Basic thought process of time-domain analysis for power electronic circuits 4 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 VT L L u2 R R L+Ria=√2U2 sin ot (2-2) dt )t=a, (r-a) sin(a-e sin(at-)(2-3)
Power Electron cs i 6 Basic thought process of time Basic thought process of time -domain analysis for power electronic circuits analysis for power electronic circuits The time The time -domain behavior of a power electronic domain behavior of a power electronic circuit is actually the combination of consecutive circuit is actually the combination of consecutive transients of the different linear circuits when the transients of the different linear circuits when the power semiconductor devices are in different states. power semiconductor devices are in different states. a) b) VT R L VT R L u2 u2 Ri U t t i L 2 sin ω d d d 2 d + = (2-2) ωt = α ，i d= 0 sin( ) 2 sin( ) 2 2 ( ) 2 d α ϕ ω ϕ ω α ω = − − + − − − t Z U e Z U i t L R (2-3)
E Single-phase half-wave controlled rectifier with freewheeling diode Inductive load( L is large enough) T t L dvT 丌 丌+C dvdr (26) f) V2I ∫mrad 2-7) 2丌+a 丌+a VDR d(or) d(28) 丌 2 4 Maximum forward voltage, maximum reverse voltage 4 Disadvantages: Only single pulse in one line cycle DC component in the transformer current 7
Power Electron cs i 7 Single -phase half phase half-wave controlled wave controlled rectifier with freewheeling diode rectifier with freewheeling diode Maximum forward voltage, maximum reverse voltage Maximum forward voltage, maximum reverse voltage Disadvantages: antages: – Only single pulse in one line cycle Only single pulse in one line cycle – DC component in the transformer current Inductive load (L is large enough) Inductive load (L is large enough) VT i a) T u 1 u 2 u VT L R d ud VD i R VD R u2 ud i d uVT iVT Id I d ωt 1 ωt ωt ωt ωt ωt O ωt O O O O O π - α π + α b) c) d) e) f) g) iVD R dVT d 2 I I π π − α = d 2 VT d 2 ( ) 2 1 I I d t I π π α ω π π α − = = ∫ dVD d 2 R I I π π + α = d 2 2 VD d 2 ( ) 2 1 R I I d t I π π α ω π π α π + = = ∫ + (2-5) (2-6) (2-7) (2-8) DC component in the transformer current
F2.1.2 Single-phase bridge fully-controlled rectifier Resistive load T R e For thyristor: maximum forward voltage maximum reverse voltage 事 Advantages 2 pulses in one line cycle No dc component in the transformer current
Power Electron cs i 8 2.1.2 Single -phase bridge phase bridge fully -controlled rectifier controlled rectifier π ωt ωt 0 ωt 0 0 i 2 ud i d b) c) d) ud (i d ) α α uVT1,4 Resistive load Resistive load d R T u1 u2 i 2 a b VT 1 VT 3 VT2 VT4 ud i a) For thyristor thyristor: maximum forward voltage, maximum reverse : maximum forward voltage, maximum reverse voltage voltage Advantages: Advantages: – 2 pulses in one line cycle 2 pulses in one line cycle – No DC component in the transformer current No DC component in the transformer current
F2.1.2 Single-phase bridge fully- controlled rectifier Resistive load 4 Average output(rectified )voltage 2√2U,1+cosa 1+cosa √2U2 singed(or) 0.9 (29) 丌 丌 4 Average output current U2√2U,1+cosa U I+ cos a 0.9 R R 2 2-10) 中 For thyristor 01+cos a dvt 1=0.45 R (2-11) 12 ( sin ot)d(or)=U2 (2-12) sin za+ 2RV2Z e For transformer =12 sin at) d(ot) U2 sin2a+a (2-13) R R\2T 丌
Power Electron cs i 9 2.1.2 Single -phase bridge fully phase bridge fully - controlled rectifier controlled rectifier Resistive load Resistive load Average output (rectified) voltage Average output (rectified) voltage ( 2 -9) Average output current Average output current (2 -10) For thyristor thyristor (2 -11) (2 -12) For tra For tra nsform e r (2 -13) ∫ + = + = = π α α α π ω ω π 2 1 cos 0.9 2 2 2 1 cos 2 sin d ( ) 1 2 2 d 2 U U U U t t 2 1 cos 0.9 2 2 2 1 cos d 2 2 d α α π + = + = = R U R U R U I 2 1 cos 0 .45 2 1 2 dVT d + α = = R U I I π π α α π ω ω π π α − = = + ∫ sin 2 2 1 2 sin ) d( ) 2 ( 2 1 2 2 2 VT R U t t R U I π π α α π ω ω π π α − = = = + ∫ sin 2 2 1 sin ) ( ) 2 ( 1 2 2 2 2 R U t d t R U I I
F2.1.2 Single-phase bridge fully-controlled rectifier Inductive load (L is large enough a L 3O2 丌+a 2 2U, Sinad(ot) U, cosa=0902 cosa (2-15) e Commutation Thyristor voltages and currents 事 Transformer current
Power Electron cs i 10 2.1.2 Single -phase bridge phase bridge fully -controlled rectifier controlled rectifier Inductive load Inductive load (L is large enough) (L is large enough) T a b R L a) u1 u 2 i 2 VT1 VT3 VT2 VT4 u d i d u2 O ωt O ωt O ωt ud i d i 2 b) O ωt O ωt uVT1,4 O ωt O ωt I d Id Id Id I d iVT2,3 iVT1,4 ∫ + = = = π α α α α π ω ω π cos 0.9 cos 2 2 2 sin d ( ) 1 d 2 U2 U2 U U t t (2-15) Commuta Commuta tion Thyristor Thyristor voltages and currents voltages and currents Transformer current Transformer current