Chapter 4

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

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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 " ! ...
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