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Old Apr 9th 2018, 08:02 AM   #1
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Torque required for synchronising generators

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:

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

where

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

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?
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