AY 2021 22 Test 3 Numerical part with solutions

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ELECTRIC CONVERSION FROM GREEN SOURCES OF ENERGY Prof. Alberto Dolara ©Prof. Alberto Dolara – All rights reserverd Numerical exercise 1 < 31 August 2022 > Consider the power conversion chain of a wind turbine in the full converter configuration in the figure below. The turbine shaft is mechanically connected to the PMSG with a gearbox. The electrical machine is a 8-pole Permanent Magnet Synchronous Generator (PMSG). The static powe r processor is composed by the cascade connection of an AC/DC three-phase diode rectifier , a unidirectional DC/DC converter and a three-phase full-bridge PWM inverter . At the end of the power conversion chain, a three-phase transformer adjust the voltage level to allow the connection to a 33 kV - 50 Hz Medium Voltage (MV) three-phase grid. Main ratings are reported in the follow: ► Wind turbine Minimum speed 5 rpm ► Wind turbine Maximum speed 23 rpm ► Gearbox Gear ratio, GR 72 (multiplies the turbine speed ( Ωt) by 72) ► PMSG Voltage constant, kV 0.81 V/rpm (V = kV ∙ Ωm) ► Transformer Voltage ratio, VLVn /V MVn 0.69/33 kV ► MV grid Voltage range, VMV 33 kV ± 10% Assume all the converters to be ideal. Preliminary Definitions and Calculations 1. Calculate the minimum voltage at the inverter DC te rminals that allows the inverter to operate in the linear region for any allowable value of the MV voltage (neglect the AC low frequency filter voltage drop). 2. According to the minimum voltage at the inverter DC terminals previously calculated, define the type of DC/DC converter that allows the entire system to operate for any turbine speed within the allowed range. Characterization of an Operating Conditions Assume the following operating conditions: ► Wind turbine speed, Ωt 18 rpm ► Grid voltage, VMV 34.5 kV ► Inverter power factor, cos (ϕinv )…