3-bus power flow

 

The figure shows a single-line diagram for an elementary 3-bus power system (N=3). Bus 1 is the slack bus; bus 2 is a voltage-controlled (PV) bus; bus 3 is a load (PQ) bus.

 

Phasors:

                                        Vk  =  Vk ejdk                                                      m = 1…..N

 

Bus equations:

                     Ik = Ykm Vm = (Gkm + jBkm)Vm             m = 1…..N

 

Bus Powers:

Sk = Pk + jQk = Vk Ik* = (GkmjBkm)(Vk Vm*)]

                                      = [(GkmjBkm)Vk Vm ej(dk-dm)]  

                                      = {Vk Vm (Gkm-jBkm) [(cos(dk-dm) + jsin(dk-dm)]} 

                                                                                                 m = 1…..N                     

        Pk =  Gkk Vk2 + Vk Vm[Gkm cos(dk-dm) +Bkm sin(dk-dm)]     

        Qk = -Bkk Vk2 + Vk Vm[Gkm sin(dk-dm) -Bkm cos(dk-dm)]        

                                                                                              m =1 ...k-1, k+1…N