symbolically an all-thermal power generation system connected to an equivalent load bus through a transmission network.

**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, F_{T}** ,** 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, P_{i}** ,** it must be recognized that the
loss in the transmission network, P

^{Ø} For our purposes, the currents will be
considered only as a function of the independent variables P_{i} and
the load P_{load} taking the derivative of the Lagrange function with
respect to any one of the ** N** values of P

^{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 *

^{ }

^{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*.*^{}

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