AY 2020 21 Test 5 Numerical part with solutions

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ELECTRIC CONVERSION FROM GREEN SOURCES OF ENERGY Prof. Alberto Dolara Numerical exercise 1 < 18 February 2022 > Consider a wind turbine in the full converter configuration with a Permanent Magnet Synchronous Generator (PMSG) in the figure below. 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 three-phase transformer . The turbine shaft is mechanically connected to the PMSG with a gearbox that multiplies the turbine speed (Ωt). The main ratings of this power conversion system are: ► PMSG number of poles, p 48 poles ► PMSG speed/voltage ratio, kV 1.15 V/rpm ( Eline-to-neutral,RMS = kV ∙ Ωm) ► PMSG synchronous reactance, Xs 0.1 Ω @50 Hz ► Wind turbine gearbox ratio, τG 64 ► Transformer: rated low voltage, VLV,n 330 V ► Transformer: rated high voltage, VHV,n 15 kV ► Transformer: rated frequency, fn 50 Hz Calculate: 1. The minimum turbine speed ( Ωt) that allows the inverter to operate in linear region. Assume ideal converters. Now assume the following operating conditions: ► DC-link voltage, VDC 650 V ► MV grid voltage, VMV 15.3 kV ► Turbine speed, Ωt 4.6 rpm ► Inverter input power, Pinv 240 kW Calculate: 2. The PMSG output frequency, fPMSG . 3. The firing angle, α, of the thyristor controlled rectifier. Take into a ccount the voltage drop due to source inductance. 4. The inverter amplitude modulation ratio, ma. 2 Solution 1. Minimum turbine speed (Ω t) that allows the inverter to operate in linear region. Assume ideal converters. The minimum DC-link voltage that allows the inverter to operate in the linear region is: , , 2 2 538.89V 3 DC min…