Torque required for synchronising generators

Oct 2017
I had a query a while back on the physics part of MyMathForum. However, I never did manage to resolve it, so hopefully I'll have more success with you guys :)

I'm trying to work out the answer to the following problem:

Two, four-pole (p=2), 50 Hz synchronous generators are paralleled. Their phase displacement is 2 degrees mechanical. The synchronous reactance, \(\displaystyle X\), of each machine is 10 Ohms/phase and the common busbar voltage is 6.6 kV. Calculate the synchronizing torque (answer = 968 Nm).

The equation in the example problem for calculating this is:

\(\displaystyle \tau_{synch} = \frac{P_{synch}}{2\pi \frac{f}{p}}\)


\(\displaystyle P_{synch} = \frac{3}{2} \frac{E^2}{X} \times \delta'_{el}\)

I have no idea where this formula has come from. In the textbook the power of a turbo-generator is given as

\(\displaystyle P = \frac{EV}{X} \sin \delta\)

where \(\displaystyle V = E/\sqrt{3}\). However, this gives a different result. Does anyone know how the first formula is derived?