PEREC 4.1 AC voltage controllers 4.1.1 Single-phase AC voltage controller 4.1.2 Three-phase AC voltage controller Applications 命 Lighting control 4 Soft-start of asynchronous motors 4 Adjustable speed drive of asynchronous motors 4 Reactive power control
Power Electron cs i 6 4.1 AC voltage controllers AC voltage controllers 4.1.1 Single -phase AC voltage controller phase AC voltage controller 4.1.2 Three 4.1.2 Three -phase AC voltage controller phase AC voltage controller Applications Applications Lighting control Lighting control Soft -start of asynchronous motors start of asynchronous motors Adjustable speed drive of asynchronous motors Adjustable speed drive of asynchronous motors Reactive power control Reactive power control
4.1.1 Single-phase AC voltage controller Resistive load lo R at l 4 The phase shift range (operation range of phase delay angle) at 0≤a<π 7
The phase shift range The phase shift range (operation range of phase (operation range of phase delay angle): delay angle): 0 ≤ α ≤ π Resistive load Resistive load Power Electron cs i u1 u o R io VT1 VT2 O u1 u o io uVT ω t O ωt O ωt O ωt 4.1.1 Single -phase AC voltage controller phase AC voltage controller 7
PEREC Resistive load, quantitative analysis 4 RMs value of output voltage 6u2u,sino d(ot)=UNLT 丌-a sinza z(4-1) t RMS value of output current R (4-2) RMS value of thyristor current 1 r v2U, sinat d(ot) a sinza 丌 R R12 2丌 (4-3) e Power factor of the circuit sin 2a +a S U 2丌
Power Electron cs i 8 Resistive load, quantitative analysis Resistive load, quantitative analysis RMS value of output voltage RMS value of output voltage RMS value of output current RMS value of output current RMS value of RMS value of thyristor thyristor current current Power factor of the circuit Power factor of the circuit ( ) ( ) π π α α π ω ω π π α − = = + ∫ sin 2 2 1 2 sin d 1 1 2 Uo U1 t t U R U I o o = ( ) ) 2 sin 2 ( 1 2 2 sin 1 2 1 1 2 1 π α π α ω ω π π α = − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ∫ R U d t R U t I T (4 -1) (4 -2) (4 -3) π π α α π λ − = = = = sin 2 + 2 1 1 o 1 o o o U U U I U I S P (4 -4)
F Inductive(Inductor-resistor) load, operation principle R ◆ The phase shift range qsasπ
Power Electron cs i 9 Inductive (Inductor Inductive (Inductor -resistor) load, resistor) load, operation principle operation principle 0.6 O u1 u o i o uVT O ωt ωt O ωt O ωt uG1 uG2 O O ωt ωt u1 uo R i o VT1 VT 2 The phase shift range: The phase shift range: ϕ ≤ α ≤ π
PEREC Inductive load, quantitative analysis Differential equation 180 L=°+Ri=√2U1 snot dt (45) 140 Solution [sin(at-)-sin(a-o)eg9] Z a<ot≤a+b 20 Considering io=0 when ot=ac+8 02060100140180 We have /(°) a+b-)=sn(a-0)e(4-7) The rms value of output voltage output current, and thyristor current can then be calculated
Power Electron cs i 10 Differential equation Differential equation Solution Solution Considering Considering i o=0 when =0 when ωt = α+ θ We have We have 0 2 sin d d o o 1 o = + = ω = α ω t i Ri U t t i L (4 -5) α ω α θ ω ϕ α ϕ ϕ α ω ≤ ≤ + = − − − − t t e Z U i tg t o [sin( ) sin( ) ] 2 1 (4 -6) ϕ θ α θ ϕ α ϕ tg sin( ) sin( ) − + − = − e Inductive load, quantitative analysis Inductive load, quantitative analysis 0 2 0 60 100 140 180 20 100 60 θ /(°) 180 140 α /(°) ϕ = 90° 75° 60° 45° 30° 15° 0° (4 -7) The RMS value of output voltage, output current, and The RMS value of output voltage, output current, and thyristor thyristor current can then be calculated. current can then be calculated