Question

QUESTION 1 (30 points) A high voltage distribution line of 25kV (RMS line to line) is supplied by a generator. The system is shown in Fig. 1.1. synchronous Synchronous motor Distribution Line (3) Synchronous generator Load 2 Load 1 Figure 1.1 The line frequency is 60HZ. Two loads are connected to the line. Load 1 is a bank of 50n resistors connected in star (Y). Load 2 is a bank of 12uF capacitors connected in delta (A). A synchronous motor is also connected to the line. Both machine parameters are presented in table 1.1 Synchronous motor Synchronous generator Parameter 0.350 1.20 Synchronous reactance (Xs) Negligeable Negligeable Armature resistance (RA) 42 40 Machine constant (K) 10 Number of poles (P) Flux () See question b) Not specified Y (star) Y (star) Connexion Table 1.1 By using all the parameters described before, answer the following questions: a) Compute both real and reactive powers drawn by loads 1 and 2. (10 pts) b) If the flux in the synchronous motor is set to 3.1Wb and the active power delivered by this motor is 75MW, compute the power factor of the synchronous generator. (15 pts) c) By using the conditions obtained in question b, compute the torque angle of the synchronous generator. (5 pts)

Answer 1

Date Paoe Sene Gun Spaes Load2 Coad 1 Loo d - Sor Swz 260000/0 25000 Linu vaitoye So phau I 00 urront CI) CPer phan) 5000 Bx S0 E288.625b lo A Hcue pouer 31,RE 12.S mu Pepshiue " 2 80.675 10 A

for (aad 2 12uf Co 221-0432 12tr F Vin Vna 25000 10 = lurrent pen phow for loal2 25000 - 221-0485 0919 113.092c 190° Line Caurred leode proxe Currens Ize Tuias B3.09d 190 +30 95.89 11204 hetiue Pearru coniumid O pauser =-3x25000 113.09 Reauriu pouun -848MVAR

tar modo Pez phas eq chi- O.35 2 25000 M12ο Jb0160 ά -1 30 IT- G4.247radle Wz2n N 60 dt 3.lwh S kdw - 42 &3.1 x 94.247 EE12270 969 3 VafSis Nt paus ta uen by moter = 35 K10-3X 25000 122 70.969 SinS O-35 >Sin &= O.0494 - 2.8310

Date Page Iurkent tohan by motu Leb Caluiot 2500 0 10-14(i0 VB 2270 9 59 283 sh7 5- 99 89h9 t 11 2 88351 195.89 /120 + 6458-667 /-74.4480 E2 6360.S0& 1-7I.38 Cen Per phau lood 2 5000 10 Voitee toed @ Ser generate 7-22 T

Dete Pooe 0-3027 ECos 12.38

To ind toxaus angle wehour to find &LG = +6350 S081-12.38 x.252 29000 10 toraue aye= So