Operating cost of thermal plants

According to the input-output curve of thermal power plant,

the cost function is simplified in a quadrate form:

C = α + β*P + γ*P2

This relation gives a good approximation to the actual 

variation of the cost with the variation of the output power

Economic Dispatch Neglecting Losses

It is assumed that all generators are connected at the same bus without losses in transmission 

lines The economic dispatch problem neglecting all losses in the transmission

system is defined 

Steps of obtaining the solution:

Define the coefficients of the cost functions of all
generating units (β i and γg g i, i=1,2,…n) , , )

• For a certain load demand, calculate the value of λ

• Depending on the calculated value of λ, compute the individual power P1, P2, ... Pn

corresponding to incremental fuel cost of production

• Check for max. and min. output power for each plant. In case of violating the generation limits, 

the output power of that generator is fixed at its extreme limit

• The remaining load demand is calculated and distributed among the remaining generators

Graphical solution

Graphically, the Lagrange multiplier λ can be defined by plotting the value of β + 2γ*Pfor all generators on the same graph

A random value of γ is selected and the corresponding generated power from each unit is obtained

The total power is compared with the total demand If the demand exceeds the generated power, the line representing the Lagrange multiplier λ is shifted up to increase the power and vice versa

Graphically, the Lagrange multiplier λ can be defined by plotting the value of β + 2γ*Pfor all 

generators on the same graph

 A random value of λ is selected and the corresponding generated power from each unit is obtained

 Check for max. and min. output power for each plant. In case of violating the generation limits, 

the output power of that generator is fixed at its extreme limit

 The total power is compared with the total demand

 If the demand exceeds the generated power, the line representing the Lagrange multiplier λ is
shifted up to increase the power and vice versa