AC to DC converters

Chapter 2 AC to DC Converters Outline 2.1 Single-phase controlled rectifier 2.2 Three-phase controlled rectifier 2.3 Effect of transformer leakage inductance on rectifier circuits 2.4 Capacitor-filtered uncontrolled rectifier 2.5 Harmonics and power factor of rectifier circuits 2.6 High power controlled rectifier 2.7 Inverter mode operation of rectifier circuit 2.8 Thyristor-DC motor system 2.9 Realization of phase-control in rectifier 2.1 Single- phase controlled (controllable) rectifier 2.1.1 Single-phase half-wave controlled rectifier Resistive load T VT R a ) u 1 u 2 u VT u d i d 0 ω t 1 π 2 π ω t u 2 u g u d u VT α θ 0 b ) c ) d ) e ) 0 0 ω t ω t ω t ∫ + =+== π α α α π ωω π 2 cos1 45.0)cos1( 2 2 )(sin2 2 1 2 2 2d U U ttdUU （ 2-1 ） Inductive (resistor-inductor) load a ) u 1 T VT R L u 2 u VT u d i d u 2 0 ω t 1 π 2 π ω t u g 0 u d 0 i d 0 u VT 0 θ α b ) c ) d ) e ) f ) + + ω t ω t ω t ω t Basic thought process of time-domain analysis for power electronic circuits The time- domain behavior of a power electronic circuit is actually the combination of consecutive transients of the different linear circuits when the power semiconductor devices are in different states. a ) b ) VT R L VT R L u 2 u 2 tURi t i L ω sin2 d d 2d d =+ ω t = a ， i d =0 )sin( 2 )sin( 2 2 )( 2 d ϕωϕα αω ω −+−−= −− t Z U e Z U i t L R （ 2-2 ） （ 2-3 ） Single- phase half- wave controlled rectifier with freewheeling diode load (L is large enough) Inductive a ) L T VT R u 1 u 2 u VT u d VD R i d i VD u 2 u d i d u VT i VT I d I d ω t O O O O O O π - α π + α b ) i VD R ω t ω t ω t ω t ω t g ) c ) e ) f ) d ) ω T 1 Maximum forward voltage, maximum reverse voltage Disadvantages: –Only single pulse in one line cycle –DC component in the transformer current ddVT 2 II π απ − = d 2 dVT 2 )( 2 1 ItdII π απ ω π π α − == ∫ d 2 2 dVD 2 )( 2 1 R ItdII π απ ω π απ π + == ∫ + ddVD 2 R II π απ + = （ 2-5 ） （ 2-6 ） （ 2-7 ） （ 2-8 ） 2.1.2 Single- phase bridge fully-controlled rectifier  Resistive load π ω t 0 0 0 i 2 u d i d b ) c ) d ) u d ( i d ) α α R T u 1 u 2 a ) i 2 a b VT 3 u d i d u VT 1 , 4 ω t ω t VT 4 VT 1 VT 2 Average output (rectified) voltage: Average output current: For thyristor: For transformer: ∫ + = + == π α αα π ωω π 2 cos1 9.0 2 cos122 )(dsin2 1 2 2 2d U U ttUU （ 2-9 ） （ 2-10 ） 2 cos1 9.0 2 cos122 22 d d αα π + = + == R U R U R U I （ 2-11 ） 2 cos1 45.0 2 1 2 ddVT α + == R U II π απ α π ωω π π α − +== ∫ 2sin 2 1 2 )(d)sin 2 ( 2 1 2 2 2 VT R U tt R U I （ 2-12 ） π απ α π ωω π π α − +=== ∫ 2sin 2 1 )()sin 2 ( 1 2 2 2 2 R U tdt R U II (2-13)  Inductive load (L is large enough) ω t ω t ω t ω t ω t ω t ω t ο ο ο ο ο ο ο u 2 u d i d I d I d I d I d I d i VT 1,4 i VT 2,3 u VT 1,4 i 2 , b ) R T u 1 u 2 a ) i 2 a b VT 3 u d i d VT 4 VT 1 VT 2  Electro- motive-force (EMF) load With resistor ∫ + === απ α αα π ωω π cos9.0cos 22 )(dsin2 1 222d UUttUU （ 2-15 ） a ) b ) R E i d u d i d O E u d ω t I d O ω t α θ δ [...]... ω t1 ωt ud2 u2L ud I uab II uac III ubc IV uba V uca VI ucb uab uac ωt O iVT 1 O uVT 1 uab uac ubc uba uca ucb uab uac ωt ωt O uab uac Resistive load, α= 30º ia T n VT1 VT3 VT5 d 1 id a b load c VT4 VT6 VT 2 d 2 ud α = 30 ua ¡ ud1 ub uc ã O ω t1 ud2 ud ωt І II III IV V VI uab uac ubc uba uca ucb uab uac ωt O uVT 1 u ab u ac u bc u ba u ca u cb u ab u ac ωt O ia O uab uac ωt Resistive load, α= 60º ia... a b load c VT4 VT6 VT 2 d 2 ud u d1 α = 60 º u b ua uc ω t1 ωt O u d2 ud u ab I uac II u bc III uba IV u ca V u cb VI uab u ac ωt O u VT 1 u ac uac ωt O uab Resistive load, α= 90º i a T n VT1 VT3 VT5 d 1 id a b load c VT4 VT6 VT 2 d 2 ud u1 d ua ub uc ua ub O u2 d u d O ωt u u u u bc u ba ab ac bc ba u ca u cb u ab u ac u ωt id O ωt O ia ωt O ωt iVT 1 Inductive load, α= 0º ia T n VT1 VT3 VT5 d 1 id... circuit, start from a diode circuit with the same topology The behavior of the diode circuit is exactly the same as the thyristor circuit when firing angle is 0 A power electronic circuit can be considered as different linear circuits when the power semiconductor devices are in different states The time- domain behavior of the power electronic circuit is actually the combination of consecutive transients... O I II uab uac ωt III IV V VI ubc uba uca ucb uab uac ωt id O iVT ωt O ωt 1 Inductive load, α= 30º i a T n VT1 VT3 VT5 d 1 id a b load c VT4 VT6 VT 2 d 2 ud ud1 O ud2 ud O α = 30° ua ub uc ωt1 ωt I uab II uac III ubc IV uba V uca VI ucb uab uac ωt id O ia ωt O ωt Inductive load, α= 90º ia T n VT1 VT3 VT5 d 1 id a b load c VT4 VT6 VT 2 d 2 ud ud1 α = 90° ud uc ua ω t1 O ud2 ub uab II I uac ubc ωt III... O id Id iVTO iVD1 ωt Id iVTO iVD 2 π−α 4 Id R O i2 O Id ωt π−α 3 iVDO ωt ωt α Id ωt ωt Id  Another single- phase bridge half-controlled rectifier VT1 T VT3 load u2 VT2 VT4 Comparison with previous circuit: –No need for additional freewheeling diode –Isolation is necessary between the drive circuits of the two thyristors Summary of some important points in analysis When analyzing a thyristor circuit,... cosα （2-18） 2π Thyristor voltage and currents, transformer current : I 2 = I VT = 1 I d = 0.577 I d （2-23） 3 U FM = U RM = 2.45U 2 （2-25） I VT(AV) = I VT = 0.368I d （2-24） 1.57 2.2.2 Three- phase bridge fully-controlled rectifier Circuit diagram ia T n VT1 VT3 VT5 d 1 id a b load c ud VT4 VT6 VT 2 d 2 Common- cathode group and common- anode group of thyristors Numbering of the 6 thyristors indicates the... consecutive transients of the different linear circuits Take different principle when dealing with different load – For resistive load: current waveform of a resistor is the same as the voltage waveform –For inductive load with a large inductor: the inductor current can be considered constant 2.2 Three- phase controlled (controllable) rectifier 2.2.1 Three- phase half- wave controlled rectifier Resistive load,... b VT2 c ud R VT3 O ω t1 ua ub ω t2 uc ωt ω t3 uG ud ωt O iVT1 ωt O uVT1 O ωt id Common-cathode connection Natural commutation point ωt uab uac Resistive load, α= 30º u2 ua ub uc ωt O T a VT1 b VT2 c ud R id uG ωt O ud VT3 O ω t1 iVT1 ωt O uVT1 u ωt ac O ωt uab uac Resistive load, α= 60º u2 T O a ub uc ωt VT1 b VT2 uG c ud R ua id O VT3 u ωt O iVT ωt O ωt d 1 Resistive load, quantitative analysis When... 6 2U 2 sin ωtd (ωt ) = Average load current Thyristor voltages 3 2  π π    U 2 1 + cos( + α ) = 0.6751 + cos( + α ) (2-19) 2π  6 6    Id = Ud R （2-20） 1.2 1.17 0.8 Ud/U2 1 3 0 4 2 0 30 90 60 α/(° ) 120 150  Inductive load, L is large enough ua ud O T a uc ωt α ia L b eL ud VT2 c VT3 ub id O ωt O ωt O ωt O ωt ib R ic id uVT 1 O uac uab uac ωt 1 Ud = 2π 3 5π +α 6 π +α 6 ∫ 3 6 2U 2 sin ωtd... uac ωt id O ia ωt O ωt Inductive load, α= 90º ia T n VT1 VT3 VT5 d 1 id a b load c VT4 VT6 VT 2 d 2 ud ud1 α = 90° ud uc ua ω t1 O ud2 ub uab II I uac ubc ωt III uba IV uca V ucb VI uab ωt O uVT 1 uac uac uac ωt O uab . Chapter 2 AC to DC Converters Outline 2.1 Single-phase controlled rectifier 2.2 Three-phase controlled rectifier 2.3 Effect of transformer leakage inductance on rectifier circuits 2.4 Capacitor-filtered. rectifier 2.5 Harmonics and power factor of rectifier circuits 2.6 High power controlled rectifier 2.7 Inverter mode operation of rectifier circuit 2.8 Thyristor -DC motor system 2.9 Realization of. thyristors load T u 2 VT 2 VT 4 VT 1 VT 3 Summary of some important points in analysis When analyzing a thyristor circuit, start from a diode circuit with the same topology.