Transmission-loss Formula for Economic Dispatch Calculations

In economic dispatch study, when transmission-loss IS also considered,
partial differential derivatives of transmission-loss with respect to generating plant
output powers appear in the coordination equations. Obviously, an attempt for
expressing transmission-losses as a function of generating plant outputs simplifies
the calculations. In this paper a method based on Kron's six reference frames,
and Kirchmayers developments on the calculation of loss formula is described.
In a bus reference frame transmission network is expressed as:
E =z I
We have to eliminate the individual load currents as variables, since
the final result should involve only generator powers. First the sum of the load
currents is defined as a total equivalent load, and then it is assumed that each
load current remains a constant complex fraction of the total equivalent load.
By applying Kron's transformation theory to the equation (1) a new formulation
for the transmission network ;will be obtained which involves only generator
currents :
E=ZIG
The real losses of the transmission network may be calculated as follows:
PL=Re(E IG*)=Re(IG Z I *)=Re(i * ZI )
substituting IG=Id+j Ig and Z=R+jX into equation (3) and using the rules
of matrix theory results to :
PL=Id ( )Id+Ig ( )Ig-2Id ( )Ig
It is noted that only the symmetric past of the R and skew-symmetric part of
the X contribute to real loss.
Finally, to express PL in terms of generator powers J another transformation
is performed on the equeation (4) which puts PL into the desired form:
Pl=p BP
where the elements of B matrix are caned transmission-loss formula Coefficients.
Also procedures for representation of source-reactive characteristics and
representation of loads are briefly discussed.