Why Is My Voltage Regulation Calculation Incorrect for a Synchronous Machine?

[mayeh]

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

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 don't have any idea if I've done this right

 

[KataKoniK]

or wrong

Thank you for sharing your attempt at solving this problem. I can see that you have made some correct calculations, but there are a few mistakes in your solution.

Firstly, the phase voltage should be calculated as V_phi = V_L / √3 = 440 / √3 = 254.0341 V. This is because the given voltage is 440 V line-to-line, not line-to-neutral.

Next, the phase current should be calculated as I_phi = S / (V_L * √3) = 10 kVA / (440 * √3) = 13.1216 A. This is because the apparent power is given in kVA, not in amperes.

Finally, the formula for V_LCOMP is incorrect. It should be V_LCOMP = √((V_L*R + I_phi*R_e)^2 + (V_L*X + I_phi*X_e)^2). Plugging in the correct values, we get V_LCOMP = √((440*0.5 + 13.1216*0.5)^2 + (440*10 + 13.1216*10)^2) = √(225 + 19360) = √19585 = 139.8444 V.

Using this value for V_LCOMP, the voltage regulation can be calculated as %VR = (139.8444 - 254.0341) / 254.0341 * 100 = -45.9594%. This means that the voltage output of the alternator decreases by 45.9594% when the rated load is applied.

I hope this helps clarify the correct solution. Keep practicing and don't hesitate to ask for help if you encounter any difficulties in your future problem-solving. Good luck!

 

[Mene]

or wrong

I would suggest double checking your calculations and equations to ensure accuracy. It may also be helpful to consult with a professor or tutor for guidance on solving this problem. Additionally, make sure you are using the correct units for each variable and that your calculations are consistent. It is important to practice and understand the concepts behind the equations rather than just relying on sample problems and their answers.