AY 2019 20 Test 2 Numerical part with solutions

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ELECTRIC CONVERSION FROM GREEN SOURCES OF ENERGY Prof. Alberto Dolara Numerical exercise 1 < 21 July 2020 > The numerical data of this problem depend on your ID number, as follows: Example: ID number = 10123456 → U = 1, V = 2; W = 3; X = 4; Y = 5; Z = 6. Numerical data that depend on your ID number are highlighted by the symbol “←” along the text. A large offshore wind farm is connecter to the mainland electrical grid by means of a high voltage DC (HVDC) cable. The output of wind generators is AC three-phase, with the following ratings: ► Wind generators grid voltage, VW 30 kV ► Wind generators grid frequency, fW 50 Hz The mainland utility grid is AC three-phase, with the following ratings: ► Utility grid voltage, Vgrid 100 kV ► Utility grid frequency, Vgrid 50 Hz The HVDC cable is interconnected to both AC grids my means of l ine frequency phase controlled converters based on thyristors (three-phase, full bridge configuration). The ratings of the HVDC cable are the following: ► DC voltage, VHVDC 200 kV ► DC current, IDC,max 400 A ► Electrical resistance, RHVDC 20 Ω The offshore AC grid voltage may vary within the range from -15 % to +15 % of its rated voltage. The offshore converter has to keep the DC voltage constant at VHVDC = 200 kV any allowed AC grid voltage. The mainland AC grid voltage may vary within the range from -5 % to +5 % of its rated voltage. The mainland converter can operate with a maximum firing angle of 165°. Calculate: 1. The rated primary and secondary voltage, as well as the apparent power, of the offshore transformer. Assume ideal transformer. 2. The rated primary and secondary voltage, as well as the apparent power, of the mainland transformer (neglect the voltage drop across the HVDC cable, then assume a DC voltage equal to 200 kV). Assume…