- #1
mayeh
- 15
- 0
Homework Statement
This was a lecture that wasnt taught to us but we were given sample problems with answer but no solutions and i tried to solve some but ends up with wrong answer.. so here's the given:
a 3 phase 10kVA, 440V 60 Hz, y-connected alternator supplies the rated load at 0.8 power factor lagging. if the armature resistance is 0.5 and synchronous reactance is 10, find the voltage regulation at rated load. ANS: VR=48.0406%
Homework Equations
i think this are the equations to be used:
%VR=[tex]\frac{V_{LCOMP}-V_{LRATED}}{V_{LRATED}}[/tex]*100
V[tex]_{COMP\phi}[/tex]=V[tex]_{RATED\phi}+(I_{\phi}Z_{S\phi})[/tex]
Z_{S\phi}=Re_{\phi}+JXe_{\phi}
I_{\phi}=S/(V_{L}[tex]\sqrt{3}[/tex])
The Attempt at a Solution
THIS IS WHAT I'VE DONE:
the given voltage is line and its a star connected :V_{L}=[tex]\sqrt{3}[/tex]V_{\phi}
V_{\phi} is phase voltage
so, i solved for the phase voltage:
V_{\phi}=V_{L}/[tex]\sqrt{3}[/tex]=254.0341184V
the phase current, I_{\phi}
I_{\phi}=10kVA/(440[tex]\sqrt{3}[/tex])=13.12159703A
and
Z_{S\phi}=0.5+j10
solution:
V_{LCOMP}=[tex]\sqrt{((V_{LRATED}cos{\phi}+IR)^{2}+(V_{LRATED}sin{\phi}+IX)^{2}\[/tex]
V_{LCOMP}=[tex]\sqrt{((254.0341*0.8+13.12159*0.5)^{2}+(254.0341*0.6+13.12159*10)^{2}}[/tex]
V_{LCOMP}=352.78769V
%VR=[tex]\frac{352.78769-254.0341}}{254.0341}[/tex]*100
%VR=38.8749%
please correct my solution.. i don't have any idea if I've done this right