Line-Commutated Rectifiers 17.1 The single-phase full-wave 17.3 - - PowerPoint PPT Presentation

Fundamentals of Power Electronics

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Chapter 17: Line-commutated rectifiers

Chapter 17

Line-Commutated Rectifiers

17.1 The single-phase full-wave rectifier 17.1.1 Continuous conduction mode 17.1.2 Discontinuous conduction mode 17.1.3 Behavior when C is large 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 17.3 Phase control 17.3.1 Inverter mode 17.3.2 Harmonics and power factor 17.3.3 Commutation 17.4 Harmonic trap filters 17.5 Transformer connections 17.6 Summary

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Chapter 17: Line-commutated rectifiers

17.1 The single-phase full-wave rectifier

vg(t) ig(t) iL(t) L C R + v(t) – D1 D2 D3 D4 Zi 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)

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Chapter 17: Line-commutated rectifiers

17.1.1 Continuous conduction mode

vg(t) ig(t) THD = 29% t

10 ms 20 ms 30 ms 40 ms

Large L Typical ac line waveforms for CCM : As L →∞, ac line current approaches a square wave

distortion factor = I1, rms Irms = 4 π 2 = 90.0%

THD = 1 distortion factor

2

– 1 = 48.3% CCM results, for L →∞ :

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Chapter 17: Line-commutated rectifiers

17.1.2 Discontinuous conduction mode

vg(t) ig(t) THD = 145% t

10 ms 20 ms 30 ms 40 ms

Small L Typical ac line waveforms for DCM : As L →0, ac line current approaches impulse functions (peak detection) As the inductance is reduced, the THD rapidly 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.

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Chapter 17: Line-commutated rectifiers

17.1.3 Behavior when C is large

Solution of the full-wave rectifier circuit for infinite C: Define

KL = 2L RTL M = V Vm

50% 100% 150% 200%

THD THD M PF cos (ϕ1 − θ1)

0.4 0.5 0.6 0.7 0.8 0.9 1.0

PF, M cos (ϕ1 − θ1), KL

0.0001 0.001 0.01 0.1 1 10

CCM DCM

0˚ 45˚ 90˚ 135˚ 180˚

β β

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Chapter 17: Line-commutated rectifiers

17.1.4 Minimizing THD when C is small

vg(t) ig(t) iL(t) L C R + v(t) – D1 D2 D3 D4 Zi 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 Zi has zero phase shift at the second harmonic of the ac line frequency, 2 fL.

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Chapter 17: Line-commutated rectifiers

Approximate THD

Q

THD=1% THD=3% THD=10% THD=0.5% THD=30%

f0 / fL

1 10 100 0.1 1 10 50

f0 = 1 2π LC R0 = L C Q = R R0 fp = 1 2πRC = f0 Q

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Chapter 17: Line-commutated rectifiers

Example

vg(t) ig(t) THD = 3.6% t

10 ms 20 ms 30 ms 40 ms

Typical ac line current and voltage waveforms, near the boundary between continuous and discontinuous modes and with small dc filter capacitor. f0/fL = 10, Q = 1

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Chapter 17: Line-commutated rectifiers

17.2 The Three-Phase Bridge Rectifier

L iL(t) + V – C dc load R øa øb øc ia(t) 3ø ac D1 D2 D3 D4 D5 D6 iL –iL

90˚ 180˚ 270˚ 360˚

ia(ωt) ωt

Line current waveform for infinite L

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Chapter 17: Line-commutated rectifiers

17.2.1 Continuous conduction mode

iL –iL

90˚ 180˚ 270˚ 360˚

ia(ωt) ωt

ia(t) = 4 nπ IL sin nπ 2 sin nπ 3 sin nωt

Σ

n = 1,5,7,11,... ∞

Fourier series:

• Similar to square wave, but

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

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Chapter 17: Line-commutated rectifiers

A typical CCM waveform

van(t) ia(t) THD = 31.9% t

10 ms 20 ms 30 ms 40 ms

vbn(t) vcn(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 ia(t).

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Chapter 17: Line-commutated rectifiers

17.2.2 Discontinuous conduction mode

van(t) ia(t) THD = 99.3% t

10 ms 20 ms 30 ms 40 ms

vbn(t) vcn(t)

Phase a current contains pulses at the positive and negative peaks of the line-to-line voltages vab(t) and vac(t). Distortion factor and THD are increased. Distortion factor of the typical waveform illustrated above is 71%.

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Chapter 17: Line-commutated rectifiers

17.3 Phase control

L iL(t) + V – C dc load R øa øb øc ia(t) 3ø ac Q1 Q2 Q3 Q4 Q5 Q6 + vd(t) –

Q5 Q6 Q4 Q5 Q6 Q4 Q1 Q2 Q3 Q1 Q3 Q2 α Upper thyristor: Lower thyristor:

90˚ 180˚ 270˚ 0˚

ωt ia(t) iL – iL van(t) = Vm sin (ωt) – vbc – vca vab vbc – vab vca vd(t)

Replace diodes with SCRs: Phase control waveforms: Average (dc) output voltage:

V = 3 π 3 Vm sin(θ + 30˚)dθ

30˚+α 90˚+α

= 3 2 π VL-L, rms cos α

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Chapter 17: Line-commutated rectifiers

Dc output voltage vs. delay angle α

30 60 90 120 150 180

Inversion Rectification α, degrees V VL–L, rms

–1.5 –1 –0.5 0.5 1 1.5

V = 3 π 3 Vm sin(θ + 30˚)dθ

30˚+α 90˚+α

= 3 2 π VL-L, rms cos α

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Chapter 17: Line-commutated rectifiers

17.3.1 Inverter mode

L IL + V – øa øb øc 3ø ac + –

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.

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Chapter 17: Line-commutated rectifiers

17.3.2 Harmonics and power factor

Fourier series of ac line current waveform, for large dc-side inductance:

ia(t) = 4 nπ IL sin nπ 2 sin nπ 3 sin (nωt – nα)

Σ

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 Ia, rmsVL-L, rms sin α = IL 3 2 π VL-L, rms sin α

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Chapter 17: Line-commutated rectifiers

Real and reactive power in controlled rectifier at fundamental frequency

Q P || S || sin α || S || cos α α S = IL 3 2 π VL–L rms

Q = 3 Ia, rmsVL-L, rms sin α = IL 3 2 π VL-L, rms sin α

P = IL 3 2 π VL-L, rms cos α

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Chapter 17: Line-commutated rectifiers

17.4 Harmonic trap filters

ir is Z1 Z2 Z3

. . .

Zs Rectifier model ac source model Harmonic traps (series resonant networks)

A passive filter, having resonant zeroes tuned to the harmonic frequencies

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Chapter 17: Line-commutated rectifiers

Harmonic trap

ir is Z1 Z2 Z3

. . .

Zs Rectifier model ac source model Harmonic traps (series resonant networks)

Zs(s) = Zs'(s) + sL s' Ac source: model with Thevenin-equiv voltage source and impedance Zs’(s). Filter often contains series inductor sLs’. Lump into effective impedance Zs(s):

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Chapter 17: Line-commutated rectifiers

Filter transfer function

ir is Z1 Z2 Z3

. . .

Zs Rectifier model ac source model Harmonic traps (series resonant networks)

H(s) = is(s) iR(s) = Z1 || Z2 || Zs + Z1 || Z2 ||

H(s) = is(s) iR(s) = Zs || Z1 || Z2 || Zs

• r

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Chapter 17: Line-commutated rectifiers

Simple example

R1 L1 C1 Fifth-harmonic trap Z1 Ls ir is

Q1 = R01 R1 fp ≈ 1 2π L sC1 f1 = 1 2π L 1C1 R1 ω L

1

ω L

s

Z1 Zs Z1 || Zs 1 ωC1 R01 = L 1 C1 R0p ≈ L s C1 Qp ≈ R0p R1

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Chapter 17: Line-commutated rectifiers

Simple example: transfer function

f1 fp Q1 Qp 1 L 1 L 1 + L s

– 40 dB/decade

• Series resonance: fifth

harmonic trap

• Parallel resonance: C1

and Ls

• Parallel resonance

tends to increase amplitude of third harmonic

• Q of parallel

resonance is larger than Q of series resonance

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Chapter 17: Line-commutated rectifiers

Example 2

Ls ir is R1 L1 C1 5th harmonic trap Z1 R2 L2 C2 7th harmonic trap Z2 R3 L3 C3 11th harmonic trap Z3

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Chapter 17: Line-commutated rectifiers

Approximate impedance asymptotes

ωLs R1 ωL1 f1 Q1 1 ω C1 R2 ωL2 f2 Q2 R3 ωL3 f3 Q3 1 ω C

2

1 ω C

3

Zs || Z1 || Z2 || Z3

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Chapter 17: Line-commutated rectifiers

Transfer function asymptotes

f1 1 Q2 f2 Q1 f3 Q3

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Chapter 17: Line-commutated rectifiers

Bypass resistor

Rn Ln Cn Rbp Rn Ln Cn Rbp Cb

ω L

1

ω L

s

Z1 Zs Z1 || Zs 1 ωC1 fp f1 Rbp fbp

f1 fp 1

– 40 dB/decade

fbp

– 20 dB/decade

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Chapter 17: Line-commutated rectifiers

Harmonic trap filter with high-frequency roll-off

R7 L7 C7 Rbp Cb R5 L5 C5 Fifth-harmonic trap Seventh-harmonic trap with high- frequency rolloff Ls

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Chapter 17: Line-commutated rectifiers

17.5 Transformer connections

Three-phase transformer connections can be used to shift the phase of the voltages and currents This shifted phase can be used to cancel out the low-order harmonics Three-phase delta-wye transformer connection shifts phase by 30˚:

T1 T2 T3 T1 T2 T3 a b c a' b' c' 3 : n

n'

T1 T2 T3 T1 T2 T3 a b c a' b' c'

n' 30˚

Primary voltages Secondary voltages ωt

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Chapter 17: Line-commutated rectifiers

Twelve-pulse rectifier

T4 T5 T6 T4 T5 T6 3 : n

n'

T1 T2 T3 T1 T2 T3 a b c

n'

1:n L IL + vd(t) – dc load 3øac source ia1(t) ia2(t) ia(t)

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Chapter 17: Line-commutated rectifiers

Waveforms of 12 pulse rectifier

ia1(t) ia2(t) ia(t)

90˚ 180˚ 270˚ 360˚

nIL – nIL nIL 3 nI L 1 + 2 3 3 nI L 1 + 3 3

ωt

• Ac line current contains

1st, 11th, 13th, 23rd, 25th,

• etc. These harmonic

amplitudes vary as 1/n

• 5th, 7th, 17th, 19th, etc.

harmonics are eliminated

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Chapter 17: Line-commutated rectifiers

Rectifiers with high pulse number

Eighteen-pulse rectifier:

• Use three six-pulse rectifiers
• Transformer connections shift phase by 0˚, +20˚, and –20˚
• No 5th, 7th, 11th, 13th harmonics

Twenty-four-pulse rectifier

• Use four six-pulse rectifiers
• Transformer connections shift phase by 0˚, 15˚, –15˚, and 30˚
• No 5th, 7th, 11th, 13th, 17th, or 19th harmonics

If p is pulse number, then rectifier produces line current harmonics of number n = pk ± 1, with k = 0, 1, 2, ...