EPS 2019 2020 01

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Electric Power Systems Exam #1: 30/06/2020 1° Part Exercise 1 The power plant PP depicted in the figure bellow consists of two identical generation groups (synchronous machine SG and transformer T) characterized by the following data: Transformer T: Nominal power 50 (kVA) Nominal transformer ratio 15/3.8 (kV/kV) Short-circuit voltage (vsc) 10 (%) Synchronous machine SG: Nominal power 45 (kVA) Nominal voltage (line-to-line) 3.8 (kV) Stator winding connection Star Synchronous reactance (xs) 45 () Synchronous resistance (rs) 5 () Maximum turbine mechanical power 40 (kW) Maximum electromotive force (phase) 2.7 (kV) The power plant PP operates at a line-to-line voltag e 𝑉𝑃𝑃 = 14.5 + 0.2 ∙ 𝑵 (kV) and produces a total real power of 𝑃𝑃𝑃 = 60 + 2 ∙ 𝑵 (kW) with a lagging power factor of cos 𝜑𝑃𝑃 = 0.90. Moreover, as depicted in the figure, the complex power produced by the power plant is evenly distributed between the two generation groups. For the given operating conditions: 1. determine the real and reactive powers produced by each SG (𝑃𝐺1/𝑄𝐺1 and 𝑃𝐺2/𝑄𝐺2); 2. determine the magnitudes of the line-to-line voltages at the terminals of the two SG, 𝑉𝐺1 and 𝑉𝐺2; 3. determine the phasors of the emf of the two SG (𝐸𝐺1̅̅̅̅̅ and 𝐸𝐺2̅̅̅̅̅); 4. draw, in a qualitative manner, the phasor diagrams of both SG; 4. determine the mechanical power of the turbines of each SG; 5. check the capability limits for both SG; In the above data, N is the last number of the student’s Person Code/Codice Persona (e.g. if Person Code is 10381486 then N = 6); Please substitute accordingly. Exercise 2 Consider the following electric network Line xl [p.u.] L1 0.1 L2.1 0.08 + 0.1∙N L2.2 0.18 Generator Real power output: PG Operating voltage: VG [p.u.] [kV] G 1.25 1.02 + 0.02∙N Demand Absorbed apparent power: AD…