacity of the plant is always somewhat greater than the maximum demand on the plant.

Reserve capacity = Plant capacity – Maximum demand

If the maximum demand on the plant is equal to plant capacity, then load factor and plant capacity factor will have the same value. In such a case, the plant will have no reserve capacity.

Load factor: The ratio of average load to the maximum demand during a given period is known as the load factor.

Load factor = average load / maximum demand

Energy generated = Average load x Time (T)

__Calculation:__

Given that,

Load factor = 60% = 0.6

Plant capacity factor = 50% = 0.5

Maximum demand = 40 kW

Average demand = Load factor × Maximum demand

Average demand = 0.6 × 40 = 24 kW

Plant capacity = Average demand / Plant capacity factor

Plant Capacity = 24 / 0.5 = 48 kW

Reserve capacity = 48 – 40 = 8 kW