Question

6. Consider the system shown below. The generator initially supplies 10 MW at unity power factor to the infinite bus. The voltage atthe infinite bus has a magnitude of 1 pu. Note that there is no load at bus 4 L1 G 1 D2 G1 20 kV 20 MVA 3 phase 60 Hz 4 pole X' 0.15 pu H 5 S T 20 kV Y- 169 kV Y 20 MVA 3 phase 60 Hz X-0.1 pu L1, L2 Short lines Z j 0.1 pu on 20 MVA 169 kV base. a. Calculate the voltage behind transient reactance E' andthe initial power angle

PLEASE COMPLETE ALL PARTS AND SHOW ALL WORK.

Answer 1

A)Take base MVA=20, Base KVA=20. As all the elements are rated to base levels, there will be no change in per unit impedance values. So take x'=j0.15 p.u, t/f x=j0.1p.u and Z=j0.1 p.u. Now E is given by. E=V+I(x'+x+z). Where I= (p/v cos$\Phi$), given v &cos$\Phi$ =1 and given power p= 10MW , So P.u power delivered P=10/20= 0.5. So I=0.5. Now E=1+0.5(j0.15+j0.1+j0.1), on solving we get E=1.015$\angle$9.926. B) If fault occur on 4th bus , the network looks like star connected network. So use star- delta rule, the effective x between E & V given by Xeff= j0.25+j0.1+(j0.25*j0.1)/j0.1 =j0.6. So we know power angle equation P=( EVsin$\delta$)/Xeff . so [P =1.69sin$\delta$]