First Course on Electric Drives Electric Drives: An Integrated Approach Chapter 1 Introduction to Electric Ned Mohan Drive Systems Oscar A. Schott Professor of Power Electronics and Systems Department of Electrical and Computer Engineering University of Minnesota Minneapolis, MN 55455 USA ©Copyright Ned Mohan 2003 1 ©Copyright Ned Mohan 2003 2 Print Audio TOC  (cid:66) Trend : Adjustable Speed Drives History (ASDs) Constant frequency AC -essentially constant pump speed (cid:134) (cid:134) Inefficient -Heat generated in pump and throttling valve Outlet Not amenable to automation (cid:134) Adjustable Speed Drive (ASD) Inlet Constant frequency Adjustable frequency Adjustable Pump AC electric converter speed Throttling Valve Outlet Driven at appropriate speed (cid:134) MOTOR Inlet (cid:139) High Efficiency Constant Pump frequency ⇒ Essentially AC Constant Speed ©Copyright Ned Mohan 2003 3 ©Copyright Ned Mohan 2003 4 Audio TOC  (cid:66) Audio TOC  (cid:66) What is an Electric-Motor Drive? World Market and Scope Electric Drive Power Processing Motor Load fixed Unit (PPU) form Elec(truitcil iStyo)urce adjfuosrtmable psopseietido n/ Sensors Controller measured Power speed/ position Signal input command (speed / position) Role of Electric Drive: Efficient conversion of power (cid:138) from electrical to mechanical (cid:138)healthy growth rate (cid:138)A very wide range of Role of PPU: Delivers appropriate form of frequency to (cid:138) motor (as required by the load) ~ 25% per year speed and power ©Copyright Ned Mohan 2003 5 ©Copyright Ned Mohan 2003 6 Audio TOC  (cid:66) Audio TOC  (cid:66) Typical Applications Factors for Growth Process Industry -agitators, pumps, fans, compressors (cid:134) Machining -planers, winches, calendars, chippers, drill presses, (cid:134) Technical Advances in sanders, extruders, grinders, mills, presses (cid:134) Heating and Air Conditioning -blowers, compressors (cid:139) Linear ICs and Digital Signal Processors (cid:134) Paper and Steel Industry -hoists, rollers (cid:134) (cid:139) Power devices (cid:134) Transportation -elevators, trains, automobiles Textile -looms (cid:134) Packaging -shears Market Needs (cid:134) (cid:134) Food -conveyors, fans (cid:134) (cid:139)$20 Billion market in 1997 Oil, Gas , Mining -compressors, pumps, cranes, shovels (cid:134) Residential -heat pumps, freezers, washing machines (cid:139) 25% Growth rate (cid:134) ©Copyright Ned Mohan 2003 7 ©Copyright Ned Mohan 2003 8 Audio TOC  (cid:66) Audio TOC  (cid:66) Application for Energy Conservation Energy Conservation in Pumps (cid:134)Heat Pumps and air-conditioners -cycled operation throttling ideal actual valve outlet Pressure (H) loss ∆H Q2 A ( H2+ ∆H , Q2) ( H1, Q1) Compressor motor H2+∆H H2 Output Q2 Pump curve at pump inlet D C B full speed full speed Throttled ( H2, Q2) t System Pump curve at no throttling outlet Curve reduced speed ON OFF S Apdeejuds Dtarbilvee valve H2 Q2 UnStyhsrtoetmtled thPrroetstlsiunrge vaaclrvoes,s ∆H 30% improvement in efficiency by running (ASD) Curve (cid:138) compressor at appropriately reduced speed reduced pump inlet Q2 0 Q2 Q1 Flow Rate (Q) speed using an ASD (cid:139)Throttling introduces extra pressure drop,∆H (cid:139)ASD reduces pump speed to match load requirement ©Copyright Ned Mohan 2003 9 ©Copyright Ned Mohan 2003 10 Audio TOC  (cid:66) Audio TOC  (cid:66) Energy Conservation in Blower Harnessing Wind Energy Systems Constant Variable frequency 100 Outlet damper V awriianbdle V sapreiaebdle F r e AquCency P rPoocwesesring AC Variable generator Unit 80 speed Utility Power Consumption 60 Inlet vane Wind turbine (% of full flow rate) 40 Electric drive 20 0 100 90 80 70 60 50 40 30 % Flow Rate (cid:134)Relative power consumption using three methods to reduce blower flow rate ©Copyright Ned Mohan 2003 11 ©Copyright Ned Mohan 2003 12 Audio TOC  (cid:66) Audio TOC  (cid:66) Hybrid Electric Vehicles Multi-disciplinary Nature of Electric Drives Machine Utility Theory Power Interaction Electronics IC Continuously Variable Engine Transmission Electric Control Sensors Drives Theory Electric Motor Mechanical Real-time system modelling DSP control ©Copyright Ned Mohan 2003 13 ©Copyright Ned Mohan 2003 14 Audio TOC  (cid:66) Audio TOC  (cid:66) Summary Evolution of Power Processing Unit •What is an electric drive? Draw the block diagram and explain the roles of its various components. 120 200 •What has been the traditional approach to controlling flow % 104680000 SWiezeig (hvtolume) Relative unit 11055000 CFuonmcptioonnesnts •Wrathea ti na rteh et hper omcaejsosr i nddisuasdtvrya?ntages which can be overcome 20 0 0 by using adjustable speed drives? 1968 Y19e8a8r 1998 1968 1983 1988Yea1993r 1998 •What are the factors responsible for the growth of the adjustable-speed drive market? 4kW DanfossVLTR power processing unit •How does an air conditioner work? (Consult a handbook such as [10].) •How does a heat pump work? •How do ASDssave energy in air conditioning and heat pump systems? ©Copyright Ned Mohan 2003 15 ©Copyright Ned Mohan 2003 16 Audio TOC  (cid:66) Audio TOC  (cid:66) Summary (cid:134)What is the role of ASDsin industrial systems? Chapter 2 (cid:134)There are proposals to store energy in flywheels for load leveling in utility systems. During the off-peak period for energy demand at night, these flywheels are charged to high speeds. At peak periods during the day, this energy Understanding Mechanical is supplied back to the utility. How would ASDsplay a role System Requirements in this scheme? (cid:134)What is the role of electric drives in electric transportation systems of various types? (cid:134)List a few specific examples from the applications mentioned in section 1-4 that you are personally familiar with. (cid:134)What are the different disciplines that make up the study and design of electric-drive systems? ©Copyright Ned Mohan 2003 17 ©Copyright Ned Mohan 2003 18 Audio TOC  (cid:66) Print Audio TOC  (cid:66) Motivation Systems With Linear Motion (cid:134)How can the ASD accelerate and decelerate the load to fe M fL fM M give desired speed profile ⇒ x u=ddxt ; a=ddut = feM−fL u=dx ; a=du = fM dt dt M ASD Load (cid:139)Figure on left includes load force, f , that must be overcome L ω L (cid:139)Figure on right shows only the force, f , available to accelerate M the mass, M ω(rad/sec) L desired speed profile Accelaration Power Input Kinetic energy 100 a= feM−fL= fMM Pe(t)=fe⋅u= fM⋅u+fL⋅u WM=12Mu2 0 1 2 3 4 5 6 7 ( ) t sec ©Copyright Ned Mohan 2003 19 ©Copyright Ned Mohan 2003 20 Audio TOC  (cid:66) Audio TOC  (cid:66) Rotating Systems (cid:134)Torque in an electric drive f f ω 90o Motor Tem TL Load M β r θ torque Mg θ (cid:139)Tem electromagnetic torque produced by motor (cid:139)Tem is opposed by load torque, TL (cid:139) Torque = force radius (cid:139) The difference, T e m − T L = T J , will accelerate the system [Nm] [N] [m] (cid:139) dω=Tem −TL=TJ dt J J (cid:139) Example: what torque is needed to hold M motionless where Jis the moment of inertia ©Copyright Ned Mohan 2003 21 ©Copyright Ned Mohan 2003 22 Audio TOC  (cid:66) Audio TOC  (cid:66) Calculation of Moment of Inertia Accelaration, Speed and Position, Power J and Energy of a Uniform Cylinder d(cid:65) dr (cid:65) rdθ drf dM Motor Tem ωm TL Load Tem+−Σ TJ J1eq α ∫ ωm ∫ θ r1 ω dθ TL θ acceleration, α = dωm = 1 (T −T )= TJ df=dM d v dM =ρr(cid:78)dθ d(cid:78)r d(cid:78)(cid:65) dt (Jm+JL) em L Jeq dt arc heightlength ⇒dT=r2dM dω=ρ(r3drdθd(cid:65))dω ⇒speed, ωm(t) =ωm(0)+∫0t α(τ)dτ dt dt ⇒position, θ(t) =θ(0)+ ∫t ω(τ)dτ T=ρ(r∫1r3dr2∫πdθ(cid:65)∫d(cid:65))dω= (πρ(cid:65)r14)dω 0 0 0 0 dt (cid:8)2(cid:11)(cid:9)(cid:11)(cid:10)dt Power P =T ⋅ω ; P =T ⋅ω em em m L L m J Jsolid =π2ρ(cid:65)r14=21Mr12 KineticEnergy W = 1Jω2 2 ©Copyright Ned Mohan 2003 23 ©Copyright Ned Mohan 2003 24 Audio TOC  (cid:66) Audio TOC  (cid:66) Frictional Torque (cid:134)Example: Aerodynamic coloumb drag T friction f Drag power at different speeds stiction visTcfou=sB fωriction pfL==0fL.0⋅4u6CwAv2; (Cw: drag coefficient) 0 ω  stiction ∴powerαspeed3  coloumb Power (W) friction Speed (km/h) Stiction: static component C =0.3 C =0.5 (cid:139) w w (cid:139) Coulomb friction: dynamic component 50 0.86 kW 1.44 kW (constant magnitude) 100 6.9 kW 11.5 kW Viscous friction: speed dependent 150 23.3 kW 38.8 kW (cid:139) In general, friction is non-linear (cid:139) ©Copyright Ned Mohan 2003 25 ©Copyright Ned Mohan 2003 26 Audio TOC  (cid:66) Audio TOC  (cid:66) Torsional Resonances Mechanical - Electrical Analogy ω ω m L Motor Tem TL Load T shaft J L At motor end T Jm = T −J dωm (cid:132) Torque (cid:132) Current shaft em m dt (cid:132) Angular Velocity (cid:132) Voltage dω Angular Displacement Flux Linkage At load end T = T +J L (cid:132) (cid:132) shaft L L dt Moment of Inertia Capacitance (cid:132) (cid:132) T (θ −θ ) = shaft Spring Constant 1/Inductance m L (cid:132) (cid:132) K θm andθL :angularrotationat thetwoendsof theshaft (cid:132) Damping Coefficient (cid:132) 1/Resistance (cid:139) If K →∞, θ =θ (cid:132) Coupling Ratio (cid:132) Transformer ratio m L ( J a n d J can be treated as one inertial mass ) M L (cid:139)Finite K may lead to resonances ©Copyright Ned Mohan 2003 27 ©Copyright Ned Mohan 2003 28 Audio TOC  (cid:66) Audio TOC  (cid:66) Coupling Mechanisms Electrical Analogy of Motor & Load Required when (cid:134) ωm ωL (cid:139) a (rotary) motor is driving a load which requires linear Motor Tem TL Load (translational) motion JL (cid:139) motors prefer higher rotational speed than that required J m by the load ωM 1/K ωL ωm (cid:139) the axis of rotation needs to be changed Tem TJM Tshaft TJL TL Tem TJ TL J J M L (cid:134)Types J =J +J eq M L (cid:139)Conveyor belts (belt and pulley) Finite shaft stiffness Infinite shaft stiffness (cid:139)Rack and pinion or a lead-screw type of arrangement (cid:139)Gear mechanisms ©Copyright Ned Mohan 2003 29 ©Copyright Ned Mohan 2003 30 Audio TOC  (cid:66) Audio TOC  (cid:66) Conversion between Linear and Rotary Gears Systems T r f Tem 1 1 M uL Jm=motor inertia MotJor ωM r M = mass of load M r T2 TL ω r = pulley radius 2 Load m ω Motor Tem du L JL f = M + f (cid:139) Basic relationships: radius, speed, torque L J dt m u = rω Equal speeds at gear surfaces ⇒r1ωM = r2ωL m dω Power transferred across gears ⇒ωMT1 = ωLT2, T = r fd=ωr2M dtm +rfLdω ⇒rr21 = ωωML = TT21 & (cid:8)Te(cid:11)m(cid:11)−(cid:11)J(cid:9)M(cid:11)dω(cid:11)dtM(cid:11)(cid:10)ωωML = (cid:8)TL(cid:11)+(cid:11)J(cid:9)L(cid:11)ddω(cid:11)tL(cid:10) T = J m + r2M +r f T T em m L 1 2 (cid:8)(cid:11)(cid:9)d(cid:11)t(cid:10) (cid:8)(cid:11)(cid:11)(cid:9)dt(cid:11)(cid:11)(cid:10) (cid:139)Geared up: speed increased, torque decreasedωL >ωM; T2<T1; r2<r1 required toaccelerate due toload (cid:139) Geared down: speed decreased, torque increased motor ωL <ωM; T2>T1; r2 >r1 ©Copyright Ned Mohan 2003 31 ©Copyright Ned Mohan 2003 32 Audio TOC  (cid:66) Audio TOC  (cid:66) Gears (cont’d) Types of Loads (cid:139) Equivalent Inertia Centrifugal loads  ω 2dω ω  Tem = Jm+JLωmL  dtm+ωmLTL (cid:8)(cid:11)(cid:11)(cid:11)(cid:9)(cid:11)(cid:11)(cid:11)(cid:10) Fan Jeq ω 2 r 2 ⇒ Jeq = Jm+JLωmL = Jm+JLr21 Constant Torque loads (cid:139)Optimum gear ratio (to minimize T ) em 2 r  r  J Jm =  1 ⋅JL ⇒  1 = m r2opt. r2opt. JL Hoist and (Tem)opt.= 2Jmddωtm =2Jmrr21opt.ddωtL ©Copyright Ned Mohan 2003 33 ©Copyright Ned Mohan 2003 34 Audio TOC  (cid:66) Audio TOC  (cid:66) Types of Loads Four-Quadrant Operation Squared power loads ω m (2) (1) ω =+ ω =+ Compressor m m T =− T =+ em em ω p=− p=+ T m em T Load em Constant power loads Motor ω =− ω =− m m Power T =− T =+ em em p=+ p=− (3) (4) Winder ©Copyright Ned Mohan 2003 35 ©Copyright Ned Mohan 2003 36 Audio TOC  (cid:66) Audio TOC  (cid:66) Summary Dynamic Operation (cid:137)What are the MKS units for force, torque, linear velocity, How the operating point changes with time (cid:134) angular velocity, speed, and power? Important for High Performance Drives (cid:137)What is the relationship between force, torque, and power? (cid:134) (cid:137)Show that torque is the fundamental variable in controlling Speed change: rapid and without any oscillations (cid:134) speed and position. Requires good controller design (cid:137)What is the kinetic energy stored in a moving mass and a (cid:134) rotating inertia? ©Copyright Ned Mohan 2003 37 ©Copyright Ned Mohan 2003 38 Audio TOC  (cid:66) Audio TOC  (cid:66) Summary Chapter 3 (cid:134)What is the mechanism for torsionalresonances? (cid:134)What are the various types of coupling mechanisms? Review of (cid:134)What is the optimum gear ratio to minimize the torque Basic Electric Circuits required from the drive to accelerate a load? (cid:134)What are the torque-speed and the power-speed profiles for various types of loads? ©Copyright Ned Mohan 2003 39 ©Copyright Ned Mohan 2003 40 Audio TOC  (cid:66) Print Audio TOC  (cid:66)