Vehicle Propulsion Systems. Lecture 8 Electric & Hybrid Electric Propulsion Systems Part II

Transcription

1 Vehicle Propulsion Systems Lecture 8 Electric & Hybrid Electric Propulsion Systems Part II 1

2 Planning of Lectures and Exercises: Week Lecture, Friday, 8:15-10:00, ML F34 Book chp. 38, Introduction, goals, overview propulsion systems and options Exercise, Friday, 12:00-13:30, CHN E46 1 Introduction 39, Fuel consumption prediction I 2 Exercise I, Milestone 1 40, Fuel consumption prediction II 2 Exercise I, Presentation 41, IC engine propulsion systems I 3 Exercise II, Milestone 1 42, IC engine propulsion systems II 3 Exercise II, Milestone 2 43, ICE III & Case Study Hybrid Pneumatic Engine 4 Exercise II, Presentation 44, Hybrid electric propulsion systems I 4 Exercise III, Milestone 1 45, Hybrid electric propulsion systems II 4 Exercise III, Milestone 2 46, Hybrid electric propulsion systems III 5 Exercise III, Presentation 47, Supervisory Control Algorithms I 7 Exercise IV, Milestone 1 48, Supervisory Control Algorithms II 7 Exercise IV, Milestone 2 49, Supervisory Control Algorithms III 7 Exercise IV, Milestone 3 50, Non-electric hybrid propulsion systems Exercise IV, Presentation 51, Tutorial Lecture, Q & A 2

3 Today Range Extender Batteries 3

4 Range Extender 2 Degrees of freedom: Rotational speed Electric power Control: control speed and power to setpoints Optimization: For each value of desired power, find best possible operating point 4

5 Engine Generator Unit 5

6 ሶ Engine Generator Unit Efficiency: η g = P g H lhv m f 6

7 Quick Check Assume an Engine (p me = p mf e p me,0 ) is connected to a generator (P g = P e e el P g,0 ), calculate the optimal operating line. P f = mሶ f H l = p mfv d ω e Pe e + p me,0v d ωe Nπe Nπ = P g+pg,0 e el e = p me+pme,0 V d ωe = Nπe + p me,0v d ωe Nπe TeNπ V d +pme,0 V d ωe Nπe = = P g + P g,0 + p me,0v d ωe e el e e el e Nπe dp e = p me,0v d > 0 dω e Nπe Choose engine speed as small as possible until max torque is reached. Then go along max torque line until max power is reached. 7

8 Today Range Extenders Batteries Overview Equivalent Circuit Model Battery Packs Dynamic Models 8

9 Battery Technologies Lead-acid cheap, robust, reliable, short bursts of high power low energy density, low cycle life Ni-MH medium cost, energy & power density, reliable Li-Ion Good energy and power density Lifetime? 9

10 Li-Ion Battery 10

11 Battery Technologies Cathode: LiCoO 2 (LCO) LiMn 2 O 4 (LMO) LiNiMnCoO 2 (NMC) LiFePO 4 (LFP) LiNiCoAlO 2 (NCA) Anode: Carbon Li 4 Ti 5 O 12 (LTO) Higher energy density typically compromises other criteria such as power density or durability 11

12 Battery Technologies Tesla Li-Ion Pack: ~140 Wh kg and ~516 W kg 12

13 Ragone Plot 13

14 Today Range Extender Batteries Overview Equivalent Circuit Model Battery Packs Dynamic Models 14

15 Battery Equivalent Circuit Battery behaves like a voltage source in series with resistance Both, open circuit voltage and internal resistance, are functions of battery charge U oc = f U (Q b ) R b = f R (Q b ) 15

16 Voltage Characteristic 16

17 Voltage Characteristic 17

18 Battery Equivalent Circuit Choices for state variable: Charge: Q b dq b dt Energy: E b = 0 Q b U oc Q dq de b dt = I b = I bu oc 18

19 Normalization People like to think in normalized values State of charge: State of energy: x SOC = Q b Q max x SOE = Q b Q b,min U oc Q dq E max xሶ SOC = I b Q max xሶ SOE = I bu oc E max 19

20 Approximations Often, the open circuit voltage can be approximated with an affine function U oc = f U Q b Q b ሚ C + U 0 Same with internal resistance Q R b = f R Q b ρ b 1 + ρ Q max 0 20

21 Quick Check Express the energy stored in a battery as a function of open circuit voltage E b = න 0 Q buoc Q dq = න 0 Q b Q ሚC + U 0 dq = Q b 2 2 ሚC + Q bu 0 With Q b = ሚC U oc U 0 E b = 1 ሚ 2C U 2 oc U 2 0 = 1 ሚ 2CU 2 oc E 0 21

22 How to estimate energy content? Voltage curve is rather flat Coulomb-counting Q b = න I b (τ)dτ 0 Sometimes Coulomb counting and voltage measurements are combined via a Kalman filter. t 22

23 C-Rate = current normalized with capacity Eg. A C-Rate of c = 1 1 is the current that h discharges a battery completely once within one hour. I b c = Q b,nom c Easy, if Q b is expressed in Ah. 23

24 Quick Check AAA-Cell Battery capacity 1200mAh, Current 25mA Corresponding c-rate? c = I b c Q b = 25mA 1200mAh = 1 48h One discharge in 2 full days 24

25 AAA-cell 25

26 Capacity Current Dependency Higher currents lead to lower capacity? Voltage drop over internal resistance leads to reaching the lowest possible voltage earlier. Increasing losses over internal resistance Cut-off voltage reached earlier 26

27 Inverse Current Model Kirchhoff Law U b = U oc RI b Power P b = I b U oc RI b 2 Inverse model for current I b = 1 2R U oc U 2 oc 4P b R b 27

28 Quick Check Justify graphically, why the solution to the equation P b = I b U oc RI b 2 is truly the one with the minus sign: I b = 1 2R U oc ± U 2 oc 4P b R b 28

29 Solution I b U oc I b U oc RI b 2 I b RI b 2 29

30 Operating Limits Allowed Voltage at terminals Allowed SOC-Range 30

31 Today Range Extender Batteries Overview Equivalent Circuit Model Battery Packs Dynamic Models 31

32 First Tesla Tesla roadster was using standard laptop battery cells 32

33 Quick Check Tesla Roadster Battery Pack: 56kWh, 375V Cells 18650: 3.75V and 2500mAh How many cells in serial and parallel? n s = 375V 3.75V = 100 U b Q b n s = 3.75V 2.5Ah 100 = 937Wh n p = 56kWh 937Wh = 60 n t = n p n s = 6000 Tesla Roadster: 6831 Cells 33

34 Quick Check Estimate the c-rate when the battery delivers 100kW. (Peak power is around 200kW) c = 100kW 56kWh = 1.78 Capacity of Pack Q pack = Q cell n p = 2500mAh 60 = 150Ah Current at 100kW I b = Q pack = E pack U pack = 150Ah P b U = 100kW pack 375V c = 267A 150Ah = 1.78 = 267A 34

35 Advanced Battery Packs Cells in serial and parallel connection Cell balancing system DC/DC converter Integrated cooling circuit Fans Secure housing 35

36 Today Range Extender Batteries Overview Equivalent Circuit Model Battery Packs Dynamic Models 36

37 Model Type? Dynamic state variable Charge or energy In VPS book: QSS-model since dynamic effects were neglected DC/DC converter and its controller Temperature Pseudo capacitance Aging 37

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40 Battery Health End of life = when capacity drops below some percentage of the original value. Capacity loss depends on temperature -> 40