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(McGraw-Hill) (Instructors Manual) Electric Machinery Fundamentals 4th Edition Episode 2 Part 6

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Tham khảo tài liệu '(mcgraw-hill) (instructors manual) electric machinery fundamentals 4th edition episode 2 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Appendix C Salient Pole Theory of Synchronous Machines C-1. A 480-V 200-kVA 0.8-PF-lagging 60-Hz four-pole Y-connected synchronous generator has a direct-axis reactance of 0.25 Q a quadrature-axis reactance of 0.18 Q and an armature resistance of 0.03 Q. Friction windage and stray losses may be assumed negligible. The generator s open-circuit characteristic is given by Figure P5-1. a How much field current is required to make Vt equal to 480 V when the generator is running at no load b What is the internal generated voltage of this machine when it is operating at rated conditions How does this value of EA compare to that of Problem 5-2b c What fraction of this generator s full-load power is due to the reluctance torque of the rotor Solution a If the no-load terminal voltage is 480 V the required field current can be read directly from the opencircuit characteristic. It is 4.55 A. b At rated conditions the line and phase current in this generator is P 200 kVA IA Il -_ Tt-7 T 240.6 A at an angle of -36.87 V3 Vl 73 480 V 295 E Vộ RaI a jXq IA E 277Z0 0.03 Q 240.6Z- 36.87 A j 0.18 Q 240.6Z- 36.87 a eA 310Z5.61 V Therefore the torque angle s is 5.61 . The direct-axis current is Id IA sin 0 s ZS- 90 I d 240.6 A sin 42.48 Z- 84.4 I d 162.5 Z- 84.4 A The quadrature-axis current is Iq IA cos 0 s ZS I q 240.6 A cos 42.48 Z5.61 E 177.4 Z5.61 A q Therefore the internal generated voltage of the machine is E A Vộ RaI a jXd Id jXqIq Ea 277Z0 0.03 240.6Z-36.87 j 0.25 162.5Z-84.4 j 0.18 177.4Z5.61 E A 322Z5.61 V E A is approximately the same magnitude here as in Problem 5-2b but the angle is about 2.2 different. c The power supplied by this machine is given by the equation p-3Vộ E 3V2 Xd - Xq Ì P sin o sin 2o Xd 2 XdXq D_ 3 277 322 . o 3 277 2 0.25 - 0.18 P _ - sin 5.61 v I _ -7- I sin 11.22 0.25 2 0.25 0.18 J P 104.6 kW 34.8 kW 139.4 kW The cylindrical rotor term is 104.6 kW and the reluctance term is 34.8 kW so the reluctance torque accounts for about 25 of the power in this .