Power Electronics (25) Please prepare your student ID card (with photo) on your desk for the attendance check.

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1 Depatment of Powe Electoncs and Electcal Dves Pof D ng Joachm Böcke Powe Electoncs Suname Student numbe Fst name Couse of study Task (Ponts) Total (100) Mak Duaton 120 mnutes Pemtted esouces a non pogammable calculato wthout gaphc dsplay dawng mateals (compasses, potacto, ule, pens ) Please note Please pepae you student D cad (wth photo) on you desk fo the attendance check Please label each exam sheet wth you name and student numbe Use a new exam sheet fo each task Do not use pencls o ed pens Wth numecal calculatons, the unts must be consdeed n evey step Not followng that ule wll esult n deducton of ponts All solutons must be clealy documented and wheeve equed explaned The enty of a mee fnal esult wthout any appoach wll not be counted You can only take pat n the exam, f you ae egsteed n the PAUL system f you take pat wthout egstaton, the exam esult wll not be consdeed Good Luck Powe Electoncs Fnal Examnaton WS Page 1 of 5

2 Depatment of Powe Electoncs and Electcal Dves Pof D ng J Böcke Task 1 Buck Boost Convete (25 Ponts) Fgue 1 shows a convete whch can be called buck boost convete The nput voltage to the convete s U 1 = 10 V The convete supples a DC load cuent of 5 A at the output The powe swtches ae assumed to be deal dung conducton and blockng states (0 V dung conducton and 0 A n blockng) The convete s opeated at a swtchng fequency of 10 khz The capactance of the capacto C s 100 μf Fgue 1 Buck Boost convete f the duty cycle of swtch S 1 s chosen as 025, estmate the followng 11 The DC contents of the nput cuent 1 and of the output voltage u 2 12 Evaluate the equed nductance L to lmt the pple cuent of 1 to 20% of the DC content (assume the output voltage appoxmately constant) 13 Fo what value of the nductance L does the convete opeate at the bounday between contnuous and dscontnuous conducton modes? 14 Sketch the cuent though the capacto C (assume the load cuent appoxmately constant) 15 Sketch u C 16 Detemne the peak to peak voltage pple acoss the capacto C Powe Electoncs Fnal Examnaton WS Page 2 of 5

3 Depatment of Powe Electoncs and Electcal Dves Pof D ng J Böcke Task 2 Boost convete (25 Ponts) Fgue 2 shows a non deal boost convete The souce and nducto esstances ae epesented by R 1 and R L espectvely The swtches S 1 and D 1 ae assumed to be deal The state vaables ae the nducto cuent L and capacto voltage u 2 The ccut s to be opeated n contnuous conducton mode Fgue 2 Boost convete 21 Wte down the dffeental equatons of the complete system fo the two state vaables dung ON state, e when S 1 s ON 22 Wte down the dffeental equatons of the complete system fo the two state vaables dung OFF state, e when S 1 s OFF 23 Usng the above, wte down the aveaged dynamc model of the convete n state space matx notaton 24 Deve the gan /U 1 at steady state as a functon of duty cycle 25 Evaluate the effcency of the convete based on the aveage modelng, η= ( )/(U 1 ) Powe Electoncs Fnal Examnaton WS Page 3 of 5

4 Depatment of Powe Electoncs and Electcal Dves Pof D ng J Böcke Task 3 Fou Quadant Convete (25 Ponts) A fou quadant convete (4QC) s connected to the sngle phase gd The ovehead lne delves a sngle phase snusodal AC voltage wth gd fequency The two fou quadant convetes ae opeated n nteleavng opeaton to mnmze the cuent pple The tacton tansfome has two pmay wndngs connected n paallel and two seconday wndngs Fgue 3 Powe supply fo an electc locomotve Nomnal output voltage 18 kv Relatve shot ccut voltage 19% (each seconday) Nomnal output powe 24 MW Swtchng fequency 500 Hz Gd voltage 25 kv Gd fequency 50 Hz 31 Daw the ccut dagam of a fou quadant convete, whee the semconductos ae teated as deal swtches 32 Daw qualtatvely the swtchng functons of the 4QC swtches of two paallel fou quadant convetes n nteleavng opeaton Daw the tansfome seconday voltages esultng fom the two fou quadant convetes fo a fundamental peod 33 Calculate the leakage nductances of the tansfome Assume that the pmay leakage nductances can be neglected Assume that the appaent powe of the tansfome s 26 MVA 34 The two fou quadant convetes should be contolled that way that only actve powe s suppled fom the gd (taget powe facto mode) Detemne the phase angle of the equed fundamental phasos of u 21, u 22 Consde the case of ated load at nomnal nput voltage 35 Calculate the mnmum equed tansfome wndng ato fo the case of Calculate the peak voltage stess n the tansstos and the dodes of the 4QC Explan n wods what has to be done to calculate the peak cuent stess (calculaton not mandatoy) Powe Electoncs Fnal Examnaton WS Page 4 of 5

5 Depatment of Powe Electoncs and Electcal Dves Pof D ng J Böcke Task 4 Lne Commutated Convete (25 Ponts) A 3 pulse thysto contolled convete s connected to the 3 phase gd va a Dy tansfome confguaton and supples a DC moto The moto can be epesented by an equvalent ccut consstng of a DC voltage U g and a essto R of 28 Ω The nomnal value of the lne voltage on the pmay and seconday s 400 V Fgue 4 Lne commutated convete n M3 confguaton Assumng neglgble losses and deal commutatons answe the followng 41 Assume steady state condton and DC load voltage s zeo a) Sketch the voltage u d fo a contol angle 45 Use the soluton sheet n next page fo the sketch b) Calculate the maxmum and aveage value of the load cuent at Assumng a DC output voltage U g whch s not zeo but appoxmately constant u g = U g, calculate U g a) fo the case of a load cuent d, whch s at the bode between contnuous and dscontnuous conducton mode at a contol angle of 45 b) whch ensues an aveage load cuent of d = 70 A at the maxmum output voltage 43 Consde the stat up of the system The contol angle s constantly 0, the gate s fst tggeed at 30 (efe to soluton page) Sketch on the soluton page the nstantaneous load cuent d (t) n the nteval fom t = 0 to t = 45 ms, f the counte voltage u g (t) ses as show n the fgue Assume that the commutatons ae deal and nstantaneous, and the ntal condton s d (0) = 0 Powe Electoncs Fnal Examnaton WS Page 5 of 5

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