Question

A generator, with a transient reactance of j0.5 pu, delivers 1.0 pu real power to an infinite bus through a transformer and two transmission lines in parallel as shown below. A solid three phase fault occurs at position near “F” which is cleared by opening both ends of the transmission leaving only one line in service. 

The generator has an internal voltage of 1.5 pu and an inertia constant (H) of 3 MJ/MVA. Determine whether the generator is transiently stable or not if the fault clearing time is 0.15 seconds.

Answer 1

hot rohtul Generator infinite bus go.spu E = Lolopu tj +5%8p* " 7 jo.zpur Yg - jo.5pu, delivered real power (P) = 124 H = 3 MS/AVA , clearing time (7) = 0.158 We know P-E.V gins E-generator intermal udtage XSI v- bus bar voltage X8 - reactance 15x1 sins. 0.5 '. Sindo 0.5 1.5 So = 19.470 0.34 rad The critical clearing clearing angle for this system Scr = cos'[(TT- 28.) Sin So-Coss] : Scr [(1–24.34 ) 8in 191470 – 60819470] = Cox' [ 2.46 8in19.17- Cop(9.470] Ser = 2084 [0.82-94] Sex Scr The angle Pom-mechanical power 96.290 at which fault is cleared SP Pm Wst² & So Ws - Spee of generator (elec vode] H-inertia constant I-clearing time CH So-initial operating angle

4 f=bottz 8 = 1x 21TX60 X 6.152 Чx3 0.34 Pm= Pe initially at balance Pm=1 8= 0.37 rad 8= 21.2° As we com see a'that LScr ie the fault is cleared Before the critical clearing angle , the System is transiently stable.