Syncronous generators question with power factors

[woops]

Hi everyone i am having some trouble with an electronics question I really need some help with. I keep getting 14.96 KV but that doesn't appear to be the correct answer. Is the answer given wrong or am i doing something wrong. Thanks for any help i have been stuck on this for ages.

Homework Statement

An isolated, 10 MVA, 11 kV, three-phase, star-connected synchronous generator has negligible armature resistance and a synchronous reactance of 5 Ω. At a certain field current the generator delivers rated load at 0.9 pf lagging at 11 kV. If the excitation remains unchanged determine the terminal voltage when the full load power factor is 0.9 leading.

Homework Equations

None provided- Answer given is [15.4 kV]

The Attempt at a Solution

Please see attachement

 

[Valkarie]

. The answer is 15.4 kV and not 14.96 kV as you mentioned. The reason is that when the load power factor is 0.9 leading, the terminal voltage of the generator must increase to maintain the same active power output at the rated load. This implies that the terminal voltage of the generator increases to a higher value than 11 kV, which is the rated voltage of the generator.