Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation» Dr. Philippe Barrade*, Dr. Walter LHOMME**, Prof. Alain BOUSCAYROL** * LEI, Ecole Polytechnique Fédérale de Lausanne, Suisse ** L2EP, University Lille1, France
- Outline - 2 Introduction Modelling and representation of the mechanical part Illustration of permutation, merging and combination rules Modelling and representation of the electrical part Considerations on the model level (batteries) Considerations for the modelling and representation of power converters Considerations for the modelling and representation of electrical machines Final EMR of an EV
Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation»
- Studied EV traction system - 4 Ωgear Jsh fsh Ω gear Ωlwh Tdcm Tload Ωdiff vveh Tldiff Fenv Tgear Ωrwh batteries Power Converters Electrical machine shaft Trans- wheels Trdiff chassis environ.
- Goals of the study- 5 Allow the EMR of an electric vehicle Obtained from its modelling Allow the identification an IBC Comparisons of various technologies for the electrical machine Assumptions Ideal power switches for the converters Non-saturated electrical machines Inertia of the wheels is neglected Contact wheel/ground without loss Mechanical brakes are not considered
- Methodology - 6 EMR of each sub-system is deduced from its modelling And not directly from its structural representation EMR of the mechanical subsystems will be made first EMR of the electrical subsystems will be then operated Considering 3 different kinds of electrical machines DC machines Induction machines Permanent magnets synchronous machines Comparison of the various EMR will be proposed
Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation»
- From the shaft to the environment - 8 Considering that the electrical machine is a torque generator f sh Ω lwh T dcm J sh T load Ω diff T ldiff F env T gear Ω rwh T rdiff shaft Gear-box Differential wheels chassis environ. Each sub-system is modelled and represented independently The final EMR is the last step
- Model and EMR of the shaft - 9 f sh J sh T dcm T load Model F sh : viscous friction (Nm.s) J sh : inertia moment (kg.m 2 ) EMR T dcm T load
- Model and EMR of the gearbox - 10 Ω diff T load T gear Model k gear : transformation ratio η gear : efficiency p : correction exponent EMR If k gear can be adjusted k gear constant T load T gear T load T gear Ω diff Ω diff k gear
- Model and EMR of the differential - 11 Principle side gear (wheels ) Ω diff T ldiff Ω lwh T gear T rdiff Ω rwh planet gear ring gear trans. shaft
- Model and EMR of the differential - 12 T ldiff Ω lwh Ω diff Model k diff : transformation ratio η diff : efficiency p : correction exponent EMR T gear T ldiff T rdiff Ω rwh T gear T diff Ω lwh Ω diff Ω wh T rdiff Ω rwh
- Model and EMR of the wheels - Ω wh 13 T diff v wh F wh Model R wh : wheel radius EMR T diff F wh Ω wh v wh
- Model and EMR of the wheels/ground contact - 14 l ev Model R t» R t : turning radius» l ev : vehicle width EMR F lwh v rwh F tot F rwh v rwh R t
- Model and EMR of the chassis - 15 F env Model M veh : mass of the vehicle EMR F tot F env
- Model and EMR of the environment - A F aero 16 F grade ½ F roll ½ F roll α h α Model M g F aero : aerodynamic resistance F roll : rolling resistance F grade : grade resistance L If α small (h/l<20%)
- Model and EMR of the environment - 17 Model: Aerodynamic resistance ρ air : density of air (1.223kg/m 3 @ 1013hPa, 20 C) A : frontal area (m 2 ) C x : drag coefficient vehicle C x drag coefficient convertible 0.33 to 0.50 four-wheel drive 0.35 to 0.50 saloon car 0.26 to 0.35 estate car 0.30 to 0.34 shaped 0.30 to 0.40 headlight and wheels in the fuselage 0.20 to 0.25 kammback 0.23 streamlined shape 0.15 to 0.20 Source: Mémento de Technologie Automobile, 3 ème édition, BOSCH drop of water
- Model and EMR of the environment - 18 Model: Rolling resistance k roll : coefficient of the rolling (quality of the floor-covering) floor-covering coefficient of the rolling k roll cobblestones 0.013 concrete, asphalt 0.011 macadam 0.020 / 0.025 dirt track 0.050 Source: Mémento de Technologie Automobile, 3 ème édition, BOSCH
- Model and EMR of the environment - 19 Model: total resistive forces Once F env is known Requested power can be identified: P=F env. Example for C x =0.35, A=2m 2, k roll =0.02, M veh =1000kg and h/l=5%
- Global EMR of the mechanical part - 20 f sh Ω lwh T dcm J sh T load Ω diff T ldiff T gear F env Ω rwh T rdiff shaft Gear-box chassis environ. T ldiff F lwh T dcm T load T gear T diff Ω lwh v lwh F tot ENV T load Ω diff Ω wh T rdiff F rwh F env Ω rwh v rwh R t shaft gearbox differential wheels chassis environ.
- Global EMR of the mechanical part: permutation and merging - shaft gearbox differential wheels chassis environ. 21 permutation T ldiff F lwh T dcm T load T gear T diff Ω lwh v lwh F tot ENV T load Ω diff Ω wh T rdiff F rwh F env Ω rwh v rwh R t T ldiff F lwh T dcm T eq Ω diff T gear T diff Ω lwh v lwh F tot ENV Ω diff T gear Ω diff Ω wh T rdiff F rwh F env Permutation!..!... Ω rwh v rwh R t
- Global EMR of the mechanical part: permutation and merging - T ldiff F lwh merging 22 T dcm T gear T diff Ω lwh v lwh F F tot ENV Ω diff Ω wh T rdiff F rwh F tot F env Ω rwh v rwh R t gearbox differential wheels chassis T ldiff F lwh T dcm T gear T diff Ω lwh v lwh F tot ENV Ω diff Ω wh T rdiff F rwh F tot Ω rwh v rwh R t
- Global EMR of the mechanical part: simplifications (optional) - 23 T ldiff F lwh T dcm T gear T diff Ω lwh v lwh F tot ENV Ω diff Ω wh T rdiff F rwh F tot Ω rwh v rwh R t If the vehicle drives in a straight line (R t = ), an equivalent wheel is sufficient differential gearbox ratio wheels chassis combination T dcm T gear T diff F tot ENV Ω diff Ω wh F env R wh : wheel radius
- Global EMR of the mechanical part: simplifications (optional) - 24 f sh Ω lwh T dcm J sh T load Ω diff T ldiff F env T gear Ω rwh T rdiff shaft Gear-box chassis environ. transmission chassis T dcm F tot ENV F env
- Global EMR of the mechanical part: key points - transmission chassis 25 T dcm F tot F env ENV The system has been first modelled From the model, the EMR has been established Permutations and merging are required when conflict of associations are obtained. This is mandatory. It must be done according to the model. Simplifications can be made but are optional. In all cases, the model is still valid, except if the simplifications are made following restrictive conditions. Then, adaption of the model is needed. Simplifications depend on the objectives defined for the study.
Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation»
- From the batteries to the shaft Considering that mechanical part is an energy source Ωgear Tdcm Generalities for modelling and representing Batteries, Power converters, Electrical machines Final EMR comparing the representations of various technologies 27
- Model and representation of the batteries - Principally two kinds of model: energetic model dynamic model Choice of the model depends on the objectives for the study Energetic model R + OCV = _ i bat u bat 28 Open Circuit Voltage (OCV): Internal impedance (R): State of Charge (SOC):
- Model and representation of the batteries - Parameters identification Directly from datasheets 29 identification Implementation of look-up tables From the model to the representation BAT u bat i bat
Most of the power converters are made of elementary switching cells Depending on the switches 1 quadrant (i s >0) 2 quadrants (i s >0 or <0) Fundamental rule Switches are complementary operated u e i e i1 - Model and representation of Power Converterss 1 i s 30 s 2 u s Basic behavior m Defining the modulation function m
From the model to the representation u s 31 u e <u s > T - Model and representation of Power Converterst Instantaneous model Average model u e u s u e <u s > i e m i s <i e > <m> i s
Extension to the 4 quadrants DC/DC converters and single phase voltage source inverter Using 2 parallel elementary converters i e i s 32 i1 - Model and representation of Power Converterss 11 i 2 s 21 u e u s s 12 u s1 s 22 u s2 m 1 m 2 Models for the 2 elementary converters
4 quadrants DC/DC converters and VSI Models for the 2 elementary converters 33 i e i s i1 - Model and representation of Power Converterss 11 i 1 s 21 u e u s s 12 u s1 s 22 u s2 m 1 m 2 Global model
4 quadrants DC/DC converters and VSI From the model to the representation 34 - Model and representation of Power Convertersu e u s1 u e i 1 m 1 i s u s i e u e u s2 i s i 2 m 2 i s
- Model and representation of Power Converters- 4 quadrants DC/DC converters and VSI Simplification 35 Instantaneous model Average model u e u s u e <u s > i e m i s <i e > <m> i s
- Model and representation of Power Converters- 3 phases voltage source inverter The principle is the same i s1 36 s 11 s 21 s 31 i s2 u e u 13 s 12 s 22 s 33 u 23 i e i s3 Instantaneous model Sliding average model u e u s u e <u s > i e m i s <i e > <m> i s
Summary - Model and representation of Power Converters- 37 2Q converter 4Q converter 3 phases VSI u e u s u e u s u e u s i e i s i e i s i e i s m m m Warning Representations of various converter seem to be identical Never forget the model hidden behind the representation
Main parameters Armature r a : armature resistor (Ω) L a : armature inductor (H) e dcm : motor back EMF (V) T dcm : torque (Nm) : angular rotational speed (rad/s) k Φ : motor constant (V.s/Wb) Φ f : magnetic flux (Wb) Excitation - Model and representation of DC machines - With excitation circuit r f : field resistor (Ω) L f : field inductor (H) k i : motor constant (V.s/A) With permanent magnets K: motor constant (V.s) r a u ch-a i a u ch-f r f L a i f L f 38 e dcm
Model With excitation circuit Electrical - Model and representation of DC machines - 39 r a i a L a Electro-mechanical u ch-a e dcm r f i f L f With permanent magnets Electrical u ch-f Electro-mechanical
Electrical - Model and representation of DC machines - Model Representation With excitation circuit With excitation circuit u ch-a i a 40 i a e dcm T dcm Electro-mechanical u ch-f i f i f e f With e f =0! With permanent magnets Electrical With permanent magnets Electro-mechanical u ch-a i a T dcm i a e dcm
Model Faraday law - Model and representation of squirrel cage IM- 41
Model: Flux matrix - Model and representation of squirrel cage IM- 42 1 the position θ is function of time: difficult to control AC currents 2 strong interaction between phases solution: use of park s transformation
43 Model: needs in tools for representation Park s transformation: 3-phases to 2-phases transformation Expressed in a fix reference frame (α,β) Transformation in rotating reference frame (d,q) - Model and representation of squirrel cage IM- For Induction Machines: d axis is oriented along the rotor flux i sd current related to the rotor flux i sq current related to the torque DC equivalent voltages and current equivalent DC machine in the (d,q) frame
- Model and representation of squirrel cage IM- Model Park s transformation for an Induction Machine 44 2s i s2 v s2 1r pω rotor d i sd 1r rotor θ r/s v sd 2r v s3 v s1 i s1 1s stator v rq v i rq sq i rd v rd θ r/s θ d/s 1s stator i s3 3s 3r q i sq d, q rotating reference frame: - DC current - interaction simplification Modelling simplifications:
Representation Step 1 - Model and representation of squirrel cage IM- 45 u stator θ d/s v s-dq i s-dq Coupling device Stator windings in (d,q) i stator u rotor =0 i s-dq v r-dq e s-dq i r-dq T im i rotor i r-dq e r-dq θ d/r φ r Park s transformations Rotor windings in (d,q)
Representation Step 2 - Model and representation of squirrel cage IM- 46 θ d/s Stator windings in (d,q) u stator v s-dq i s-dq i stator i s-dq e s-dq T im φ r i sd By a variable change, the rotor flux can be expressed in EMR
Model v sm3 2s i sm3 3s - Model and representation of PMSM - Principle is the same than IM, except that rotor is made of permanent magnets Rotor angular rotational speed is synchronized with the stator rotating magnetic field Same tools: Park s transformation and expression along the rotor rotating frame pω i sm2 vsm2 1r rotor θ 1s stator i v sm1 sm1 q i sq i sq d v rq v i rq sq modelling simplifications: q v sq i sd v sd i rd v rd 1r = d rotor θ i sd v sd θ d/s 1s 47 stator reduced current magnitude for same produced torque
Model Main equations Electrical - Model and representation of PMSM - 48 Electro-mechanical Representation θ u stator v s-dq i s-dq T sm i stator i s-dq e s-dq
With DC machines With excitation circuit parallel connectionchoppers u bat u ch-a - Global EMR of the electrical part - DC machine i a - With permanent magnets chopper DC machine 49 u bat BAT i tot i i ch-a a m u ch-a bat u ch-f i ch-f i f e a i f e f T dcm u bat BAT i ch-a u ch-a i a m ch-a i a e a T dcm m ch-f With AC machines Squirrel cage IM inverter induction machine - PMSM inverter PM synchronous machine Bat u bat i inv u inv i im v sdq i sdq i sdq e sdq T dcm Bat u bat i inv u inv i im v sdq i sdq i sdq e sdq T dcm m inv φ r m inv i sd
- Global EMR of the electrical part: key points - chopper DC machine 50 u bat BAT i ch-a u ch-a i a m ch-a i a e a T dcm The system must been first modelled From the model, the EMR can been established Never forget the model behind the representation The EMR from the batteries to the shaft has been made for different electrical machines The comparison of the various EMR shows that strong similarities exist Thanks to the use of the adequate transformations Underlined by the EMR
Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation»
- Global EMR (with a DC machine, excitation circuit) - 52 i a f sh Ω lwh i ch-a u ch-a T dcm J sh T load Ω diff T ldiff u bat F env T gear i tot i f u ch-f Ω rwh T rdiff i ch-f parallel connection choppers DC machine gearbox differential wheels chassis u bat u ch-a i a T ldiff F lwh u bat BAT i tot i i ch-a a m u ch-a bat u ch-f e a i f T dcm T gear Ω diff T diff Ω wh Ω lwh v lwh T rdiff F rwh F tot F tot ENV i ch-f m ch-f i f e f Ω rwh v rwh R t
Technical University of Graz, April 2012 «Energy Management of EVs & HEVs using Energetic Macroscopic Representation» Models = must be defined in function of the objective different models for the same subsystems using different assumptions EMR = causal way to organize models of different parts highlight energetic properties and conflicts of associations EV with DC machine = a basic traction system other can be deduced by using the Park s transformation
- References - 54 [1] W. Lhomme, "Gestion d énergie de véhicules électriques hybrides basée sur la Représentation Energétique Macroscopique", Thèse de doctoral de l'université Lille 1, novembre 2007. [2] A. Bouscayrol, W. Lhomme, P. Delarue, B. Lemaire-Semail, S. Aksas, Hardware-In-the-Loop simulation of electric vehicle traction systems using Energetic Macroscopic Representation, IEEE-IECON'06, Paris (France), November 2006. [3] A. Bouscayrol, M. Pietrzak-David, P. Delarue, R. Peña-Eguiluz, P. E. Vidal, X. Kestelyn, Weighted control of traction drives with parallel-connected AC machines, IEEE Transactions on Industrial Electronics, Vol. 53, no. 6, p. 1799-1806, December 2006. [4] A. Bouscayrol, A. Bruyère, P. Delarue, F. Giraud, B. Lemaire-Semail, Y. Le Menach, W. Lhomme, F. Locment, Teaching drive control using Energetic Macroscopic Representation - initiation level, EPE'07, Aalborg (Denmark), September 2007. [5] K. Chen, P. Delarue, A. Bouscayrol, R. Trigui, Influence of control design on energetic performances of an electric vehicle, IEEE-VPPC'07, Arlington (U.S.A.), September 2007. [6] K. Chen, A. Bouscayrol, W. Lhomme, Energetic Macroscopic Representation and Inversionbased control: application to an Electric Vehicle with an electrical differential, Journal of Asian Electric Vehicles, vol. 6, no.1, p. 1097-1102, June 2008.