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D. (! ) is the equivalent damping coefficient J. ( P IS 2 = 2~m, is the mechanical torque of the equivalent two pole machine The above equation represents the transformation of 'P' pole machine 2 to a 2 pole machine. The mechanical torque is reduced by a factor of p. ) 2. However, since all the equations are expressed in per unit (to be introduced later) there is no loss of generality in assuming that the machine has two poles (as stated earlier). 3 Park's Transformation The combined voltage equations (for the stator and the rotor) can be expressed as 3.

1 . 8 . 25 sin(}2 = The stability limit is also given by P emax ViV2 . - - sm((}l - (}2) X 1. 91°) O. 7204 pu. emax - - - cos I ( ) Xl X + X2 29 2. 111. It can be verified that p. 4 EgEb _ emax - (Xl + X + X2) Analysis of Transient Stability The transient stability pertains to stability under large disturbances. Hence the nonlinearities of the model have to be considered in the analysis. As analytic solutions are not available for the swing equation, numerical methods have to be used. 1 Numerical solution - Point-by-Point Method: Point-by-point (also called step-by-step) solution allows the numerical solution of the swing equation.

The detailed component models - synchronous machine, excitation and prime-mover controllers, loads, transmission lines and SVC are taken up in the next three chapters. 0. u. Assume ideal regulator. The phasor diagram is shown in Fig. 22. e-- EqEbSin8 _ VgEb . (x q Eq is the voltage behind + xe) x q . 11 From (A), E = Vg(Xq q + xe) sinO (0) sino Xe Pe is maximum when 0 = 90°. u. 900 < 0* < 1800 Xq It is interesting to note that the critical angle (corresponding to stability limit) is greater than 90°.

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