Question

For the questions on this page, assume that that an induction motor is rated to deliver 10kW (approximately 13.3HP} when operated at 240VRMS 60Hz. The motor has a lagging power factor of 0.8. The building electrical service only supplies 208VRMs, so the motor can not be connected directly to the electric service. An ideal transformer is used to create the 240VRMs required by the motor. N:N, IM + Vs M What turns ratio does the transformer need to have? What is the magnitude of source current Is (in A)? What is the magnitude of motor current In (in A)? What is the magnitude of complex power transferred through transformer's magnetic field (in KVA)? Now, assume that instead a step-up autotransformer is used to power the motor. İM N2 llllll + IN Vs M İPRI What is the required turns ratio (N>/N) required? Hint: With an autotransformer, step-up does not require Nz >N1, because the output voltage is developed across all (N2 + N) turns. What is the magnitude of source current Is (in A)? What is the magnitude of motor current In (in A)? What is the magnitude of autotransformer primary current IPRI (in A)? What is the magnitude of the complex power transferred through autotransformer's magnetic field (in KVA)? Hint: The magnetically-coupled power is the power absorbed by the primary part (N1 turns) of the coil, or the power supplied by the secondary part (N2 turns) of the coil. For this and the next question, assume that we place the capacitor in parallel with the motor. What is the required change in total reactive power in KVAR) in order to improve the power factor to 0.95 lagging?

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Answer 1

is = I, N,:"₂ im 12 + is 311 of * motor pocuer ne connected at secondary the transformer PS lokW M * Secondary roctage rouren is supplied to by * coms) motor is 240 motor power factor, cosa = oud Clagging) The transformer is supplied v = 208 Crne) Cerinary Solution! • Tuan's ratto N: H₂ r : 2 Vs voet off ) . 208 : 240 N: Haz 13:157 * Pm = V2 Iz cosa - (240) C2 (0-8) Pn (240) (0,8) (okw >> (240 108) I. 5 2.083 A 2 In case ideal trune former N2 V2 U eiland (V, II → IS 13 5-2.083 A is- xs-2.083 A » 11 60, 026 A Hence, magnitude of source current is = 1,5 60.096 A and magnitude of motor current im = {27 S-2.083 A 82 2 of for ideel transformer Input power supplied = output power received Р. orSi Transformer kVA P = Pm = lokw or) complex power rah costa cosda cos & P2 1okW (8) 12.5 kVA 2 12.5kVA > S. - SL Hence, complex power transferred through magnetic field Si - Sz 12.55 kVA