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Electric Machinery Fundamentals (Solutions Manual) Part 9

Tham khảo tài liệu 'electric machinery fundamentals (solutions manual) part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | P 3 3 211 V 429 V V E------------------ 1.5 238 kW max max X d Since E A must be decreased linearly with frequency the maximum value at 300 r min would be 15 Hz E _ 429 V129 V A 300 50 Hz e If the applied voltage V is derated by the same amount as EA then V 15 50 211 83.1 V. Also note that X S 15 50 1.5 0.45 . The maximum power that the motor could supply would be P 3 V E 83.1 V 129 v max Xs 0.45 11.5 kW f As we can see by comparing the results of c and e the power-handling capability of the synchronous motor varies linearly with the speed of the motor. 6-7. A 208-V Y-connected synchronous motor is drawing 40 A at unity power factor from a 208-V power system. The field current flowing under these conditions is 2.1 A. Its synchronous reactance is 0.8 . Assume a linear open-circuit characteristic. a Find the torque angle . b How much field current would be required to make the motor operate at 0.8 PF leading c What is the new torque angle in part b Solution a The phase voltage of this motor is V 120 V and the armature current is IA 40 0 A Therefore the internal generated voltage is . E VB I A 120 0 V S R jX 40 0 a Ea EA 124 14. V o The torque angle of this machine is -14.9 . b A phasor diagram of the motor operating at a power factor of 0.18 leading is shown below. P I A2 1A1 V V jX I A S A jX I S A 0 P E A 1 A2 Since the power supplied by the motor is constant the quantity I A cos I which is directly proportional to power must be constant. Therefore I A2 0.8 40 A 1.00 159 IA2 50 36 87 A The internal generated voltage required to produce this current would be 2 E V R . . jX J _ 7 J EA2 J 20h 0 V 5 36.87 A7 EA2 147.5 12. V The internal generated voltage E A is directly proportional to the field flux and we have assumed in this problem that the flux is directly proportional to the field current. Therefore the required field current is E 147-V 7 .7 A 3.20 A 2 E A F 1 24 V c The new torque angle of this machine is -12.5 . 6-8. A synchronous machine has a synchronous .