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1. i. A newly installed generator in a power station needs to be synchronized with the power grid through a lossless transmission line. Assume that the voltage and frequency of the power grid is not affected by the change in load. Develop the equations for the complex power and the maximum power that can be transferred through the [5] transmission line. Also draw a figure for the above mentioned system by assuming that the parameters are lumped in the circuit. ii. Justify why the error in speed should be zero in a synchronous machine with the help of an equation. [2]

Answer 1

[Page-L) 01. (1) Solna the lossless dramsmission Suppose, impedance of time = jxe pou impedance of the generator = 3xg p.u. • Voltage and frequency of power grid is not affected by the load - So, we can modele the power grid as imfinite bus i.e source with zero impedance, Assume, generator emf is ELS P.lu and imfimide bus (power grid) voldage = Vlo' piu' Here we consider power grid as reference So, we have fake angle =09 Single lime diagram can be dracum ass VIO . ELE тэх, IXg from generator Current I going to power grid (newly installed) is given by - ELS - ULO ( x +1)279 hamiled ath CamScanner

[Page-2/ ELS-90 - Xetxo VL-90' Xe +Xg complexe power, s, delivered to power arid by newly installed generator is given by SEVI* this demote conjugate. se to [6270-8 - V +90] VEL90-8 v² X, 7Xg 29 Xe tXg Comprese Powen. L .Real lower, Po Cosc9018) , cosao P = ng Simg {::c920 = 0] Rreative power, Q = VE Sim (90-8) – 1 y singo Stoned with CamScanner

dramspen from Page 3 maximum Real power that can be the tramsmission time at P= Very Sims. "maximum of above equation occur when Sims is maxinan i.e at 8=90 Sim 8 = 1. Ponase = VE 7 can be power that transfer is given : maximum As given in part i frequency of the system is constant (i.e mot vary with respect to load). and we know that, Synchronous Speed Synchronous machime rum at • speed of Pole synch ponous machine depends on which is fixed onces construction B is completed. ed with CamScanner

Page-45 f - frequency a which is given as constant with load Variation. So from the above equation we can conclude that speed error will be Zero. fisced as No = 120 fc . pe fixed speed is also finced. So, Ns - . i.e error in speed = Zero. CScared with CamScanner