Chapter 17 Line-Commutated Rectifiers 17.1 The single-phase full-wave 17.3 Phase control rectifier 17.3.1 Inverter mode 17.1.1 Continuous conduction 17.3.2 Harmonics and power mode factor 17.1.2 Discontinuous 17.3.3 Commutation conduction mode 17.4 Harmonic trap filters 17.1.3 Behavior when C is 17.5 Transformer connections large 17.6 Summary 17.1.4 Minimizing THD when C is small 17.2 The three-phase bridge rectifier 17.2.1 Continuous conduction mode 17.2.2 Discontinuous conduction mode Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 1
17.1 The single-phase full-wave rectifier L i g (t) i L (t) + D 4 D 1 Z i v g (t) v(t) C R D 3 D 2 – Full-wave rectifier with dc-side L-C filter Two common reasons for including the dc-side L-C filter: • Obtain good dc output voltage (large C ) and acceptable ac line current waveform (large L ) • Filter conducted EMI generated by dc load (small L and C ) Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 2
17.1.1 Continuous conduction mode THD = 29% Large L v g (t) Typical ac line waveforms for i g (t) CCM : 10 ms 20 ms 30 ms 40 ms t As L → ∞ , ac line current approaches a square wave CCM results, for L → ∞ : distortion factor = I 1, rms 4 I rms = π 2 = 90.0% 2 1 THD = – 1 = 48.3% distortion factor Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 3
17.1.2 Discontinuous conduction mode Small L THD = 145% v g (t) Typical ac line i g (t) waveforms for DCM : As L → 0 , ac 10 ms 20 ms 30 ms 40 ms t line current approaches impulse functions (peak As the inductance is reduced, the THD rapidly detection) increases, and the distortion factor decreases. Typical distortion factor of a full-wave rectifier with no inductor is in the range 55% to 65%, and is governed by ac system inductance. Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 4
17.1.3 Behavior when C is large cos ( ϕ 1 − θ 1 ), β THD Solution of the PF, M full-wave 1.0 200% 180˚ β cos ( ϕ 1 − θ 1 ) rectifier circuit for infinite C : 0.9 PF 150% 135˚ Define 0.8 K L = 2 L RT L 0.7 100% 90˚ M M = V 0.6 V m 50% 45˚ THD 0.5 CCM DCM 0.4 0 0˚ 0.0001 0.001 0.01 0.1 1 10 K L Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 5
17.1.4 Minimizing THD when C is small Sometimes the L-C filter is present only to remove high-frequency conducted EMI generated by the dc load, and is not intended to modify the ac line current waveform. If L and C are both zero, then the load 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 ac line current waveform provided that the filter input impedance Z i has zero phase shift at the second harmonic of the ac line frequency, 2 f L . L i g (t) i L (t) + D 4 D 1 Z i v g (t) v(t) C R D 3 D 2 – Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 6
Approximate THD 50 THD=30% 1 THD=10% f 0 = 2 π LC L THD=3% R 0 = C 10 Q = R THD=1% R 0 2 π RC = f 0 1 f p = Q Q THD=0.5% 1 0.1 1 10 100 f 0 / f L Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 7
Example THD = 3.6% v g (t) i g (t) 10 ms 20 ms 30 ms 40 ms t Typical ac line current and voltage waveforms, near the boundary between continuous and discontinuous modes and with small dc filter capacitor. f 0 / f L = 10, Q = 1 Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 8
17.2 The Three-Phase Bridge Rectifier L i a (t) i L (t) ø a + D 1 D 2 D 3 3ø dc load ø b V C ac R D 4 D 5 D 6 – ø c i a ( ω t ) i L Line current ω t 0 waveform for 90˚ 180˚ 270˚ 360˚ infinite L –i L Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 9
17.2.1 Continuous conduction mode Fourier series: i a ( ω t ) i L ∞ Σ n π I L sin n π sin n π 4 sin n ω t i a ( t ) = 2 3 n = 1,5,7,11,... ω t 0 90˚ 180˚ 270˚ 360˚ • Similar to square wave, but –i L missing 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% to 95%, because the triplen harmonics are removed Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 10
A typical CCM waveform THD = 31.9% i a (t) v bn (t) v cn (t) v an (t) 10 ms 20 ms 30 ms 40 ms t Inductor current contains sixth harmonic ripple (360 Hz for a 60 Hz ac system). This ripple is superimposed on the ac line current waveform, and influences the fifth and seventh harmonic content of i a ( t ). Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 11
17.2.2 Discontinuous conduction mode THD = 99.3% i a (t) v an (t) v bn (t) v cn (t) 10 ms 20 ms 30 ms 40 ms t Phase a current contains pulses at the positive and negative peaks of the line-to-line voltages v ab ( t ) and v ac ( t ). Distortion factor and THD are increased. Distortion factor of the typical waveform illustrated above is 71%. Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 12
17.3 Phase control Replace diodes with SCRs: Phase control waveforms: α v an (t) = V m sin ( ω t ) L i a (t) i L (t) ø a + + i a (t) i L Q 1 Q 2 Q 3 ω t 0 3ø dc load ø b v d (t) V C 180˚ 270˚ 0˚ 90˚ – i L ac R Q 4 Q 5 Q 6 – – – v ca v bc v ca – v bc v ab – v ab ø c v d (t) Average (dc) output voltage: 90˚+ α V = 3 3 V m sin( θ + 30˚) d θ π 30˚+ α Upper thyristor: Q 3 Q 1 Q 1 Q 2 Q 2 Q 3 = 3 2 V L - L , rms cos α π Lower thyristor: Q 5 Q 5 Q 6 Q 6 Q 4 Q 4 Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 13
Dc output voltage vs. delay angle α 1.5 V V L – L , rms Rectification Inversion 90˚+ α V = 3 3 V m sin( θ + 30˚) d θ π 1 30˚+ α = 3 2 V L - L , rms cos α π 0.5 0 –0.5 –1 –1.5 0 30 60 90 120 150 180 α , degrees Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 14
17.3.1 Inverter mode L I L ø a + 3ø + ø b V ac – – ø c If the load is capable of supplying power, then the direction of power flow can be reversed by reversal of the dc output voltage V . The delay angle α must be greater than 90˚. The current direction is unchanged. Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 15
17.3.2 Harmonics and power factor Fourier series of ac line current waveform, for large dc-side inductance: ∞ n π I L sin n π sin n π Σ 4 sin ( n ω t – n α ) i a ( t ) = 2 3 n = 1,5,7,11,... Same as uncontrolled rectifier case, except that waveform is delayed by the angle α . This causes the current to lag, and decreases the displacement 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 to 90˚ and the power factor becomes quite small. The rectifier apparently consumes reactive power, as follows: Q = 3 I a , rms V L - L , rms sin α = I L 3 2 V L - L , rms sin α π Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 16
Real and reactive power in controlled rectifier at fundamental frequency Q || S || sin α V L – L rms S = I L 3 2 π α || S || cos α P P = I L 3 2 V L - L , rms cos α π Q = 3 I a , rms V L - L , rms sin α = I L 3 2 V L - L , rms sin α π Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 17
17.4 Harmonic trap filters A passive filter, having resonant zeroes tuned to the harmonic frequencies Z s i s . . . Z 1 Z 2 Z 3 i r ac source Harmonic traps Rectifier model (series resonant networks) model Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 18
Harmonic trap Ac source: Z s model with Thevenin-equiv i s voltage source and impedance Z s ’ ( s ). Filter often . . . Z 1 Z 2 Z 3 i r contains series inductor sL s ’ . Lump into effective impedance Z s ( s ): ac source Harmonic traps Rectifier model (series resonant networks) model Z s ( s ) = Z s '( s ) + sL s ' Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 19
Filter transfer function H ( s ) = i s ( s ) Z 1 || Z 2 || i R ( s ) = Z s || Z 1 || Z 2 || H ( s ) = i s ( s ) i R ( s ) = or Z s + Z 1 || Z 2 || Z s Z s i s . . . Z 1 Z 2 Z 3 i r ac source Harmonic traps Rectifier model (series resonant networks) model Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 20
Simple example L s Q p ≈ R 0 p R 1 i s L s R 0 p ≈ R 1 L C 1 ω 1 Z 1 || Z s 1 ω C 1 1 i r f p ≈ L 1 1 2 π L s C 1 f 1 = 2 π L 1 C 1 Z 1 L Z s L 1 ω s C 1 R 01 = C 1 Q 1 = R 01 R 1 Fifth-harmonic R 1 trap Z 1 Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 21
Simple example: transfer function • Series resonance: fifth harmonic trap • Parallel resonance: C 1 Q p and L s 1 • Parallel resonance f p tends to increase amplitude of third – 40 dB/decade harmonic L 1 f 1 • Q of parallel L 1 + L s resonance is larger than Q of series Q 1 resonance Fundamentals of Power Electronics Chapter 17: Line-commutated rectifiers 22
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