Calculating Phase Current and Power Factor in a Y Connected Generator

[richardknox]

Homework Statement

A Y connected, 400V (line), 100KVA rated, stand alone generator is operating at 80kW at rated current with a lagging power factor and rated terminal voltage. The synchronous reactance is 2Ω.

Draw the per phase equivalent circuit and calculate:

(i) The Phase Current (Iph)
(ii) The Power Factor
(iii) The Reactive Power
(iv) The Voltage drop across the Synchronous Reactance (VXS)

Homework Equations

$V_{ph} = V_{line}/√3$
$P = IV$
$P = IVcosθ$
$Q = Ssinθ$
$S_{ph} = S/√3$
$V_{xs} = I_{ph} * jXs$

The Attempt at a Solution

$V_{ph} = 400/√3 = 230.9V$
$S_{ph} = 57735W$
$S = IV$
$I = S/V = 57735/230.9 = 250A$

$P = IVcosθ$
$cosθ = 0.8$

$Q = Ssinθ = 60VAr$

$V_{xs} = jXs * I_{ph} = 500V$

Not sure where I go wrong but I'm assuming I can't have a voltage drop of 500V over a component when I only have 230.9V of phase voltage!

 

[nilesh_pat]

A:There are lots of mistakes in the stated problem. Vph = 400/√3 = 230.9V is correct.Sph = 57735W is wrong. Use 100000VA = 100kVA = 100000/√3 = 57735VA.I = S/V = 57735/230.9 = 250A is wrong. Use 57735VA/230.9V = 248.6A.P = IVcosθ is wrong. Use P = Sph*cosθ = 57735*0.8 = 46188W.Q = Ssinθ is wrong. Use Q = Sph*sinθ = 57735*0.6 = 34631.Vxs = jXs * Iph = 500V is wrong. Use Vxs = jXs * Iph = 2*248.6*j = 497V.