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Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Rectifiers (Line Commutated Rectifiers) Rectifiers - 1 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Introduction Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Line-Commutated or Naturally Commutating Rectifers ]Un-Controlled (diodes) ]Semi- or Full-Controlled (thyristors) This Lecture Force-Commutated Rectifiers ]Switch mode (PWM) Rectifiers - 2 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 What are used for Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste High Current loads (or multiple low current ones) ] Conventional Magnets (low time constant) ] SC Magnets (very high time constant) Elettra – Storage Ring Magnets High Voltage Loads ] Klystrons for RF plants Elettra – Storage Ring RF Amplifier klystron in its trolley with the modulating cavities Rectifiers - 3 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The principles of Rectification Distribution Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Rectification Conversion of the AC mains in DC º Fully Controlled Bridge (mostly used) º Current Regulator & Un-controlled Rectifier º Rectifier and Linear Output Stage Harmonics Filtering Load Rectifiers - 4 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Performance Parameters (some) º º Assumptions: Ideal Devices (instantaneous switching, no losses) Resistive Load Vp(t) DC voltage on load T VDC 1 = ∫ v L(t)dt T 0 T 1 rms voltage V = vL2(t)dt L ∫ on load T 0 Form Factor Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste V FF = L VDC Vs(t) VL(t) Rectification Ratio (a.k.a efficiency) Ripple Factor Load 2 2 PDC V DC 1 V DC 1 RD = 0 η= ⇒ 2 → η = 2 = PL + PD VL 1 + RD VL FF 2 R 2 VL2 − VDC RF = = FF 2 − 1 VDC Transformer Utilization Factor TUF = PDC PDC = Transformer VA rating VAp + VAs 2 Some Diode/Thyristor Parameters: Peak Inverse Voltage, Peak Direct Voltage (Thy. Only), Peak Forward Current, Average Current, Rms Current,… Rectifiers - 5 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Single-Phase topologies - 1 Single–Way Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste (half-wave, just for comparison) iL(t) Vs(t) iL(t) Vs(t) R=2Ω 2π VL(t) Single–Way (full-wave, Centre-Tapped) iL(t) Vs+(t) Vs+(t) VL(t) iL(t) 2π Vs-(t) Rectifiers - 6 R=2Ω Vs-(t) CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Single-Phase topologies - 2 Double–Way Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste (full-wave, Bridge) iL(t) Vs(t) Vs(t) iL(t) VL(t) º º 2π R=2Ω Applications Low power loads as stand-alone rectifiers Output stage of PWM rectifiers Rectifiers - 7 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Comparison among topologies 1–Ph. º º º Secondary voltage is sinusoidal: vs(t) = Vs sin (2πfmainst) Resistive Load Ideal devices (no device losses) Vp(t) Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Vs(t) VL(t) Load Half–Wave Full – Wave (Center–tapped) Full – Wave (Bridge) Rectified Voltage – VDC Vs/π = 0.318 ·Vs 2 ·Vs/π = 0.636 ·V s 2 ·Vs/π = 0.636 ·V s rms Output Voltage – VL Vs/2 = 0.318 ·Vs Vs/√ 2 = 0.707 ·Vs Vs/√ 2 = 0.707 ·Vs 1.57 1.11 1.11 0.405 0.81 0.81 1.21 0.482 0.482 0.286 0.572 0.81 Diode Peak Inverse Voltage (PIV) – VRRM Vs = π · VDC 2 · Vs = π · VDC Vs = π/2 · VDC Peak Direct Voltage (PDV – thyristors only) – VDRM Vs = π · VDC 2 · Vs = π · VDC Vs = π/2 · VDC π · IDC π/2 · I DC π/2 · I DC IDC 0.5 · I DC 0.5 · I DC π/2 · I DC π/4 · I DC π/4 · I DC fmains 2 · fmains 2 · fmains Parameter Form Factor – FF Rectification Ratio – η Ripple Factor – RF Transformer Utilization Factor – TUF Diode Peak Forward Current – IFRM Diode Average Current – IF(AV) Diode Rms Current – IF(RMS) Fundamental Ripple Frequency – fR *Extracted from: M.H. Rashid, “Power Electronics Handbook”, Academic Press Rectifiers - 8 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Mostly Used Configurations Multi-Ph. Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste º º º º Some Considerations: number of phases → ∞ ⇒ FF → 1 & RF → 0 Max Practical Numbers: 12 or 24 The higher the number of phases the more complicated the transformer is for Star-Connected (single-way) diode rectifiers Bridge configurations allow to have 6 or 12 pulses without complex transformer connections • Single Bridge (6 pulses) • Double Bridge – Series/Parallel (12 pulses) 3-Phase Star (single-way, just for comparison) VR(t) VR(t) Vs(t) VT(t) iL(t) iL(t) 2π VS(t) R=2Ω VT(t) Rectifiers - 9 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 6-p Configuration: Bridge Bridge: iL(t) Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste iL(t) VR(t) VT(t) VS(t) VR(t) 2π VS(t) VS(t) -V T(t) VT(t) R=1Ω º º º VS(t) -V T(t) Comments: Mostly used configuration It is the base for structures with a higher number of pulses • Series (same output current, double output voltage) • Parallel (double output current, same output voltage) This configuration (and those derived) are the best for FF, RF and TUF Rectifiers - 10 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 12-p Configurations (Σ & //) Series: R=1Ω Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste iL(t) iL(t) 2π iL(t) Parallel (with inter-phase reactance): 2π R=1Ω iL(t) Rectifiers - 11 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Comparison among topologies 3–Ph. º º º Secondary voltage is sinusoidal: vs(t) = Vs sin (2πft) Resistive Load Ideal devices (no device losses) Vp(t) Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Vs(t) VL(t) Load 3-Phase Star (Single-Way) 6p Bridge (Double-Way) 12p Bridge (Series) 12p Bridge (Parallel+) Rectified Voltage – VDC 0.827 · Vs 1.654 · Vs 3.308 · Vs 1.654 · Vs rms Output Voltage – VL 0.84 · Vs 1.655 · Vs 3.310 · Vs 1.655 · Vs Form Factor – FF 1.0165 1.0009 1.00005 1.00005 Rectification Ratio – η 0.986 0.998 1.00 1.00 Ripple Factor – RF 0.182 0.042 0.01 0.01 Transformer Utilization Factor – TUF 0.73 0.95 0.97 0.97 Diode Peak Inverse Voltage (PIV) – VRRM 2.092 · VDC 1.05 · VDC 0.524 · VDC 1.05 · VDC Peak Direct Voltage (PDV – thyristors only) – VDRM 2.092 · VDC 1.05 · VDC 0.524 · VDC 1.05 · VDC 1.21 · I DC 1.05 · I DC 1.01 · I DC 0.524 · I DC Diode Average Current – IF(AV) 0.333 · I DC 0.333 · I DC 0.333 · I DC 0.167 · I DC Diode Rms Current – IF(RMS) 0.587 · I DC 0.579 · I DC 0.576 · I DC 0.409 · I DC 3 · fmains 6 · fmains 12 · fmains 12 · fmains Parameter DiodePeak Forward Current – IFRM Fundamental Ripple Frequency – fR *Extracted from: M.H. Rashid, “Power Electronics Handbook”, Academic Press Rectifiers - 12 + With inter-phase transformer CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Three-Phase Controlled Rectifiers Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Goal º º º To be able to vary the output voltage on the load according to the needs To be able to recover, if needed, energy from the load to the mains or other energy storage device To minimize the losses on some devices when the load requirements are low Possible Solutions º º º Use of thyristors in place of diodes Use thyristors AND diodes Use diodes or thyristors AND transistors Applications º º º º High Current loads (magnets) High Voltage loads (klystrons) Several low current loads supplied from a multi-channel converter (small magnets) Supply of current to loads of different characteristics Rectifiers - 13 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Three-Phase Fully Controlled Bridge ] ] ] Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Delay Angle α: the span of period between the instant when the thyristor could start to conduct and the instant when the trigger pulse is applied Since in stable conditions also the subsequent couple of thyristors are delayed the conduction continues until the next trigger pulse The average value, VDC, is anyway lower and depends on α Trigger!!! 3⋅ 3 π ⋅ Vm ⋅ cos( α ) = V DC 0 ⋅ cos( α ) 0 ≤ α ≤ π 3 3⋅ 3 π π 2 ⋅π VDC ( α ) = ⋅ Vm ⋅ 1 + cos( α + ) <α ≤ π 3 3 3 VDC ( α ) = Rectifiers - 14 º º Assumptions: Ideal Devices (instantaneous switching, no losses) Resistive Load CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Conduction vs. α (Resistive Load) α = 10° º º º º 0°= α =60° Continuous conduction: the output voltage is always positive The current flows continuously in the resistive load 60°< α =120° Discontinuous conduction: the output voltage goes to zero for part of each pulse The current flows as “pulses” in the resistive load Rectifiers - 15 Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste α = 50° a = 70° a = 110° CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 3-Ph.Current Regulator & Diode Br. Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Comments: º High Voltage Loads (like klystrons) require series connections of switches º Thyristors in series means a VERY good equalization of their firing pulses, º diodes are naturally commutating devices Pre-regulation of the AC input of the Bridge Ripple Factor 2 VL2 − VDC RF = = FF 2 − 1 VDC Elettra – Linac Modulator Klystron Rectifiers - 16 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 3-Ph.Multi-Channel (unregulated) Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Comments: º Good solution when there are several low-power loads. º The common part (transformer, bridge, filter) and the n channels can be º housed in a single cabinet. Using two bridges in series it is possible to supply bipolar channels (e.g. for corrector magnets) … = Ch. Regulation Ch. 1 Ch. 2 Ch. n = Load Elettra – Transfer Line Quadrupole followed by 2 correctors Rectifiers - 17 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 3-Ph.Contr. Br. & Linear Output º º Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Comments: Good for load which change their characteristics or for loads which need “fast” output current changes Acting on the controlled bridge it is possible to reduce the voltage on the linear transistor output stage and minimize the power dissipation at low current conditions = Trans. Regulation Elettra – Storage Ring Electromagnetic Elliptical Wiggler (EEW): for a short time in 2001, due to a major fault to its PWM PS, it was powered by a couple of PS of this type. Rectifiers - 18 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The “real” world – DC Side ⇒ The load has a strong inductive component (usually it is a magnet) ⇒ The current doesn’t follow the output voltage and it is smoothed by the inductance ⇒ If the inductance is big enough, the current waveform is continuous even if the voltage one is not ⇒ The output voltage can go negative(when α > 60°) but the current is still flowing in the same direction (keeping the thyristor in conduction) ⇒ The load inductance has a strong influence also on the waveform of the AC line current: the higher the inductance the less distorted the input current ⇒ The ripple on the output direct current is normally too high for the applications in accelerators’ field ⇒ There is the need for a Low-Pass Filter ⇒ Cut-off frequency f0 should be much lower than ripple's 1st harmonic (fripple1 = p x fmains, p = # pulses) ⇒ Dumped passive L-C filters are used ⇒ If additional attenuation is needed, additional Active Filters on the DC output are also used Rectifiers - 19 Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste i-PES applet: courtesy of Prof. J. W. Kolar and Dr. U. Drofenik ETH Zurich f0 = Lf > 1 2 ⋅π ⋅ L f ⋅ ( C1 + C 2 ) Vripple 2 ⋅ π ⋅ f ripple1 ⋅ I DC min C 2 = 5 ⋅ C1 R f = 0. 4 ⋅ L ( C1 + C 2 ) CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Parenthesis: Inversion Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste ⇒ With an inductive load, when α > 60°, the output voltage goes temporarily negative while the current is still flowing in the “positive” direction ⇒ For α > 90°, the average output voltage becomes negative but the current is still positive: the power is flowing back from the DC side to the AC, the converter is operating in “inverting mode” ⇒ The inverting mode can be used to recover energy from an inductive load (or a more stable source of DC like a battery or a solar cell panel) and send it to the AC mains or store in a capacitor. ⇒ The maximum delay angle is α ≈ 150° (taking into account the commutation angle µ and the thyristor turn-off time tq) ⇒ In “pure” rectifiers to avoid inversion and keep a working range up to α = 120°, a free-wheeling diode is put in parallel to the rectifier output. ⇒ The free-wheeling diode creates a path for the load current when the output voltage would become negative. ⇒ The free-wheeling diode has a positive effect in the ripple reduction and reactive power. Rectifiers - 20 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The “real” world – AC Side ⇒ ⇒ ⇒ ⇒ Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste There is a FINITE inductance on the mains side (the inductance of the secondary of the transformer and the leakage inductance of the line): Ls The thyristors change their status (on or off) in a FINITE time During commutation from one phase to another there is an “overlapping time” when two thyristors on the same side of the bridge are conducting at the same time shorting the phases through the L s of each phase – it is indicated as the “overlap angle” µ. For a given ID and α, the duration of the overlapping depends on Vf-f and Ls (LD>>0) ID = Vf − f 2 ⋅ω ⋅ Ls ⋅ [cos( α ) − cos( α + µ )] (Vf-f = peak value of inter-phase voltage) *Extracted from: M.H. Rashid, “Power Electronics Handbook”, Academic Press Rectifiers - 21 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The effects on the mains (current) Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Current: ⇒ The current drawn from AC supply system is not a pure sinusoid ⇒ Fundamental component with superimposed harmonic component ⇒ Harmonic frequency: (n x p ± 1) x fmains with n = 1, 2,… p = # pulses) ⇒ A 12 pulse converter has a lower harmonic impact on the mains than two 6 pulse units of a comparable size Line Current Harm. # = 250 Hz 7th = 350 Hz 11th = 550 Hz 13th = 650 Hz … Fundamental frequency component of Line Current 5th 6 pulse – mains line current (THD=28.45%) Line Current Harm. # = 550 Hz 13th = 650 Hz 23rd = 1150 Hz 25th = 1250 Hz … Fundamental frequency component of Line Current 11th 12 pulse – mains line current (THD=9.14%) *Data extracted from: G.J. Wakileh, “Power Systems Harmonics”, Springer Rectifiers - 22 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The effects on the mains (voltage) º º º Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Voltage: Notches (due to the commutation between phases) Spikes Distortion Notch Width = 2 ⋅ ω ⋅ Ls ⋅ I DC V f − f ⋅ sin( α ) Phase voltages Vf-f = peak value of interphase voltage THDV = ∑ (I n≥ 2 ⋅ n ⋅ ω ⋅ Ls ) 2 n Vphase Line-line voltage Vphase = peak value of interphase voltage In = n-th harmonic of the AC input current Ls = AC source impedance *Extracted from: N. Mohan-T.M. Undeland-W.P. Robbins, “Power Electronics”, Wiley Rectifiers - 23 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 The effects on the AC mains (def’s) ⇒ ⇒ ⇒ Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Assuming LD large enough in order that phase R line current iR(t) ~IDC First assumption: Ls = 0 (instantaneous commutation, µ = 0) Than considering Ls > 0 (overlapping, µ > 0) Displacement Power Factor DPF = cos( φ 1 ) = cos( α ) vT(t) vR(t) iR(t) i (t) cos( α + µ ) = cos(R1 α )− P VRrms ⋅ I Rrms 1 ⋅ cos( φ1 ) PF = = Power S VRrms ⋅ I Rrms Factor I Rrms 3 1 PF = rms ⋅ cos( α ) = ⋅ cos( α ) IR π IR1 = peak value of fundamental component of R-Phase line current Displacement Power Factor (Ls >0) DPF ≅ cos( α ) + cos( α + µ ) 2 α 2 ⋅ ω ⋅ Ls Vf − f Φ1= α *Extracted from: N. Mohan-T.M. Undeland-W.P. Robbins, “Power Electronics”, Wiley vT(t) vR(t) iR(t) iR1(t) α µ *Extracted from: N. Mohan-T.M. Undeland-W.P. Robbins, “Power Electronics”, Wiley Rectifiers - 24 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Example: existing 12p Magnet PS Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste 12-pulses Fully controlled Bridge Rectifier: ⇒ Two 6-p bridges in parallel ⇒ Free-wheeling diodes ⇒ Passive Filter VBr1 VOut VBr2 Elettra – Transfer Line Dipole Power Supplies: 2 PS (200 V / 1080 A, 12p-bridge & 60 V / 1080 A, 6p-bridge) in one cabinet. Rectifiers - 25 Elettra – Transfer Line Dipole Power Supply PSB_T2.2: 200 V / 1080 A, 12p fully controlled bridge – General Scheme. Elettra – Transfer Line Dipoles: 2 out of 7 dipole magnets. The first one (arrow) is powered separately from the others. CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 “Real” 3-Ph.12p Contr. Br. Output Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste ⇒ Output voltages of both bridges and PS output voltage (Vf-n = 166 V; Iout = 1000 A) ⇒ Delay angle is α ≈ 22.5° ⇒ Overlapping angle is µ ≈ 3.4° (overlapping time ~190 µs) ⇒ Ls = 23 µH (as calculated from the formula shown before) Elettra – Transfer Line Dipole Power Supply PSB_T2.2: 200 V / 1080 A, 12p fully controlled bridge (without inter-phase reactor) – Output Voltage waveforms. Rectifiers - 26 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Protection & Interlock - Switches Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Protection of Thyristors (Diodes): º Overcurrent (preventing the junction temperature to exceed the limit) • Fuses • Proper choice of components (ratings 30 to 50% • º higher than specified) Anode current monitoring acting on the trigger delay angle Overvoltage (avoid the reverse break down and the unwanted turn-on) • Proper choice of components (ratings 30 to 50% higher than specified) both VRRM and VDRM º Voltage Transients or Surges Golden Rule: store quickly the surge energy (in C) and dissipate it slowly (in R) • • Rectifiers - 27 AC Input side surges (e.g. due to opening of the main contactor) ⇒ “Bucket Circuit” Reverse Recovery charge of Thyristor (at turnoff) ⇒ “Snubber Circuit” Note Sometimes a diode is placed in parallel to R1 to charge C1 more efficiently CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Protection & Interlock - Converter Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Main Items: º Circuit Breaker & Contactor (with “Soft Start”) º Transformer (overcurrent, over-temperature) º Thyristor Bridge (over-temperature) º Passive Filter (excessive ripple, over-temperature) º Load (overvoltage, over-temperature) º Personnel (interlock on doors, emergency off button, …) “Soft Start” Circuit Breaker Rectifiers - 28 Main Switch Transformer Thyristor Bridge F-W Diode Passive Filter F-W Diode Load CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Example: Elettra’s SR Dipoles’ PS 1. 2. 3. 4. 5. 6. Circuit Breaker Transformer Bridge (a) & Thyristor (b) Passive Filter PS cabinet Magnets 2 Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste 3 6 1 4 3b 1 Rectifiers - 29 2 3a 4 5 5 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Example: Elettra’s SR quads’ PS Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste º 6-p and 12-p Elettra – Storage Ring QD and S1Power Supplies Cabinet. Converters º Single and Multiple converters in each cabinet Elettra – Storage Ring QF Power Supply Cabinet. Elettra – Storage Ring Quadrupoles. Rectifiers - 30 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Example: Elettra’s SR Steerers’ PS Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Elettra – Storage Ring Combined H+V corrector. Elettra – Storage Ring Corrector Power Supply. Elettra – Storage Ring Correctors Power Supplies Cabinet. Rectifiers - 31 Linear Multichannel: º Thyristor PreRegulator º 12-p Diode Bridge (in series, “zero” is common point) º 14 Channels + 2 spares CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Line Comm. Rectifiers – Pros & Cons º º º º º Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Pros Very well known and established technology with simple structures The effect of “parasitic” parameters (inductance and capacitance) is low High Efficiency High Voltage and High Power Capability Used as “building blocks” inside Switched Mode converters with “Unity Power Factor” Cons º º º º º º Bandwidth limited (not really important for DC applications) Power factor depending on firing angle, in any case below 0.75 Strong Harmonic content on input current Thyristors notches in mains and noise spikes Large and heavy magnetic elements (transformers, chokes) Residual ripple at low frequency (300 Hz up) which require large passive filters and, often, active filters to meet specifications Rectifiers - 32 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004 Emerging Topologies… Line Commutated Rectifiers Roberto Visintini Sincrotrone Trieste Goals: Ø Ø Ø Ø Ø Reduce alternating current harmonic content Improve Power Factor Better filtering of output current ripple Higher dynamic response More flexible control… ð PWM Techniques On the other hand: Ø High Switching Frequency ⇒ parasitic elements ARE important Ø Sometimes quite complicated structures Ø EM noise Rectifiers - 33 CAS – “Power Converters” – Warrington, UK – 12 to 18 May 2004