Economic distribution of load between generating units within a plant
The simplest case of economic dispatch is the case when transmission losses are neglected. The model does not consider the system configuration or line impedances. Since losses are neglected, the total generation is equal to the total demand PD (or PR).
Consider a system with n number of generating plants supplying the total demand PR. The problem is to determine the P1, P2, …, Pn dispatch levels to be able to serve PR in the most economical way.
If Ci is the cost of plant i in Rs/h and the power output of the ith unit is Pi. The input cost can be expressed in terms of the power output as
Ci = αi + βi Pi + ϒi (Pi )2 = f(Pi )
The mathematical formulation of the problem of economic scheduling can be stated as follows:
Minimize C = sum(Ci) ; i = 1, 2, ....n.
Such that f(Pi) = PR - sum(Pi) = 0
where, C = total cost, Pi = generation cost of ith plant, PD or PR = total demand.
This is a constrained optimization problem, which can be solved by Lagrange’s method. Such problem can be solved by using Lagrange multiplier (λ) and Lagrange cost function (C*).
C* = C + λ f
When losses are neglected & there is no generator limits, for most economic operation, all units must operate at equal incremental production cost.