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* = ∑ (Gkm –jBkm)(Vk Vm*)]
= ∑ [(Gkm –jBkm)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
To continue, erase this page…