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By R. T. Compton

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10). To obtain a time solution for the rotor angle, we need to develop expressions for the mechanical and the electrical powers. In thi s sect ion the simplest mathematical model is used. This model, which will be referred to as the classical model, requires the following assumptions: I. The mechanical power input remains constant during the period of the transient. 2. Damping or asynchronous power is negligible. 3. 1). 4. The mechanical angle of the synchronous machine rotor coincides with the electrical phase angle of the voltage behind transient reactance.

These equations are nonlinear; therefore, time solutions will be obtained by numerical methods. A partial survey of these methods is given in Appendix B. To illustrate the procedure used in numerical integration, the modified Euler method is used in this example. This method is outlined in Appendix B. l . l. These are called the predicted values of the variables and are based only on the values of 0(1), w(l), and their derivatives. l are calculated. l) is obtained using the mean derivative over the interval.

Q. Fig. 6 Representation or a synchronous machine by a constant voltage behind trans ient reactance. The constant voltage source Ell. • pretransient conditions . During the transient the magnitude E is held constant, while the angle 0 is considered as the angle between the rotor position and the terminal voltage V. 8 PF. Solution Using Vas reference. 2 pu. 6 E = Ell. 1314. This will be held constant during the transient, although 8 may vary. The initial value of 8. 13° . 24 Chapter 2 During the transient period, assuming that V is held constant, the machine power as a function of the angle 0 is also given by a power-angle curve.

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