# Synchronous machine help asap- with solution attempt but wrong answer

1. Jun 30, 2009

### mayeh

1. The problem statement, all variables and given/known data

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%

2. Relevant equations

i think this are the equations to be used:

%VR=$$\frac{V_{LCOMP}-V_{LRATED}}{V_{LRATED}}$$*100
V$$_{COMP\phi}$$=V$$_{RATED\phi}+(I_{\phi}Z_{S\phi})$$
Z_{S\phi}=Re_{\phi}+JXe_{\phi}
I_{\phi}=S/(V_{L}$$\sqrt{3}$$)

3. The attempt at a solution

THIS IS WHAT I'VE DONE:

the given voltage is line and its a star connected :V_{L}=$$\sqrt{3}$$V_{\phi}
V_{\phi} is phase voltage

so, i solved for the phase voltage:
V_{\phi}=V_{L}/$$\sqrt{3}$$=254.0341184V
the phase current, I_{\phi}
I_{\phi}=10kVA/(440$$\sqrt{3}$$)=13.12159703A
and
Z_{S\phi}=0.5+j10

solution:

V_{LCOMP}=$$\sqrt{((V_{LRATED}cos{\phi}+IR)^{2}+(V_{LRATED}sin{\phi}+IX)^{2}\$$

V_{LCOMP}=$$\sqrt{((254.0341*0.8+13.12159*0.5)^{2}+(254.0341*0.6+13.12159*10)^{2}}$$
V_{LCOMP}=352.78769V

%VR=$$\frac{352.78769-254.0341}}{254.0341}$$*100
%VR=38.8749%

please correct my solution.. i dont have any idea if i've done this right
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution