AY 2019 20 Test 4 Numerical part with solutions

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ELECTRIC CONVERSION FROM GREEN SOURCES OF ENERGY Prof. Alberto Dolara Numerical exercise 1 < 29 January 2021 > 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. Consider a wind turbine in the full converter configuration with a 48- pole Permanent Magnet Synchronous Generator (PMSG). The power processor is composed by the cascade connection of a AC/DC three -phase thyristor controlled rectifier and a three -phase full-bridge PWM inverter, sharing a common DC -link. The output terminals of the wind turbine are connected to the Medium Voltage (MV) grid by means of a 330 V/15 kV – 50 Hz three-phase transformer. The turbine shaft is mechanically connected to the PMSG with a gearbox that multiplies the turbine speed (Ωt) by 64. Calculate: 1. The minimum DC-link voltage that allows the inverter to operate in the linear region (assume ideal transformer and ideal inverter). 2. The minimum turbine speed (Ωt) that allows the system operation (i.e. the inverter operates in linear region). The output voltage (V) vs. PMSG rotor speed (Ωm) curve is V = kV ∙ Ωm, with kV = 1.9 V/rpm. Now assume the following operating conditions: ► DC-link voltage VDC = (825 + 5 ∙ Y) V; ← ► MV grid voltage VMV = 14.8 kV; ► Turbine speed Ωt = 7 rpm. Calculate: 3. The firing angle, α, of the thyristor controlled rectifier. 4. The inverter amplitude modulation ratio, ma. 5. The Permanent Magnet Synchronous Generator output frequency, fPMSG. 1 0 U V W X Y Z 2 Solution 1. The minimum DC-link voltage that allows the inverter to operate in the linear region is: ,, 22 538.89 V 3 DC min AC LVVV = = 2. Minimum turbine speed…