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# Line-Commutated Rectifiers

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Fundamentals of Power Electronics1Chapter 16: Line-commutated rectifiersChapter 16Line-Commutated Rectifiers16.1 The single-phase full-waverectifier16.1.1 Continuous conductionmode16.1.2 Discontinuousconduction mode16.1.3 Behavior when C islarge16.1.4 Minimizing THD when Cis small16.2 The three-phase bridgerectifier16.2.1 Continuous conductionmode16.2.2 Discontinuousconduction mode16.3 Phase control16.3.1 Inverter mode16.3.2 Harmonics and powerfactor16.3.3 Commutation16.4 Harmonic trap filters16.5 Transformer connections16.6 SummaryFundamentals of Power Electronics2Chapter 16: Line-commutated rectifiers16.1 The single-phase full-wave rectifiervg(t)ig(t) iL(t)LCR+v(t)–D1D2D3D4ZiFull-wave rectifier with dc-side L-C filterTwo common reasons for including the dc-side L-C filter:• Obtain good dc output voltage (large C) and acceptable ac linecurrent waveform (large L)• Filter conducted EMI generated by dc load (small L and C)Fundamentals of Power Electronics3Chapter 16: Line-commutated rectifiers16.1.1 Continuous conduction modevg(t)ig(t)THD = 29%t10 ms 20 ms 30 ms 40 msLarge LTypical ac linewaveforms forCCM :As L →∞, acline currentapproaches asquare wavedistortion factor =I1, rmsIrms=4π 2= 90.0%THD =1distortion factor2–1 = 48.3%CCM results, for L →∞ :Fundamentals of Power Electronics4Chapter 16: Line-commutated rectifiers16.1.2 Discontinuous conduction modevg(t)ig(t)THD = 145%t10 ms 20 ms 30 ms 40 msSmall LTypical ac linewaveforms forDCM :As L →0, acline currentapproachesimpulsefunctions(peakdetection)As the inductance is reduced, the THD rapidlyincreases, and the distortion factor decreases.Typical distortion factor of a full-wave rectifier with noinductor is in the range 55% to 65%, and is governedby ac system inductance.Fundamentals of Power Electronics5Chapter 16: Line-commutated rectifiers16.1.3 Behavior when C is largeSolution of thefull-waverectifier circuitfor infinite C:DefineKL=2LRTLM=VVm050%100%150%200%THDTHDMPFcos (ϕ1 − θ1)0.40.50.60.70.80.91.0PF, Mcos (ϕ1 − θ1),KL0.00010.0010.010.1110CCMDCM0˚45˚90˚135˚180˚ββFundamentals of Power Electronics6Chapter 16: Line-commutated rectifiers16.1.4 Minimizing THD when C is smallvg(t)ig(t) iL(t)LCR+v(t)–D1D2D3D4ZiSometimes the L-C filter is present only to remove high-frequencyconducted EMI generated by the dc load, and is not intended tomodify the ac line current waveform. If L and C are both zero, then theload resistor is connected directly to the output of the diode bridge,and the ac line current waveform is purely sinusoidal.An approximate argument: the L-C filter has negligible effect on the acline current waveform provided that the filter input impedance Zi haszero phase shift at the second harmonic of the ac line frequency, 2 fL.Fundamentals of Power Electronics7Chapter 16: Line-commutated rectifiersApproximate THDQTHD=1%THD=3%THD=10%THD=0.5%THD=30%f0 / fL1 10 1000.111050f0=12π LCR0=LCQ =RR0fp=12πRC=f0QFundamentals of Power Electronics8Chapter 16: Line-commutated rectifiersExamplevg(t)ig(t)THD = 3.6%t10 ms 20 ms 30 ms 40 msTypical ac line current and voltage waveforms, near the boundary between continuousand discontinuous modes and with small dc filter capacitor. f0/fL = 10, Q = 1Fundamentals of Power Electronics9Chapter 16: Line-commutated rectifiers16.2 The Three-Phase Bridge RectifierLiL(t)+V–Cdc loadRøaøbøcia(t)3øacD1D2D3D4D5D60iL–iL90˚ 180˚ 270˚ 360˚ia(ωt)ωtLine currentwaveform forinfinite LFundamentals of Power Electronics10Chapter 16: Line-commutated rectifiers16.2.1 Continuous conduction mode0iL–iL90˚ 180˚ 270˚ 360˚ia(ωt)ωtia(t)=4nπILsinnπ2sinnπ3sin nωtΣn = 1,5,7,11,...∞Fourier series:• Similar to square wave, butmissing triplen harmonics• THD = 31%• Distortion factor = 3/π = 95.5%• In comparison with single phase case:the missing 60˚ of current improves the distortion factor from 90% to95%, because the triplen harmonics are removedFundamentals of Power Electronics11Chapter 16: Line-commutated rectifiersA typical CCM waveformvan(t)ia(t)THD = 31.9%t10 ms 20 ms 30 ms 40 msvbn(t) vcn(t)Inductor current contains sixth harmonic ripple (360 Hz for a 60 Hz acsystem). This ripple is superimposed on the ac line current waveform,and influences the fifth and seventh harmonic content of ia(t).Fundamentals of Power Electronics12Chapter 16: Line-commutated rectifiers16.2.2 Discontinuous conduction modevan(t)ia(t)THD = 99.3%t10 ms 20 ms 30 ms 40 msvbn(t) vcn(t)Phase a current contains pulses at the positive and negative peaks of theline-to-line voltages vab(t) and vac(t). Distortion factor and THD are increased.Distortion factor of the typical waveform illustrated above is 71%.Fundamentals of Power Electronics13Chapter 16: Line-commutated rectifiers16.3 Phase controlLiL(t)+V–Cdc loadRøaøbøcia(t)3øacQ1Q2Q3Q4Q5Q6+vd(t)–Q5Q6Q4Q5Q6Q4Q1Q2Q3Q1Q3Q20αUpper thyristor:Lower thyristor:90˚180˚ 270˚0˚ωtia(t)iL– iLvan(t) = Vm sin (ωt)– vbc– vcavabvbc– vabvcavd(t)Replace diodes with SCRs:Phase control waveforms:Average (dc) output voltage:V =3π3 Vmsin(θ + 30˚)dθ30˚+α90˚+α=32πVL-L, rmscos αFundamentals of Power Electronics14Chapter 16: Line-commutated rectifiersDc output voltage vs. delay angle α0 30 60 90 120 150 180InversionRectificationα, degreesVVL–L, rms–1.5–1–0.500.511.5V =3π3 Vmsin(θ + 30˚)dθ30˚+α90˚+α=32πVL-L, rmscos αFundamentals of Power Electronics15Chapter 16: Line-commutated rectifiers16.3.1 Inverter modeLIL+V–øaøbøc3øac+–If the load is capable of supplying power, then the direction of powerflow can be reversed by reversal of the dc output voltage V. The delayangle α must be greater than 90˚. The current direction is unchanged.Fundamentals of Power Electronics16Chapter 16: Line-commutated rectifiers16.3.2 Harmonics and power factorFourier series of ac line current waveform, for large dc-side inductance:ia(t)=4nπILsinnπ2sinnπ3sin (nωt – nα)Σn = 1,5,7,11,...∞Same as uncontrolled rectifier case, except that waveform is delayedby the angle α. This causes the current to lag, and decreases thedisplacement factor. The power factor becomes:power factor = 0.955 cos (α)When the dc output voltage is small, then the delay angle α is close to90˚ and the power factor becomes quite small. The rectifier apparentlyconsumes reactive power, as follows:Q =3Ia, rmsVL-L, rmssin α = IL32πVL-L, rmssinαFundamentals of Power Electronics17Chapter 16: Line-commutated rectifiersReal

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