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Introduction to Power Electronics ECEN 2060 Spring 2008 References ECEN47975797 Intro to Power Electronics ececoloradoeduecen5797 Textbook RWErickson DMaksimovic Fundamentals of Power Electronics 2 d ed Springer 2000 httpececoloradoedupwrelectbookSecEdhtml Example GridConnected PV System One possible gridconnected PV system architecture DC input PV array VPV IPV PPV VPVIPV Power electronics converter i AC output vac t JEVRMS sinW iac t JEIRMS Sid AC utility V M grid Pac VRMS IRMS p110 Vaciac VRMS IRMS 0052wt Functions of the power electronics converter Operate PV array at the maximum power point MPP under all conditions Generate AC output current in phase with the AC utility grid voltage Achieve power conversion efficiency close to 100 ncorwerter P 16 PPV VRMS IRMS VPV IPV Provide energy storage to balance the difference between PPV and pact Desirable features Minimum weight size cost High reliability ECEN2060 Power electronics converter IPV Power electronics P V V converter array PV Inverter One possible realization IPV V PV DCDC S ingle phase V t V DC AC army PV Gamer er D C inverter Energy star ge capacitor Class objectives introduction to circuits and control of a DCDC converter and a singlephase DCAC inverter ECEN2060 Introduction to electronic power conversion Power input Dc dc conversion Acdc rectification Dcac inversion Switching power converter output Four types of power Iggy electronics converters Change and control voltage magnitude Possibly control dc voltage ac current Produce sinusoid of controllable magnitude and frequency Acac cycloconversion Change and control voltage magnitude Control is invariably required In the PV system for example POW Control input voltage of the DCDC input voltage to operate PV at MPP Control shape of the DCAC output input current to follow a sinusoidal reference Control current amplitude to balance the input and output power ECEN2060 and frequency Switching Power input converter output n Control feedforward feedback Controller reference High efficiency is essential P P law In mt P l MT 1 1 High efficiency leads to low power loss within converter Small size and reliable operation 04 is then feasible Efficiency is a good measure of converter performance 0392 I l l 06 PP 10s out ECEN2060 ECEN2UBU Circuit components for efficient electronic power conversion Raystars i T Caprcilm 393 Mugncrim DT T L mca 397 5 5 ume SM l39fi39I IUKI HIUIL Semiwnducmr ericcx Ideal switch Switch closed vt 0 it Switch open it 0 V In either event pt vl it 0 Ideal switch consumes zero power Power semiconductor devices eg MOSFETs diodes operate as nearideal power switches When a power switch is ON the voltage drop across it is relatively small When a power switch is OFF the switch current is very close to zero ECEN2060 Capacitor pCltrgtvCltrgtiCltrgt VC T For periodic VCz iCz No losses average capacitor power 0 1T CVCT C P 2 tdtz Iv tdv 2 12 T v2 0 0 C TOpCU T OClt C 2TCltgt Cm Capacitor charge balance average capacitor current O 1 T C VCT C I i tdt Idv v T v 00 C TOCU T C TClt C v 0 ECEN2060 C Inductor 39 l VLZ dlL L V L L pLtVLtlLZ For periodic VLt iLz No losses average inductor power O T iLT 1 L L 2 2 Pz I tdtz I tdl lT 10O L TOM Imam L 2TH Llt gt Inductor voltsecond balance average inductor voltage O 1 T LiLT L V v tdt Idi i T i 0 0 L To L0 of Tm Lu ECEN2060 9 Circuit components for efficient electronic power conversion 1 T Resist7m 39uJm imxx Mugwrits Semicondudur Ki39iL KA DTS Ts St fit1M4an Power electronics converters are circuits consisting of semiconductor devices operated as nearideal switches capacitors and magnetic components inductors transformers ECEN2UBU if Boost stepup DCDC converter L 2 C iLt vLt l t C Boost converter I 1 With ideal switch Vg i C R s v switch control Position 1 Position 2 DT S A L r T S TS 2 switching period f 1 TS 2 switching frequency D 2 switch duty ratio or duty cycle 0 S D S 1 ECEN2060 11 Boost converter circuit iLt vLt l t C Boost oon verter 1 with ideal switch Vg C T R s v L D1 gt f6 6391539 Realization using I39LU VLO l I power MOSFE T 1 C and diode V Power MOSFET and diode operate as nearideal switches ECEN2060 12 Power MOSFETs and diodes Characteristics of several commercial power MOSFETs Part number Rated max voltage Rated avg current Qg typical IRFZ48 60V 50A 1 1011C IRFSlO 100V 56A 8311C IRF540 100V 28A 7211C A 39 Cgt APT10M25BNR 100V 75A LOW on 00259 171nC DTS T IRF740 400V 10A irrISIS Eance 0559 6311C MTM15N40E 400V 15A pl39eS 39OW03Q 110nC APT5025BN 500V 23A condUCtlon 259 8311C losses APTlOOlRBNR lOOOV 11A 1052 15011C Fast switching enables high switching frequencies eg 100 s of kHz to MHz Part number Rated max voltage Rated avg current V typical l r max Ultrafast recovery rectifiers MUR815 150V 8A 0975V 35ns MUR1560 600V 15A 12V 60ns RHRU100120 1200V 100A 2 6V 60ns S chottky rectifiers MBR6030L 30V 60A 048V 444CNQ045 45V 440A 0 69V 30CPQ150 150V 30A 119V ECEN206O Characteristics of several commercial switching power diodes 13 Voltage current and frequency ratings of power semiconductor devices ruling 39Uv amlmurs 39 Voltage rating m 39urrunl Ill Hr 39 lilH Q Q I m 5 n 06 5 39 l x s In Ltuakllz Q l i 39 quot 39 1 Bill 1 qun IL I n 2 Current rating Iml u l ml u u nga MOSFET Metal Oxide Semiconductor Field Effect Transistor IGBT Insulated Gate Bipolar Transistor SCR or Thyristor Silicon Controlled Rectifier ECEN2060 GTO Gate Turn Off thyristor Boost converter analysis L 2 M c 1 original V C R con verter g 3 T S V switch in position 1 switoh in position 2 L L iCt iLt VLU iCt CT Rsv Vng CT RSV iLt VLt ECEN2060 15 Position 1 Inductor voltage and capacitor current vL Vg L iC v R VLOL Small ripple approximation Vg t C R 5 V VL 2 V8 T i0 V R ECEN2060 16 Position 2 Inductor voltage and capacitor current szVg v iCiL vR V Small ripple approximation g VL Vg V i0 I V R ECEN2060 Ci iLt L vLt ica C T RSV Inductor voltage and capacitor current waveforms v t L A Vg lt DTS gt lt D39TS gt I Vg V D 1D icm n 1 VR lt DTS gtlt D39TS gt VR Periodic steadystate operation Inductor voltsecond balance average inductor voltage O Capacitor charge balance average capacitor current O ECEN2060 Inductor voltsecond balance Net voltseconds applied to inductor VLU over one switching period lt DTS gtlt D39Ts gt TS f m dt Vg DTS Vg V D39Ts 0 Equate to zero and collect terms VgDD39 VD390 Solve for V v E D The voltage conversion ratio is therefore V 1 1 MD 2 2 2 U Vg D39 1 D ECEN2060 19 Boost DC voltage conversion ratio M Vom Vg 5 4 3 quot E 2 1 O i 0 02 04 06 08 1 D Boost DCDC converter stepsup a DC input voltage by a ratio M which is electronically adjustable by changing the switch duty ratio D ECEN2060 20 Simulink model ECEN2060 Switchedmode Boost boostSWItchngmd L 2 DCDC converter quotK675quot R 1Rload ioul L u V2 C V 100 V9 7 a 3 vow DCDC V39 gt39 switching 39L 05 D switch control D iL switch control Duty cycl e Boost DCDC Input voltage Vg 100 V Inductance L 200 pH Capacitance C 10 uF Load resistance R 100 2 Switch duty cycle D 05 Output voltage V0 200 V Input current IQ IL 4 A Power P 400 W Switching frequency f3 100 kHz Switching period T3 10 us ECEN2060 L 39 21 Averaged DC model No losses 1 1 out Vg 1D g 1D out Vglg V I Obit Obit Ideal boost DCDC converter works as an ideal DC transformer with an electronically adjustable stepup ratio g 1271 out 1 V V nMD g out ECEN2060 22 Modeling of losses Losses in switchedmode power converters Conduction losses due to voltage drops across inductor winding resistance and across power semiconductor switches when ON Conduction losses depend strongly on the output power Switching losses due to energy lost during ONOFF transitions Switching losses are not strongly dependent on output power a portion of switching loss remains even at zero output power Switching losses are proportional to the switching frequency Other losses including Losses in magnetic cores Power needed to operate control circuitry ECEN2060 23 Switching waveforms and switching losses MOSFET tumron transition zoomrin TLMVAynasx 5 J MEET mmth a ham m at mm mm Switching power loss Transition energy loss Switching irequency EcENzoso 24 Switching waveforms and switching losses MOSFET Iurnroii transition Dram Vaiuae 39 s M27 m i i 39 CH wian mam i m cm mm Mm ECENzoeo Switching power loss Transition energy loss Switching frequency Averaged DC model with losses 1g RL 1 D 1 out Mv V8 Isw Vow Small FiL models conduction losses due to inductor winding resistance and power switch resistances Small lSW models switching and other loadindependent losses Efficiency with losses when the load current IOUt is known 1 RL 1Wt 1 2 I 1 12 V I I out out 77 1 out ECEN2060 26 Example efficiency for various RL Assume Resistive load R Voullo 0 SW ut 1 1 RLI lt1 Dgt2 E 100 90 80 70 60 50 40 30 20 10 039 0002 001 002 005 RLR 01 Note that it is more difficult to achieve high efficiency if a large stepup ratio is required ie if dutyratio D is close to 1 ECEN2060 Singlephase DCAC gridconnected inverter 1 iL L ac 2 Q W 2 lac lt 1 Switches in position 1 during DTS in position 2 during 1 DTs Switching frequency fs is much greater than the AC line frequency 60 Hz or 50 Hz By controlling the switch duty ratio D it is possible to generate a sinusoidal AC current iac small switching ripple in phase with the AC line voltage as long as the input DC voltage VDC is sufficiently high ie as long as VDC is greater than the peak AC line voltage ECEN2060 28 Position 1 ECEN2060 29 Position 2 ECEN2060 30 Inductor voltsecond balance Note that switching frequency fs gtgt ac line frequency Over a switching period vact z const V VDC vacOStSDTS L VDC v DTSlttSTS 616 T 1 S VL T JVL 0dr DVDC Vac 1 DVDC Vac 2D1VDC Vac 0 S 0 MDVi2D 1 MD VDC 1 MDSl 05 I D VDC must be greater than the peak of vac ECEN2060 31 Control of AC line current 1 iL L ac 2 Q W 2 lac t 1 Control objectives iac M sin wt in phase with AC line voltage vact Amplitude IM or RMS value adjustable to control power delivered to the AC line vac t JEVRMS sinat idea 511m sinwr Pac I Vaciac VRMSIRMS 1 COSQW Pac VRMS IRMS ECEN2060 32 A simple current controller multiplier E39 comparator switch control with hysteresis iref I Mref sinwt iL lt iref Ai2 position 1 iL gt iref Ai2 position 2 iL is always within Ai2 of iref ECEN2060 comparator with hysteresis 4 2 A lt A switch control V gt A f Ai2 Ai2 4 D current ripple 33 Simulink model EcEmusu SwimmdrMade mic mm dcaciswitching mdl Waveforms Vact lac I39m and switch control er one AC line period 160 s Input voltage v00 200 v Inductance L 2 mH AC 120Vrms 60Hz 1W 342 42 A AIL 1 A Pac 360 w With this simple controller switching frequency is variable ECENZUBO 1 4 Averaged DCAC inverter model with losses V VDC Isw vac Y Ideal transformer Small FlL models inductor winding resistance and power switch resistances Small lSW models switching and other losses ECEN2060 DCAC inverter efficiency example ECEN2060 SwitchedrMode 0er inverter averaged model a VVVVVV 0er Scope Inverter efficiency of about 95 is typical At high power levels conduction losses due to El dominate At low power levels efficiency drops due to switching and other fixed losses ECEN2060 Simulink model dcacaveragedmd Input voltage VDC 200 V AC 120Vrms 60Hz FiL 08 2 lSW 50 mA Pac O to 600 W 100 90 80 70 60 50 40 30 20 10 0 Pac W 36 ECEN 2060 Hybrid and Electric Vehicles 3 Series Hybrid Electric Drive Train Figure 31 shows configuration of a typical series hybrid electric drive train All system components are connected in series ICE electric drive 1 EDI battery electric drive 2 ED2 and transmission to wheels inverter in ve rte r generator rectifier 39 1 1 rectfier generator 2 2 Energy EDI storage Battery charging alternator Traction Wheels ICE starting Regenerative braking radius r 4 4 Figure 31 Series hybrid electric drive train architecture Main functions of the system components are as follows 0 The vehicle is propelled by the electric drive 2 ED2 consisting of the 3 phase inverterrectifier 2 and the electric motor generator 2 In the traction mode at the input of the inverter 2 power comes from the ICE via generator 1 and rectifier 1 andor the battery From the DC battery voltage VDC inverter 2 generates variable frequency 3 phase voltages and currents for motor 2 Motor 2 shaft turns at n2 rpm and produces traction torque T2 A single gear transmission turns the wheels at nV rpm with torque TV The resulting traction force Ft 7 31 propels the vehicle at speed v where rV is the wheel radius The traction power propelling the vehicle forward is PV 2 FV v 2 TV nV 21E60 The mechanical power at the output of generator 2 is Pm2 Tznz lit60 5 32 77 where I is the transmission efficiency Electrical power supplied by the battery andor rectifier 1 is P m2 77i277m2 P2 where 772 is the efficiency of inverter 2 and Umz is the efficiency of motor 2 0 When negative traction power is required ie when the vehicle is decelerating or descending the power ows in the opposite direction from the wheels back to the battery This mode of operation is called regenerative braking DM Spring 2008 l ECEN 2060 Hybrid and Electric Vehicles 0 Generator 1 takes mechanical power PiceT1n12Tt60 and via rectifier 1 produces electrical power P1 P1 7lg17lrlPic2 7 34 where ngl and 771 are the efficiencies of generator 1 and rectifier 1 respectively Electrical power P1 charges the battery andor supplies a part of or the entire traction power P2 Electric drive 1 ED1 serves two main functions controls the battery state of charge SOC and sets the operating point of ICE Note the ICE operating point can be set independent of the traction power requirement Hence it is possible to improve efficiency by setting the ICE operating point close to its maximum efficiency point 0 ED1 also serves as an ICE starter During ICE start up power ows in the opposite direction from battery via inverter 1 and motor 1 to the ICE crankshaft A system controller in the series hybrid electric drive train has two main objectives 1 Control traction and braking based on the driver command This is accomplished by electronically controlling inverter 2 to deliver the requested torque T2 at the output of motor 2 Upon braking command ED2 performs regenerative braking as long as the requested braking torque and power are within the capabilities of electric drive 2 and as long as the battery state of charge SOC is below an upper limit SOCm Any excess braking is performed by conventional mechanical hydraulic brakes 2 Control battery state of charge so that it remains between target limits soonin s soc s SOCmax 35 The limits SOCm and gt80me are system design parameters which are decided based on battery size cost and battery life trade offs This will be discussed in more detail in the section on batteries The battery SOC control is accomplished via ED1 and ICE One simple SOC control strategy is to turn ICE on and operate it at the maximum efficiency point whenever SOC drops to SOCmn and then turn ICE off whenever SOC reaches 500m 31 Sizing of series hybrid electric drive components This section discusses basic ideas behind sizing components in the series hybrid electric drive ie selecting the power ratings for ICE ED1 and ED2 as well as the power rating and the energy storage capacity for the battery To illustrate the ideas a numerical example is considered in this section based on Example 11 Vehicle parameters are as follows 0 Vehicle mass MV 2 1500 kg 0 Front area AV 2 216 m2 0 Aerodynamic drag coefficient Cd 2 026 DM Spring 2008 2 ECEN 2060 Hybrid and Electric Vehicles 0 Tire rolling resistance fr 2 001 0 Wheel radius rV 03 m The performance objectives are 0 Acceleration time ta 2 11 s from 0 to vf 100 kmh 60 mph 0 Maximum speed 11m 160 kmh 100 mph 0 Maximum continuous cruising speed 11mm 2 130 kmh 80 mph 0 Gradeability 5 at 100 kmh 60 mph Electric motors have a maximum speed n 5000 rpm and a maximum to base speed ratio x nmnb 5 Transmission efficiency is I 90 Efficiencies of electric motorgenerators and inverterrectifiers are assumed to be 95 each Sizing7 of ED2 components In the series hybrid of Fig 1 the entire traction power must be provided by ED2 Therefore motorgenerator 2 must be sized according to the maximum traction power requirement which follows from the acceleration performance specification In the considered numerical example assuming single gear transmission efficiency of I 09 the required power rating for the motorgenerator 2 has been found in Example 11 to equal 715 kW The USO6 driving cycle test resulted in the maximum power requirement of 71509 794 kW We select ng2 80 kW 107 hp 36 The maximum speed of the motorgenerator 2 nzW 5000 rpm should match the maximum vehicle speed 11m 160 kmh 2 444 ms Since mm 30TEvmrv 1413 rpm the required gear ratio is 50001413 2 354 The motorgenerator 2 base speed is nu nzymlx 1000 rpm The maximum torque TZmax that the motorgenerator 2 should produce for 0 lt n2 lt 1000 rpm is P T2max 307rnm g2764 Nm 37 217 Inverterrectifier 2 should be rated at ngzlngz which assuming 95 efficient motor generator gives the required inverterrectifier power rating Pi2 80 kW095 84 kW 38 Sizing of CE The internal combustion engine does not need to supply the maximum traction power Instead ICE should be sized so that the vehicle can meet the maximum continuous cruising speed and the gradeability performance requirements Using 12 the maximum cruising speed vow of 80 mph requires traction power of PV 2 207 kW The gradeability 5 at 60 mph requires PV 2 302 kW Taking the larger of the two and taking into DM Spring 2008 3 ECEN 2060 Hybrid and Electric Vehicles account the assumed 95 efficiency for the series components generator 1 rectifier 1 inverter 2 motor 2 transmission the required ICE power rating is PICE 302 kW09 x0954 41 kW 55 hp 39 Note that the required ICE power rating is significantly lower than the maximum required traction power The engine downsizing is one of the HEV advantages It should also be noted that even though each component in series is assumed to have relatively high efficiency the cumulative effect of losses in the series HEV drive results in relatively significant increase in the required ICE power rating from about 30 kW to about 40 kW in this example This is considered one of disadvantages of the series HEV drive train Alternative parallel or parallelseries HEV drive configurations will be discussed in a later section Si in 0 EDI ED1 components are sized based on the ICE power rating ng1 nmglPICE z PICE P irl 77mg177ir1P ICE g P ICE HEV Butte sizing In a hybrid electric vehicle battery ratings include a power rating PW ie the ability of the battery to supply power PM while keeping the output voltage VDC above a minimum threshold and an energy capacity rating Elm based on the ability to supply or absorb energy while its state of charge SOC remains within the limits SOCm and SOCm Charging or discharging of the battery depends on the driving cycle and the system control strategy A simple example is considered here assuming the USO6 driving cycle and the same test vehicle as before The battery power Pb equals the difference between the power P1 supplied by ICE via EDI and the traction power P2 delivered to the wheels via ED2 and transmission Pb Pl P2 310 Suppose that the system controller adjusts ICE to provide the average required power ie suppose that P1 P2avg With the driving cycle starting at t 0 and ending at t tmp the total energy absorbed by the battery is then AEbtmp EP2d7JP2Wg P2d70 311 0 0 neglecting electric drive losses Under the assumptions stated above the net change in energy stored over the entire driving cycle equals zero This means that the battery state of charge S 0Ctmp equals the state of charge S 0C0 at the beginning of the trip During the driving cycle however SOC changes in time as 000 SOC0 SOC0 jP2 an P2 dr 312 Ebat Ebat 0 DM Spring 2008 4 ECEN 2060 Hybrid and Electric Vehicles where Elm is the battery rated energy storage capacity From 312 the maximum change in SOC over the driving cycle is AEbmax AEbmin ASOCmax E 313 but Given a battery specification ASOCmaX 313 can be used to find the required energy storage capacity Elm AEI AEb E max ml but ASOCmax 314 Fig 32 shows the waveforms obtained for the test vehicle in the USO6 driving cycle the vehicle speed v the required vehicle traction power PV and the change in energy AEbt neglecting electric drive losses In this case AEbm 7 AEbWn is found to be about 05 kWh Assuming ASOCmax 30 is allowed by the battery system design to ensure sufficiently long battery life 314 gives the required battery capacity rating in kWh Em M kWh1jkWh 315 ASOCmax 03 It is interesting to note that this simplified example gives a battery rating requirement close to the actual battery energy storage capacity in Toyota Prius This battery capacity 315 is worth only 17 kWh127 kWhkg 134 g of gasoline The fact that the battery only supplies the difference between the ICE power and the traction power results in very modest battery size requirements Importantly HEVs can achieve sizable efficiency and therefore fuel economy improvements with relatively small batteries Although battery system design trade offs will be discussed in more detail later it is instructive at this point to brie y examine the battery capacity requirements in a pure battery electric vehicle BEV or plug in HEV PHEV Battery si ing in BE Vand PHEV vehicle In a pure electric vehicle ICE is not available and the battery must provide the total traction energy A block diagram of a pure battery electric vehicle BEV is the same as the series HEV in Fig 31 except that ICE and ED1 are not present and a way of charging the battery from the electric grid would be provided Considering the same test vehicle in the USO6 driving cycle we find that the total traction energy required over the entire cycle is Emp 12 kWh The trip distance is lmp 8 miles which means that Emplmp 015 kWhmiles of traction energy is required Assuming that the entire traction energy is supplied by the battery assuming the same ASOCmax specification 30 and neglecting losses in the electric drive train the vehicle with the battery capacity found in 313 would have a driving range range of only ASOCmaxEW 05 miles 33 miles 316 range Em amp 015 DM Spring 2008 5 ECEN 2060 Hybrid and Electric Vehicles before the battery reaches the minimum SOC From 316 it is easy to see that the range of a pure electric vehicle could be improved by deeper discharge cycles ie by allowing a larger ASOCmax which would however result in reduced battery life and by increasing the battery capacity Elm Very similar considerations hold for plug in electric vehicles PHEV that are expected to operate as pure electric vehicles over a limited range of X miles PHEVX and then have an extended driving range as needed operating as HEV In the example above a PHEV20 ie a plug in hybrid with 20 miles of all electric range would require about 2033 6 times larger battery storage compared to the HEV i i i 100 200 300 400 500 6 0 time s i i i i i 100 200 300 400 500 600 time 5 AE kWh 0 100 200 300 400 500 600 time s Figure 32 Vehicle speed v traction power PV and the required change in stored energy AEb in the series HEV example neglecting electrical drive losses and assuming that the ICE supplies the average traction power at all times DM Spring 2008 6 mafixf JiL 319 A i mat32L w aw 34333 A13 E an if 3 1H mw 612 dawns km 23 Cwmmy gaw 3 a A 244 3 3 Q 3 33E WE 3 9245 3m 53 i gn y HG ll 9 Q 23 was 6 d9 UJ Uw o 03sz ak 31 Jr 55 1 39 Ra Unm ue s m r 4 k 0 vw Cod Qr o 779 ha ksims axlal an hugger wweii s AarWC 457w lu VilaLEM 1C v lt sbSJQM a PW HDD 395 feSSJJQ I RAKE L5 54w 2 Luv Alf Lj LmL PMquot 5 43 MA 6c 2 Ac quot S Vx0SS A LAMA tw IV 15 73 EM 3 32 ER glmwlnci 1w T m A5 3 4 mJQqTAm mu 2 3x 1 am 2 erqTM f twm SJ Q03 gt L my 83 4 Apia 3 ltQn3 gtoAmm E 5 32 i i WHume m FQMIH A536 LJaQRRA dJdml jdSMJ3 Hr Nut nan T13LAJ LJSL T 1 3 3 EEE y E 3 35 arm an 78m fa 2g gum 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