EPS 2022 01

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Electric Power Systems Exam #1: 28/06/2022 1° Part Exercise 1 In the figure bellow a three -phase demand (D) is supplied by a power plant made of two synchronous generators, SG1 and SG2, respectively, through the electric line L. The demand is supplied at line-to-line voltage of 𝑉𝑠𝑢𝑝𝑝𝑙𝑦 = 9.8 [kV] and absorbs 𝑃𝐷 = 4 [MW] with a lagging power factor cos 𝜑𝐷 = 0.92. Initially, breaker B connecting SG2 to the network is opened so generator SG2 is offline. The electric line is characterized by 𝑅𝑙 = 0.5 Ω and 𝑋𝑙 = 1.5 Ω. The synchronous generator nameplates specify the following data: SG1 SG2 Nominal apparent power MVA 6 5 Nominal operating voltage (line-to-line) kV 10 10 Phase synchronous reactance Ω 20 15 Maximum turbine mechanical power MW 5.5 4.5 Emf 𝑬𝑬 (phase-to-ground) at maximum excitation current kV 11.5 6.65 Stator windings connection - Delta Y(Star) Determine: 1. the line-to-line voltage at the power plant terminals (busbars) and the real and reactive power supplied by the synchronous generator SG1 to the grid; 2. the emf 𝐸0 and the load angle (𝛿) of the synchronous generator SG1; 3. check the capability curve of the synchronous generator SG1 in the given operating conditions; 4. determine the maximum reactive power ( 𝑄𝑆𝐺1 max ) that the machine can produce when operated at the electrical power previously obtained. 5. considering breaker B closed and, thus, SG2 in operation and in no -load conditions, find the minimum reactive power SG2 needs to produce so that SG1 capability curve is satisfied and the power plant works in the same operating conditions determined previously. Exercise 2 Consider the following electric network Line L [km] xl [/km] Vn [kV] L 10 0.4 20 Shunt Capacitor Xc [] Vn [kV] C 200 20 Transformer An kT usc [MVA] [kV/kV] [%] T 5 20/150 12.5…