ENE 2XX: Renewable Energy Systems and Control. LEC 04 : Case Studies in Optimal Energy Management: New Energy Vehicles
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1 ENE 2XX: Renewable Energy Systems and Control LEC 04 : Case Studies in Optimal Energy Management: New Energy Vehicles Professor Scott Moura University of California, Berkeley Summer 2017 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 1
2 Outline 1 Intro to Electric Drive Vehicles 2 Hybrid Electric Vehicle Energy Management 3 Optimal PEV Charge Scheduling Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 2
3 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 3
4 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 4
5 HEVs, EVs projected to dominate transportation market in China by 2050 Zhou, Nan, David Fridley, Michael McNeil, Nina Zheng, Jing Ke, and Mark Levine. China s Energy and Carbon Emissions Outlook to 2050, Lawrence Berkeley National Laboratory Tech Report LBNL-4472E (2011) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 5
6 Electric Drive Vehicle Basics Hybrid Electric Vehicles (HEV) Internal combustion (IC) engine is primary energy source Battery serves as buffer Ex: Toyota Prius, Toyota Camry, Honda Civic, Honda Accord, Ford Fusion Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 6
7 Electric Drive Vehicle Basics Hybrid Electric Vehicles (HEV) Plug-in Hybrid Electric Vehicles (PHEV) Internal combustion (IC) engine is primary energy source Battery serves as buffer Ex: Toyota Prius, Toyota Camry, Honda Civic, Honda Accord, Ford Fusion IC engine & battery are depletable stores Fuel at station, charge with plug Ex: Chevy Volt, Prius PHEV Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 6
8 Electric Drive Vehicle Basics Hybrid Electric Vehicles (HEV) Plug-in Hybrid Electric Vehicles (PHEV) All-Electric Vehicle (EV) Internal combustion (IC) engine is primary energy source Battery serves as buffer Ex: Toyota Prius, Toyota Camry, Honda Civic, Honda Accord, Ford Fusion IC engine & battery are depletable stores Fuel at station, charge with plug Ex: Chevy Volt, Prius PHEV Battery only, no engine Requires charging to re-fuel Ex: Nissan Leaf, Tesla Model S Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 6
9 Degrees of Hybridization Guzzella, Lino, and Antonio Sciarretta. Vehicle propulsion systems. Vol. 2. Berlin: Springer, Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 7
10 Brake Specific Fuel Consumption (BSFC) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 8
11 Conclusions from BSFC Map Operate in sweet spot, i.e. highest efficiency Options to enhance enhance efficiency Downsizing Decouple vehicle velocity from engine velocity Recuperate kinetic energy Reduce (or eliminate) dependence on internal combustion engine Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 9
12 Hybrid Electric Vehicle (HEV) We have random power demand (driver pedal positions) We have an energy conversion device (engine) that has a single sweet spot Add an energy storage device to buffer demand! Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 10
13 Types of Hybrids Gas-Electric Diesel-Hydraulic Diesel-Electric Fuel Cell-Electric Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 11
14 Power-split HEV Mechanical Path Battery Pack Inverter Motor (Generator) Electrical Path Torque Coupler Final Drive Generator (Motor) Planetary Gear Set Engine Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 12
15 Power-Split HEV Model Ex: Toyota Prius, Ford Escape Hybrid Control Inputs Engine Torque M1 Torque State Variables Engine speed Vehicle speed Battery SOC Vehicle acceleration (Markov Chain) SUPERVISORY CONTROLLER ENGINE DRIVE CYCLE PLANETARY GEAR SET M1 M2 BATTERY PACK VEHICLE Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 13
16 Rule-based Energy Management Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 14
17 HEV Optimal Energy Management Objective Function: Constraints: min J = u(k),k=0 k f k f k=0 [Fuel Consumption(k) + Emissions(k)] subject to: x(k + 1) = f(x(k), u(k), w(k)), SOC(0) = SOC(k f ) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 15
18 HEV Operation Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 16
19 Plug-in Hybrid Electric Vehicle (PHEV) We have random power demand (driver pedal position) We have an energy conversion device (engine) that has a single sweet spot Add a second depletable energy store! Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 17
20 Examples of PHEVs Toyota Prius PHEV Chevrolet Volt Ford Fusion Energi Fisker Karma Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 18
21 Two Depletable Energy Stores Chemical Energy η 1 Mechanical Energy P tank P batt Tank/ Engine Battery/ M/Gs η 2 ω eng T eng =P eng + + P demand ω M/G1 T M/G1 + ω M/G2 T M/G2 Wheel Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 19
22 All Electric Range A misleading metric... A plug-in hybrid s all-electric range is designated by PHEV-(miles) representing the distance the vehicle can travel on battery power alone. For example, a PHEV-20 can travel 20 miles without using its internal combustion engine. Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 20
23 PHEV Optimal Energy Management Objective Function: Constraints: min J = u(k),k=0 k f k f k=0 [Fuel Consumption(k) + Emissions(k)] subject to: x(k + 1) = f(x(k), u(k), w(k)), SOC(k) SOC min, k = 0,, k f Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 21
24 Charge Depletion-Charge Sustenance vs. Blending 0.8 Chargecdepletingcandcchargecsustaining Dynamiccprogramming 0.7 SOCc Optimal Chargecdepleting Chargecsustaining Timec(s) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 22
25 PHEV Energy Management Summary Depends critically on driving distance between charge events Judiciously deplete, so you reach min SOC exactly when plugging in Accurate forecasts of driving pattern are extremely useful Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 23
26 Use Real-time Traffic Data Traffic Data Energy Management Feedback PHEV C. Sun, S. J. Moura, X. Hu, J. K. Hedrick, F. Sun, Dynamic Traffic Feedback Data Enabled Energy Management in Plug-in Hybrid Electric Vehicles, IEEE Transactions on Control Systems Technology, May DOI: /TCST Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 24
27 Approaching Optimal Performance Fuel2Optimality2(v) Standard2Deviation Terminal2SOC 50 DP CDCS C. Sun, S. J. Moura, X. Hu, J. K. Hedrick, F. Sun, Dynamic Traffic Feedback Data Enabled Energy Management in Plug-in Hybrid Electric Vehicles, IEEE Transactions on Control Systems Technology, May DOI: /TCST Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 25
28 Electric Vehicle (EV) We have random power demand (driver pedal position) We have an energy conversion device (engine) that has a single sweet spot Remove it! Replace with a battery & motor! Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 26
29 Examples of EVs Nissan Leaf Tesla Model S & Roadster Ford Focus EV Renault Zoe Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 27
30 Vehicle-to-Grid (V2G) or Vehicle Grid Integration (VGI) Plug-in electric vehicles (PEVs) communicate with the grid to provide mutually beneficial services, such as demand response through throttled charging, or selling power to the grid. Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 28
31 Government Initiatives CA Vehicle-Grid Integration Roadmap 1.5M zero emission vehicles in CA by 2025 Electric vehicle charging creates a reciprocal relationship between battery-powered cars and the power grid in a way that produces mutual benefits. Without compromising the driving habits of consumers, incentives should be pursued as a way to aggregate vehicle charging to develop valuable grid services. China Ministry of Science & Technology 5 million new energy vehicles on China s roads by end of 2020 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 29
32 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 30
33 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 30
34 Source: C. Vlahoplus, G. Litra, P. Quinlan, C. Becker, Revising the California Duck Curve: An Exploration of Its Existence, Impact, and Migration Potential, Scott Madden, Inc., Oct Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 30
35 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 30
36 Many fascinating technical questions How to optimally charge individual PEVs to minimize consumer cost? How to aggregate PEVs so they can participate in power market? Can PEVs mitigate variability of renewables? How to participate in power market, w/o sacrificing user mobility? Where to optimally locate charging station infrastructure? Does V2G sacrifice battery life, and therefore affect warranty? What are the economic benefits? To which stakeholders?... and more! Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 31
37 Outline 1 Intro to Electric Drive Vehicles 2 Hybrid Electric Vehicle Energy Management 3 Optimal PEV Charge Scheduling Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 32
38 Problem Statement Objective: Optimize power flow of engine & battery to satisfy demand. Given: Power demand time-series 30 HEV powertrain model parameters Speed Speed [m/s] [m/s] Power Power Demand Demand [kw] [kw] Time [min] 30 0 Power Demand 5 for a Toyota 10 Prius undergoing 15 UDDS cycle20 Time [min] Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 33
39 Modeling - I Engine P eng P dem Vehicle P ba- Ba-ery Power Balance P eng (k) + P batt (k) = P dem (k), k = 0,, N 1 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 34
40 Modeling - I Engine P eng P dem Vehicle P ba- Ba-ery Power Balance P eng (k) + P batt (k) = P dem (k), k = 0,, N 1 Battery dynamics E(k + 1) = E(k) P batt (k) t, k = 0,, N 1 E(0) = E 0 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 34
41 Modeling - I Engine P eng P dem Vehicle P ba- Ba-ery Power Balance P eng (k) + P batt (k) = P dem (k), k = 0,, N 1 Battery dynamics E(k + 1) = E(k) P batt (k) t, k = 0,, N 1 E(0) = E 0 Net-zero batt energy E(N) = E(0) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 34
42 Modeling - I Engine P eng P dem Vehicle P ba- Ba-ery Power Balance P eng (k) + P batt (k) = P dem (k), k = 0,, N 1 Battery dynamics E(k + 1) = E(k) P batt (k) t, k = 0,, N 1 E(0) = E 0 Net-zero batt energy 0.95 E(0) E(N) 1.05 E(0) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 34
43 Modeling - II Engine P eng P dem Vehicle P ba- Ba-ery Batt energy lims E min E(k) E max, k = 0,, N Batt pwr lims Eng pwr lims P min batt P batt(k) P max batt, k = 0,, N 1 0 P eng (k) P max eng, k = 0,, N 1 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 35
44 Modeling - II Engine P eng P dem Vehicle P ba- Ba-ery Batt energy lims E min E(k) E max, k = 0,, N Batt pwr lims Eng pwr lims P min batt P batt(k) P max batt, k = 0,, N 1 0 P eng (k) P max eng, k = 0,, N 1 min. fuel consumption J = N 1 k=0 α P eng(k) t Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 35
45 Optimization Formulation with equality constraints min P batt (k),p eng(k),e(k) N 1 J = α P eng (k) t (1) k=0 P eng (k) + P batt (k) = P dem (k), k = 0,, N 1 (2) and inequality constraints E(k + 1) = E(k) P batt (k) t, k = 0,, N 1 (3) E(0) = E 0 (4) 0.95 E(0) E(N) 1.05 E(0), (5) E min E(k) E max, k = 0,, N (6) P min batt P batt (k) P max batt, k = 0,, N 1 (7) 0 P eng (k) P max eng, k = 0,, N 1 (8) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 36
46 Optimization Formulation - reduced min P batt (k),e(k) with equality constraints N 1 J = α t (P dem (k) P batt (k)) (9) k=0 E(k + 1) = E(k) P batt (k) t, k = 0,, N 1 (10) and inequality constraints E(0) = E 0 (11) 0.95 E(0) E(N) 1.05 E(0), (12) E min E(k) E max, k = 0,, N (13) P min batt P batt (k) P max batt, k = 0,, N 1 (14) 0 P dem (k) P batt (k) P max eng, k = 0,, N 1 (15) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 37
47 LP Formulation minimize x c T x (16) subject to: Ax b (17) A eq x = b eq (18) where the decision variable is given by x = [P batt (0), P batt (1),, P batt (N 1), E(0), E(1),, E(N 1), E(N)] T (19) 2N + 1 decision variables Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 38
48 Problem Data UDDS drive cycle: N = 1369 time steps 2,739 optimization vars t = 1 sec α = 0.1 g/(s-kw) E 0 = 0.6 kwh = 2.16 MJ = 50% E min = MJ = 30%, E max = MJ = 70% P min batt = -15 kw, Pmax batt = +15 kw P max eng = 35 kw Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 39
49 Results Cumm. Fuel Cons. [g] Battery Charge [%] Power [kw] Time [min] Batt Power Eng Power Batt Limits Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 40
50 Optimal Energy Management Problem Generators G 1 G 2 G NG Power Flow Network Supply = Demand Power Flow dynamics & constraints S 1 S 2 S NS Storage Demand D 1 D 2 D ND Applications US Electric Power Grid Distribution grid on UCB campus Microgrid in Kenyan village Commercial building with solar & storage A hybrid vehicle (e.g. Prius) A solar car/aircraft A wireless sensor node with energy harvesting LARGE small Figure: Setup for the energy management problem Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 41
51 Outline 1 Intro to Electric Drive Vehicles 2 Hybrid Electric Vehicle Energy Management 3 Optimal PEV Charge Scheduling Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 42
52 Problem Statement Objective: Optimize charge schedule to minimize electricity cost Given: Time-varying price signal EV battery model parameters Electricity Cost [cents/kwh] :00 04:00 08:00 12:00 16:00 20:00 24:00 Time of Day Hypothetical time-varying electricity price Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 43
53 Modeling - I + _ + V oc I(t) V T R _ Integrator SOC(k + 1) = SOC(k) + t Q cap I(k), k = 0,, N 1 SOC(0) = SOC 0 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 44
54 Modeling - I + _ + V oc I(t) V T R _ Integrator SOC(k + 1) = SOC(k) + t Q cap I(k), k = 0,, N 1 SOC(0) = SOC 0 Kirchoff s voltage law V(k) = V oc + RI(k), k = 0,, N Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 44
55 Modeling - I + _ + V oc I(t) V T R _ Integrator SOC(k + 1) = SOC(k) + t Q cap I(k), k = 0,, N 1 SOC(0) = SOC 0 Kirchoff s voltage law V(k) = V oc + RI(k), k = 0,, N Electric Power P(k) = I(k)V(k) = V oc I(k) + RI 2 (k), k = 0,, N Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 44
56 Modeling - I + _ + V oc I(t) V T R _ Integrator SOC(k + 1) = SOC(k) + t Q cap I(k), k = 0,, N 1 SOC(0) = SOC 0 Kirchoff s voltage law V(k) = V oc + RI(k), k = 0,, N Electric Power P(k) = I(k)V(k) = V oc I(k) + RI 2 (k), k = 0,, N Charging cost J = N 1 k=0 c(k) [ V oc I(k) + R I 2 (k) ] t Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 44
57 Modeling - II + _ + V oc I(t) V T R _ SOC lims SOC min SOC(k) SOC max, k = 0,, N Current lims 0 I(k) I max, k = 0,, N 1 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 45
58 Modeling - II + _ + V oc I(t) V T R _ SOC lims SOC min SOC(k) SOC max, k = 0,, N Current lims 0 I(k) I max, k = 0,, N 1 Final SOC SOC(N) E Q capv oc + SOC min Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 45
59 Optimization Formulation min I(k),SOC(k) with equality constraints N 1 J = c(k) t V oc I(k) + c(k) tr I 2 (k) (20) k=0 SOC(k + 1) = SOC(k) + t Q cap I(k), k = 0,, N 1 (21) and inequality constraints SOC(0) = SOC 0 (22) SOC min SOC(k) SOC max, k = 0,, N (23) SOC(N) 0 I(k) I max, k = 0,, N 1 (24) E Q cap V oc + SOC min (25) Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 46
60 QP Formulation where decision variable is minimize x 1 2 xt Qx + R T x (26) subject to: Ax b (27) A eq x = b eq (28) x = [I(0), I(1),, I(N 1), SOC(0), SOC(1),, SOC(N 1), SOC(N)] T (29) 2N + 1 decision variables Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 47
61 Problem Data Given time-varying price: N = 96 time steps 193 optimization vars t = 15 min Q cap = 13.8 A-hr, V oc = 363V, R = 1.1 Ohms SOC 0 = 0.2 SOC min = 0.1, SOC max = 0.9 I max = 9.66 A E = 14.4 MJ assume PEV plugged-in 16:00-24:00 Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 48
62 Results 8 c(k)[cents/kw h] P(k)[kW ] Battery SOC :00 04:00 08:00 12:00 16:00 20:00 24:00 Time of Day Figure: Results for Optimal PEV Charge Schedule. Prof. Moura Tsinghua-Berkeley Shenzhen Institute ENE 2XX LEC 04 - New Energy Vehicles Slide 49
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