Correct Answer - Option 4 : 18.75 MW

__Concept:__

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.

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

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

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

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

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.

Plant use factor: It is the ratio of kWh generated to the product of plant capacity and the number of hours for which the plant was in operation.

\(Plant\;use\;factor = \frac{{Station\;output\;in\;kWh}}{{Plant\;capacity × hours\;of\;use}}\)

Capacity factor = Load factor × plant use factor

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

__Calculation:__

Given -

Annual load factor = 50%, Maximum demand = 15000 kW

Plant capacity factor = 40% = 0.4

Average demand = 0.5 × 15000 = 7500 kW

Now installed capacity of the plant can be calculated as

Plant capacity = Average demand / Plant capacity factor

∴ Plant capacity = 7500 / 0.4

Plant capacity = 18750 kW = 18.75 MW