Economic Dispatch




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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Ahmad Atiia

Hi. I’m Designer of Engineering Topics Blog. I’m Electrical Engineer And Blogger Specializing In Electrical Engineering Topics. I’m Creative.I’m Working Now As Maintenance Head Section In An Industrial Company.

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