THERMAL SYSTEM DISPATCHING WITH NETWORK LOSSES
Ø symbolically an all-thermal power generation system connected to an equivalent load bus through a transmission network.
Ø The economic dispatching problem associated with this particular configuration is slightly more complicated to set up than the previous case.
Ø This is because the constraint equation is now one that must include the network losses.
Ø The objective function, FT, is the same as that defined for Eq.10
Ø The same procedure is followed in the formal sense to establish the necessary conditions for a minimum-cost operating solution, The Lagrange function is shown in Eq.11.
Ø In taking the derivative of the Lagrange function with respect to each of the individual power outputs, Pi, it must be recognized that the loss in the transmission network, Ploss is a function of the network impedances and the currents flowing in the network.
Ø For our purposes, the currents will be considered only as a function of the independent variables Pi and the load Pload taking the derivative of the Lagrange function with respect to any one of the N values of Pi results in Eq. 11. collectively as the coordination equations
Ø It is much more difficult to solve this set of equations than the previous set with no losses since this second set involves the computation of the network loss in order to establish the validity of the solution in satisfying the constraint equation.
Ø There have been two general approaches to the solution of this problem.
Ø The first is the development of a mathematical expression for the losses in the network solely as a function of the power output of each of the units.
Ø This is the loss-formula method discussed at some length in Kirchmayer‟s Economic Operation of Power Systems.
Ø The other basic approach to the solution of this problem is to incorporate the power flow equations as essential constraints in the formal establishment of the optimization problem.
Ø This general approach is known as the optimal power flow.