EPS 2018 2019 03

Page 1

Electric Power Systems Exam #3: 04/09/2019 1° Part Exercise 1 A three-phase, four-pole, 50 Hz induction motor is supplied by a line-to-line voltage of 400 V. The windings of the induction motor are D-connected and the transformer ratio between the stator and the rotor is 𝑚 = 1.2. In normal operating conditions the motor develops at its shaft a mechanical torque of 𝑇𝑚 = 150 𝐽/𝑟𝑎𝑑, while the rotor angular speed is 1440 rot/min and the current in the rotor windings is 𝐼2 = 25 𝐴. In no-load operating conditions the motor absorbs an apparent power 𝐴0 = 3000 𝑉𝐴 with a power factor of cos 𝜑0 = 0.2. Neglecting the voltage drop in the stator windings, for the normal operating conditions, compute: 1. the mechanical power at the shaft of the motor; 2. the Joule losses in the rotor; 3. the phase resistance and reactance of the rotor windings; 4. the phasor of the current absorbed by the rotor from the supply network; 5. the efficiency of the motor; The reactive power required by the induction machine is provided by a synchronous generator (SG) while the real power is provided by the external grid ( Ext Grid, see the Figure below). The synchronous machine is characterized by synchronous reactance of 1.2 Ω and its stator phases are Y-connected. 6. compute the emf 𝐸0̅̅̅ induced in the stator windings of the synchronous generator; 7. the line current 𝐼𝐸𝐺̅̅̅̅ supplied by the external grid to the plant. Exercise 2 Consider the following electric network Line L [km] xl [/km] Vn [kV] L 10 0.4 20 Transformer An kT usc [MVA] [kV/kV] [%] T 40 20/150 10 Generator Vn Real power output: PG Operating voltage: VG [kV] [MW] [kV] G 20 30 20.8 Demand Vn Absorbed real power: PD Power factor [kV] [MW] D 20 12.5 0.95 - lagging Knowing that the External Grid (Ext Grid) is modeled as an infinite power…