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1-Economic Dispatch With Active Power (for lossless system)
The generation units are
connected directly to one bus to supply the required demand as shown in the following figure.
where during this we neglect the losses . for example This analysis is
applied to 14_bus system ( 5 generation units )
According to Lagrange method, the Lagrange function, L, and the optimization conditions are:
so it will be n+1 equations of
n+1 unknowns then one can get
2-Economic Dispatch With Active And Reactive losses
The economic dispatch for a system
with active and reactive power loss has the following model.
·
Minimize cost:
Where ng , n are number of generators and
total number of system buses, PL and QL are the active and reactive system
loss, and Pi
and Qi are the active and reactive power at
bus i respectively with Pi=PGi-PDi and Qi = QGi-QDi where PDi and QDi are load powers. According to
Lagrange method, the Lagrange function, L, and the optimization conditions are:
Then eq. (3-6) and (3-7) become:
Where the partials of PL
and QL are as given in eq's (2-30) the optimal solution of (2ng+2)
of unknowns represent PG, QG at ng buses plus l1 and l2 which are obtained from the
iterative solution of (2ng+2) of nonlinear eq's (3-8), (3-9), (3-10) and (3-11).
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