Chapter 7

Chapter 7 - 7-1 Chapter 7 DC Motor Drives Exit 2001 by N...

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Unformatted text preview: 7-1 Chapter 7 DC Motor Drives Exit 2001 by N. Mohan Print TOC " ! 7-2 Introduction ❏ Cost PPU PPU PPU motor 1998 motor Future DC DRIVES PPU motor motor Future 1998 AC DRIVES ❏ Demise prematurely predicted, still used in speed control ❏ Merits ! Ease of control ! Cheaper Power Processing Unit ❏ Drawbacks ! mechanical commutator and brushes require maintenance Exit 2001 by N. Mohan TOC " ! 7-3 Classification of DC drives Electrical source Power Processing unit DC machine Mechanical system Permanent Wound rotor magnet Switch-mode converter Exit 2001 by N. Mohan Line-commutated thyristor converter TOC " ! 7-4 Structure of DC motors stator magnets Permanent magnets rotor winding φ f produced by permanent magnets φ f produced by stator winding current ❏ Stator ! Establishes field flux, φ f Exit 2001 by N. Mohan TOC " ! 7-5 Structure of DC motors ❏ Rotor !Armature winding !Commutator and brushes Exit 2001 by N. Mohan TOC " ! 7-6 Operating Principles of a DC Motor ❏ Field flux density in the airgap back − end θ 1b N N 1 1' S θ=0 φf S Bf ωm s1 b1 b2 s2 0 θ ia θ =0 Exit 2001 by N. Mohan TOC " ! 7-7 Operating principles - Commutator Action + ia ea − + ia ea − + ia ea − 1' S1 θ S2 1 1' + N − S θ =0 ωm Tem θ S2 N S2 S θ =0 − N 1' 1 − + S θ =0 ωm Tem S1 1 θ S1 + e1,1 ' , i1to1 ' θ 0 Tem = 2 B f ! ia r ea = 2 B f ! (r ω m ) 0o 180 o 90 o 270 o ea (t ) 360 o Ea (average) 0 0o 180 o ea (t ) 90 o 270 o 360 o θ Tem (t ) Tem (average) 0 0o Exit 2001 by N. Mohan 90 o 180 o 270 o TOC 360 o " θ ! 7-8 Four Coil Example 4′ e +I N + 1 + 3′ ωm + 4 2′ _ 4′ ea _ b ia e +2 a c 2 4b Ia 2 e + e 1′ 1b + ea ia 3′ + e _ 1′ 3 Ia 2 a + 4 d 1 + + _ 3b Ia Ia 2 2 e 3 S 2b + + 4′ 2e _ 2 + e Ia 2 1 + ea 4 ia + 3′ 2e _ 3 1′ 2 _ 2′ 2′ e + 2e _ + 2e _ at θ = 0o 0V N 2 + a 3′ + ia 1 4′ ea 1′ _ c b 2′ 4 S e d 3 + + 0V a d 4b 2 + e + ia 2b e_ a + e e 4 c b 3′ 3b 0V 0V 1′ 1′ 1b 1 4′ 1 2′ Ia 2 Ia 2 + ea + 4′ 2 ia 2e 4 _ 2′ + 2e 3 0V 0V CCW rotation by 45° Exit 2001 by N. Mohan TOC " ! 7-9 Four Coil Example (cont’d) N + 2 + 4′ a ωm 1 +_ ea ia 1′ b S a 1b 2 2 + _ 4 4′ + e a + ea ia 4b + e Ia 2 Ia 2 d 1 c 2′ 3′ _ e +3 d + 1′ e +I + e 2′ 2b c _ b Ia 2 e Ia 2 3b + + 1′ 2e _ 3 + e Ia 2 1 ia + 4′ 2e _ 4 + ea + 2 2e _ 2′ + 2e 3′ _ 3 _ 3′ e 4 CCW rotation by 90o ea 4e Torque and emf pulsations can be reduced by increasing the number of conductors Ea 2e ( average ) 0 0o 45o 90 o 2Tcond Exit 2001 by N. Mohan 180 o 225o 270 o 315o 360 o 180 o 225o 270 o 315o 360 o θ Tem 4Tcond 0 135o Tem ( average) 0o 45o 90 o 135o TOC θ " ! 7-10 Summary of Operating Principles ❏ ♦ ia divides equally between two parallel circuits ♦Torque produced on each conductor has the same direction ♦ Direction of ia determines direction of torque ❏ ♦Induced voltage in each circuit is equal to the sum of voltages induced in each coil. ♦ Polarity of induced emf depends only on the direction of rotation. i n Net Torque, Tem = na B f a lr = a lrB f ia = kT ia 2 2 n n & ea = a B f l (ω m r ) = a lrB f ω m = k Eω m 2 2 In M.K.S. Units k E = kT Exit 2001 by N. Mohan TOC " ! 7-11 Armature reaction N N S stator flux S resultant flux rotor flux Compensating winding ❏ Assuming magnetic structure does not saturate: Exciting winding x Increased torque in some conductors is compensated by decreased torque in other conductors x Same reasoning holds for induced emf ❏ Compensating winding to reduce the effect of armature reaction Exit 2001 by N. Mohan Commutating winding Commutating pole TOC " ! 7-12 DC Machine Equivalent Circuit ia + va + N Tem ωm S va _ T ia = em kT va = ea + Ra ia + La Tem = kT ia d ia dt dω m 1 (Tem − TL ) = dt J eq Exit 2001 by N. Mohan ω m, rated + Tem , ω m ea = k E ω m _ f constant at its rated value Va1 > Va2 > Va3 > Va4 Va1 = rated Va2 Va3 Va4 La JM ea = k E ω m ωm Ra _ Basic equations φ TL JL rated Tem TOC " Steady State Ia = Tem (= TL ) kT ωm = Va − I a Ra kE ! 7-13 Operating Modes ia + ia = − Tem Motoring in forward direction ωm φa φf va Regenerative braking in forward direction − + + + + ia = − φa + − − Tem − − ωm − + − + φf va − Ra + Regenerative Braking La ωm ea = k E ω m _ JM TL Tem JL ❏ Regenerative Braking: Feeding energy back while braking x current and torque direction reversed x same polarity of induced emf ❏ Operation in reverse direction: polarity of applied voltage reversed ia < 0 x Motoring x Regenerative braking ia > 0 Exit 2001 by N. Mohan TOC " ! 7-14 Four Quadrant Operation ωm Regenerative Braking in φa Forward direction ea = + ia = − Tem Motoring in Forward direction φf φf φa ωm φa Exit 2001 by N. Mohan φf φf Tem Tem ,ω m Tem Regenerative Braking in Reverse direction Motoring in Reverse direction ea = − ia = − Tem ,ω m ea = + ia = + ωm φa ea = − ia = + TOC " ! 7-15 Flux weakening in wound field machines to Allow Overspeed Operation ωm ω m, rated 2 Va = rated I a = rated φ f = varied 1 0 1 Va = rated I = rated a φ f = rated Tem Tem, rated ❏ Below rated speed, kT maximum to ensure maximum torque/Ampere thereby minimizing resistive losses ❏ Above rated speed, B f reduced to keep Va at its rated value. ❏ B f reduced by reducing I f ❏ kT and k E changed; kT = kt B f ; k E = ke B f ; kt = ke ❏ Since I a is limited to its rated value maximum, Tem reduces Exit 2001 by N. Mohan TOC " ! 7-16 Power Processing Unit for DC Drives ❏ Draw power from utility - power quality problems Ideally power flow should be reversible ❏ Provide nearly dc voltage and current to the dc motor dc-dc converter line voltage T+ A + vd − − TA + TB − TB ia + va − " $# " $# # % # % ac to dc filter rectifier capacitor vcontrol vtri PWM-IC Exit 2001 by N. Mohan TOC " ! 7-17 Electronically Commutated Motor Drives (Trapezoidal waveform brush-less dc) ❏ “Inside out” machines ❏ Electronically commutated armature ❏ At any instant, only two sets of windings carry currents. As the rotor turns, different pairs of windings are chosen. a' − c ic S ωm utility δ magnetic axis of phase a + N c' a + ia permanent magnets ia + b ea b' ib + b Vd − + ea − a c logic Exit 2001 by N. Mohan shaft position signals TOC " ! 7-18 Rotating Field & Stationary Conductors S + ecoil λcoil δ 0 ωm δ N ecoil 0 u S a − axis − u − δ N B B u u B B + ❏ Flux linkage of a single turn coil (−π / 2 ≤ δ ≤ π / 2) λcoil = (π rl ) B f (δ /(π / 2) ) d λ d λ dδ π rlB f ω m B f lrω m ❏ emf induced ecoil = dt = dδ dt = π / 2 = 2 " $# # % econd total induced emf = 2N s B f lrω m (when all turns are under common pole) ❏ Polarity determined by assuming field to be stationary and and the conductor moving in opposite direction Exit 2001 by N. Mohan TOC " ! 7-19 Induced emf ea a' − c ic S ωm ib + b + δ δ = 0o 60o 120o 180o 240o 300o 360o δ eb ea δ b' N c' a + ia ec δ ❏ In flat regions all turns are under same pole ❏ In sloped regions some turns are under N pole while others are under S pole Exit 2001 by N. Mohan TOC " ! 7-20 Torque Production Tem, a fem S 0 δ δ = 0o Tem, a N fem ❏ Force on conductors f = Bli Tem,b Tem, c ❏ Excite two phases simultaneously0 0 0 Exit 2001 by N. Mohan δ 0 torque on rotor CCW Total Tem = 2 × (2N s B f lr ) I = kT I δ 0 a a c c a c c b b (−a ) (−b) (−b) (−c) (−c) (−a ) (− a ) (−b) (−b) ia δ ib δ ic δ TOC " ! 7-21 ❏ Equivalent circuit ia a a + Vd + b − Vd b − i a b − + Eback − emf c Phase-to-phase back induced emf eback −emf = 2e ph = 2 × (2N s B f lr )ω m = k Eω m k E = kT ❏ Hysteresis current control i IH I desired IL 1 0 Exit 2001 by N. Mohan 2 t Position 1: Pole a high, Pole b low Position 2: Pole a low, Pole b high After 60 o rotor rotation, a new pair of poles (a,c) are used TOC " ! 7-22 Summary ❏ What is the breakdown of costs in dc-motor drives relative to ac-motor drives? ❏ What are the two broad categories of dc motors? ❏ What are the two categories of power-processing units? ❏ What is the major drawback of dc motors? ❏ What are the roles of commutator and brushes? ❏ What is the relationship between the voltage-constant and the torque-constant of a dc motor? What are their units? ❏ Show the dc-motor equivalent circuit. What does the armature current depend on? What does the induced back-emf depend on? ❏ What are the various modes of dc-motor operation? Explain these modes in terms of the directions of torque, speed, and power flow. Exit 2001 by N. Mohan TOC " ! 7-23 Summary ❏ How does a dc-motor torque-speed characteristic behave when a dc motor is applied with a constant dc voltage under an open-loop mode of operation? ❏ What additional capability can be achieved by flux weakening in wound-field dc machines? ❏ What are various types of field windings? ❏ Show the safe operating area of a dc motor and discuss its various limits. ❏ Assuming a switch-mode power-processing unit, show the applied voltage waveform and the induced emf for all four modes (quadrants) of operation. ❏ What is the structure of trapezoidal-waveform electronicallycommutated motors? Exit 2001 by N. Mohan TOC " ! 7-24 Summary ❏ How can we justify applying the equation in a situation where the conductor is stationary but the flux-density distribution is moving? ❏ How is the current controlled in a switch-mode inverter supplying ECM? ❏ What is the reason for torque ripple in ECM drives? Exit 2001 by N. Mohan TOC " ! ...
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