Chapter 4

# Chapter 4 - 4-1 Chapter 4 Basic Understanding of Power...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4-1 Chapter 4 Basic Understanding of Power Processing in Electric Drives Exit 2001 by N. Mohan Print TOC " ! 4-2 Power Processing Unit (PPU) ❏ Efficient conversion of power from line frequency AC to appropriate form required by the motor Sub-blocks of PPUs utility + Vd − M switch - mode converter Rectifier controller ❏ Rectifier: Line frequency AC to DC ❏ Switch-Mode Converter: DC to form required by motor Exit 2001 by N. Mohan TOC " ! 4-3 Switch-Mode Converters for dc- and ac-motor drives + A ia M For DC Drives Exit 2001 by N. Mohan A + Vd − ia B B Vd − M C For AC Drives TOC " ! 4-4 Analysis of Switch-Mode Converters ❏ Pole as a Building Block pole-A + Vd − voltage port i A (t ) A + current v AN (t ) port − q A (t ) N vc, A (t ) vtri (t ) PWM-IC ❏ Vd uncontrolled ❏ vc, A : control voltage depicting desired output voltage ❏ Switch modulated to produce desired average voltage v AN Exit 2001 by N. Mohan TOC " ! 4-5 Pulse Width Modulation ( PWM ) if vc, A (t ) > vtri( t) ⇒ q A ) = 1 ⇒ switch "up" ⇒ v AN t = Vd ( t () if vc, A (t ) < vtri( t) ⇒ q A ) = 0 ⇒ switch "down" ⇒ ( AN t = 0 v) ( t ! Vtri vtri (t ) vc, A (t ) t 0 v AN (t ) = q A (t )Vd 1 q A (t ) 0 Vd t d ATs v AN (t ) 0 v AN t Ts = 1 / f s Exit 2001 by N. Mohan TOC " ! 4-6 Average Representation of a Pole Output Voltage Average output voltage over one switching cycle 1 v AN = ∫ v AN (t ) dt = d AVd Ts Ts Duty ratio ⇒ v AN dA = 1 1 vc, A + ˆ 2 2 Vtri Vd Vd / 2 = + vc, A ˆ 2 Vtri " " dc offset k pole Pole gain V /2 k pole = d ˆ Vtri ! Vtri vtri (t ) vc, A (t ) t 0 1 q A (t ) 0 Vd t d ATs v AN (t ) 0 v AN t Ts = 1 / f s Pulsating v AN (t ), relatively smooth i A (t ) Exit 2001 by N. Mohan TOC " ! 4-7 Average Representation of a Pole Input and Output Currents ❏ Assuming ripple in i A (t ) to be negligible, i.e. i A (t ) = iA (t ) average values of input and currents can be related as, idA (t ) = d A (t ) iA (t ) idA (t ) + Vd − vc, A (t ) Exit 2001 by N. Mohan pole-A control function t 0 i A (t ) voltage port vtri (t ) PWM-IC q(t ) q A (t ) i A (t ) ideal output current iA t A 0 + idA (t ) current idA t v AN (t ) port dTs 0 − ideal and average input current =1 / fs Ts N i A (t ) i A 0 t actual output current (ripple often ignored) TOC " ! 4-8 Average Representation of a Pole as An Ideal Transformer idA (t ) + v AN (t ) = d A (t )Vd Vd idA (t ) = d A (t ) iA (t ) iA (t ) + 1 − d A (t ) v AN (t ) − vc, A (t ) 1 + ! Σ 2Vtri + 1/ 2 ❏ Transformer turns-ratio is adjustable via Pulse Width Modulation ❏ This Transformer can pass AC and DC currents but only unipolar voltages Exit 2001 by N. Mohan TOC " ! 4-9 Pole as a Two Quadrant Converter idA (t ) ❏ v AN always positive ❏ iA can reverse x iA > 0 if v AN > Ea power Vd → Ea ⇒ + Vd − voltage port i A (t ) + v AN − N Buck Mode power Ea → Vd 2001 by N. Mohan current port + − Ea Ra IA + Vd − + 1 dA VAN = d AVd + Ea − − Boost Mode vc, A (t ) Exit Ra q A (t ) x iA < 0 if v AN < Ea ⇒ A La 1 + Σ ˆ 2Vtri + 1/ 2 TOC " ! 4-10 Calculation of Ripple Current Ra i A (t ) La + v AN (t ) − IA + Ea = − + VAN + Ea − vripple (t ) i A (t ) = I A + iripple (t ) v AN (t ) = V AN + vripple (t ) VAN − Ea Ra iripple (t ) = sawtooth with zero DC average IA = ∆i A = Exit 2001 by N. Mohan iripple Ra + − La + vripple (t ) − Vd −V AN 0 dTs t VAN Ts iripple (t ) 0 i A (t ) t IA 0 t (V − VAN )dTs V (1 − d )Ts volt − seconds = d , or AN La La La TOC " ! 4-11 Implementation of Bi-Positional Switches Buck Boost iC + iA ON Vd − q vc, A + A 0 Von q− A approx switching trajectory OFF switching power loss for a very short time VCE q A (t ) vtri ❏ Switching frequency 6kHz to 50kHz ❏ Switching power loss: kept low by fast switching devices ❏ Conduction loss: kept low by having switches fully ON or fully OFF Exit 2001 by N. Mohan TOC " ! 4-12 id Switch-Mode Converters for DC-Motor Drives idA iA Vd idB + vo + − − idA io + iB ea − + + d A (t ) 1 Vd v AN (t ) − + d B (t ) vBN (t ) 1 q A (t ) − vc (t ) qB (t ) vc (t ) vtri (t ) DC motor io idB + vo (t ) − − 1 Σ ˆ 2Vtri + + 1/ 2 −1 1 + Σ ˆ vc, B (t ) 2Vtri + 1/ 2 1 v (t ) d A (t ) = + c ˆ 2 2Vtri 1 v (t ) d B (t ) = − c ˆ 2 2Vtri V V v AN (t ) = d + d vc (t ) ˆ 2 2Vtri V V vBN (t ) = d − d vc (t ) ˆ 2 2Vtri ❏ Output voltage can be positive or negative Exit 2001 by N. Mohan TOC " ! 4-13 Analysis of DC-Motor Drives Based on Average Quantities v (t ) d (t ) = d A (t ) − d B (t ) = c ˆ Vtri ( −1 ≤ d ≤ + 1) vo (t ) = v AN (t ) − vBN (t ) = ( −Vd ≤ vo ≤ + Vd ) V k PWM = d ˆ Vtri Vd v (t ) ˆtri c V vo (t ) = k PWM ⋅ vc (t ) id DC motor io (t ) + + 1 Vd − d (t ) vo (t ) − vc (t ) 1 ˆ V tri ❏ Combined transformer ❏ Four quadrant capability ❏ Transformer can pass AC or DC currents and voltages Exit 2001 by N. Mohan TOC " ! 4-14 Three Phase Inverter AC-Motor Drives iA A + Vd iB B n − iC C q A (t ) vc, A (t ) ˆ Vc PWM v (t ) c, B f1 IC qB (t ) vc,C (t ) vtri qC (t ) # vc, A (t ) = Vc sin(ω 1t ) # vc,B (t ) = Vc sin(ω 1t − 1200 ) # vc,C (t ) = Vc sin(ω 1t − 2400 ) Exit 2001 by N. Mohan ˆ Vc sin(ω t ) d A (t ) = 0.5 + 1 ˆ 2Vtri ˆ d B (t ) = 0.5 + Vc sin(ω1t − 1200 ) ˆ 2Vtri ˆ dC (t ) = 0.5 + Vc sin(ω1t − 2400 ) ˆ 2Vtri TOC " ! 4-15 Transformer Equivalent of a Three Phase Converter iA (t ) Voltages with respect to to N V V v AN (t ) = d + d 2 2 \$ + Vd ˆ V sin(ω1t ) ˆtri c 2V " k pole ˆ = k pole Vc sin(ω1t ) \$ + ˆ Vd Vc sin(ω1t ) ˆ Vtri − + d B (t ) 1 v A (t ) 1 d A (t ) 1 vB (t ) − − idC (t ) A B C iB (t ) iC (t ) + dC (t ) eB (t ) n eC (t ) vC (t ) − N Voltages with respect to load-neutral n v An (t ) = idB (t ) idA (t ) e A (t ) vc, A (t ) 1 + Σ ˆ 2Vtri + vc, B (t ) 1 + Σ ˆ 2Vtri + vc,C (t ) 1 + ˆ 2Vtri + Σ 1/ 2 DC offset voltages disappear when voltages are with respect to load neutral Exit 2001 by N. Mohan TOC " ! 4-16 Power Devices ❏ Voltage rating up to 9kV ❏ Current rating ~ kA ❏ Switching items ~ 0.1 µ s ❏ On-State voltage drop 1V to 3V ❏ Cost Exit 2001 by N. Mohan TOC " ! 4-17 Controlled Switches ❏ MOSFET + iD G VDS G x Insulated gate for low gate requirements D D iD VGS − S S VGS = 7V 6V on state 5V 4V VDS x Built-in diode x rds increases exponentially with voltage rating x Good for low voltage, high frequency Exit 2001 by N. Mohan TOC " ! 4-18 ❏ IGBT - Insulated Gate Bipolar Transistor C iC + G VCE VGE + VGE − − E VCE x Insulated Gate for low drive requirements x Moderately high switching frequency x Lower conduction losses than MOSFETs in high voltage devices x Higher voltage (up to 3.3 kV) and current rating (up to 1200A) Exit 2001 by N. Mohan TOC " ! 4-19 ❏ Smart Power Modules • Gate Driver ICs • Power Modules (some with Gate drivers) Exit 2001 by N. Mohan TOC " ! 4-20 Summary ❏ What is the function of PPUs? ❏ What are the sub-blocks of PPUs? ❏ What are the roles of the rectifier and the filter-capacitor sub-blocks? ❏ Qualitatively, how does a switch-mode amplifier differ from a linear amplifier? ❏ Why does operating transistors as switches result in much smaller losses compared to operating them in their linear region? ❏ How is a bi-positional switch realized in a converter pole? ❏ What is the gain of each converter pole? ❏ How does a switch-mode converter pole approach the output of a linear amplifier? ❏ What is the meaning of v AN (t ) ? Exit 2001 by N. Mohan TOC " ! 4-21 Summary ❏ How is the pole output voltage made linearly proportional to the input control signal? ❏ What is the physical significance of the duty-ratio, for example d A (t ) ? ❏ How is pulse-width-modulation (PWM) achieved and what is its function? ❏ Instantaneous quantities on the two sides of the converter pole, for example pole-A, are related by the switching signal q A (t ) . What relates the average quantities on the two sides? ❏ What is the equivalent model of a switch-mode pole in terms of its average quantities? ❏ How is a switch-mode dc-dc converter which can achieve an output voltage of either polarity and an output current flowing in either direction realized? Exit 2001 by N. Mohan TOC " ! 4-22 Summary ❏ What is the frequency content of the output voltage waveform in dc-dc converters? ❏ In a dc-drive converter, how is it possible to keep the ripple in the output current small, despite the output voltage pulsating between 0 and Vd , or 0 and −Vd , during each switching cycle? ❏ What is the frequency content of the input dc current? Where does the pulsating ripple component of the dc-side current flow through? ❏ How is bi-directional power flow achieved through a converter pole? ❏ What makes the average of the dc-side current in a converter pole related to the average of the output current by its duty-ratio? Exit 2001 by N. Mohan TOC " ! 4-23 Summary ❏ How are three-phase, sinusoidal ac output voltages synthesized from a dc voltage input? ❏ What are the voltage and current ratings and the switching speeds of various power semiconductor devices? Exit 2001 by N. Mohan TOC " ! ...
View Full Document

## This note was uploaded on 02/06/2012 for the course EE 4002 taught by Professor Scalzo during the Fall '06 term at LSU.

Ask a homework question - tutors are online