Question

The incremental cost characteristics of two generators delivering 200 MW are as follows:

\(\frac{{d{F_1}}}{{d{P_1}}} = 2.0 + 0.01\;{P_1}\) and \(\frac{{d{F_2}}}{{d{P_2}}} = 1.6 + 0.02\;{P_2}\)

For economic operation, the generation P₁ and P₂ should be

1. 100 MW and 100 MW
2. 80 MW and 120 MW
3. 200 MW and 100 MW
4. 120 MW and 80 MW

Answer 1

Correct Answer - Option 4 : 120 MW and 80 MW

Economic distribution of the loads between the units of Power plant:

To determine the economic distribution of a load amongst the different units of a plant, the variable operating costs of each unit must be expressed in terms of its power output.

The fuel cost is the main cost and it must be expressed in Rs./ hour

The fuel cost of a unit can be expressed as

F_i = a P_i² + b P_i + c Rs/ hour

The incremental cost is expressed as

\(IC_i = \frac{dF_i}{dP_i} = 2aP_i + b\) in Rs. /MWh or Rs / kWh.

For the economic operation of the system, the incremental cost of each generator must be equal.

Calculation:

Total delivering power is

P₁ + P₂ = 200 MW .....(1)

The incremental cost of Generator-1 is 

\(IC_1=\frac{dF_1}{dP_1}=2+0.01P_1\)

The incremental cost of Generator-2 is 

\(IC_2=\frac{dF_2}{dP_2}=1.6+0.02P_2\)

For the optimum cost, the incremental cost of each generator must be equal.

IC₁ = IC₂ 

⇒ 2 + 0.01 P₁ = 1.6 + 0.02 P₂

⇒ 2 P₂ - P₁ = 40 .....(2)

By solving equations (1) and (2), we get

P₁ = 120 MW

P₂ = 80 MW