EPS 2018 2019 01

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Electric Power Systems Exam #1: 02/07/2019 1° Part Exercise 1 In the figure bellow (a.) a three-phase induction motor (IM) is supplied by a external grid (EG) through the electric line L. a. b. The induction motor nameplate specifies the following data: Nominal mechanical power 65 kW Nominal supply voltage 6.0 kV Nominal stator current 8 A Nominal mechanical speed 970 turns/min Number of poles 6 Stator/rotor phases connection Y Stator phase resistance 15 Ω The electric line is characterized by 𝑅𝑙 = 5 Ω and 𝑋𝑙 = 15 Ω. Moreover, the induction motor operating in no-load conditions absorbs from the network a line current of 2.5 A with a power factor of cos 𝜑0 = 0.12 - lagging. Neglecting the mechanical losses in the induction motor, considering the iron losses in the induction motor constant and considering the induction motor operating in nominal operating conditions, determine: 1. the iron losses in the induction motor IM; 2. the Joule losses in the stator and rotor windings of the induction motor IM; 3. the real and reactive power absorbed by the induction motor from the electrical grid (PM and QM in Fig a.); 4. the real and reactive power supplied by the external grid EG at the sending end of the electric line L (PEG-L and QEG-L in Fig a.) and the line to line voltage at the sending end of the electric line L (VEG in Fig a.); 5. Considering the addition of the synchronous generator SG at the terminals of EG (Fig. b) and that the EG will supply the entire real power required by the induction motor IM at cos 𝜑𝐸𝐺 = 0.95 – lagging, find the real and reactive power injected by the synchronous generator SG (PSG and QSG in Fig b.); 6. knowing that SG is characterized by a synchronous reactance 𝑋𝑠 = 21 Ω and that it’s stator windings are D- connected, calculate the emf 𝐸0 and…