ENE 2XX: Renewable Energy Systems and Control

LEC 04 : Case Studies in Optimal Energy Management:New Energy Vehicles

Professor Scott MouraUniversity of California, Berkeley

Summer 2017

Prof. Moura | Tsinghua-Berkeley Shenzhen Institute ENE 2XX | LEC 04 - New Energy Vehicles Slide 1

Outline

1 Intro to Electric Drive Vehicles

2 Hybrid Electric Vehicle Energy Management

3 Optimal PEV Charge Scheduling

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)

Electric Drive Vehicle Basics

Hybrid ElectricVehicles (HEV)

Internal combustion(IC) engine is primaryenergy source

Battery serves asbuffer

Ex: Toyota Prius, Toyota

Camry, Honda Civic, Honda

Accord, Ford Fusion

Plug-in HybridElectric Vehicles

(PHEV)

IC engine & batteryare depletable stores

Fuel at station, chargewith plug

Ex: Chevy Volt, Prius PHEV

All-Electric Vehicle(EV)

Battery only, no engine

Requires charging to“re-fuel”

Ex: Nissan Leaf, Tesla Model S

Accord, Ford Fusion

(PHEV)

Accord, Ford Fusion

(PHEV)

Degrees of Hybridization

Guzzella, Lino, and Antonio Sciarretta. Vehicle propulsion systems. Vol. 2. Berlin: Springer,2005.

Brake Specific Fuel Consumption (BSFC)

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

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!

Types of Hybrids

Gas-Electric

Diesel-Electric

Diesel-Hydraulic

Fuel Cell-Electric

Power-split HEV

Battery

(Generator)

Generator

(Motor)

Torque Coupler Final Drive

Inverter

Planetary Gear Set

Engine

Mechanical

Electrical

Power-Split HEV ModelEx: Toyota Prius, Ford Escape Hybrid

Control Inputs

EngineTorqueM1 Torque

State Variables

Engine speedVehicle speedBattery SOCVehicleacceleration(MarkovChain)

SUPERVISORY

CONTROLLER

PLANETARY

GEAR SET

BATTERY PACK

ENGINE

VEHICLE

Rule-based Energy Management

HEV Optimal Energy Management

Objective Function:

minu(k),k=0···kf

kf∑k=0

[Fuel Consumption(k) + Emissions(k)]

Constraints:

subject to: x(k + 1) = f(x(k),u(k),w(k)),

SOC(0) = SOC(kf )

HEV Operation

Plug-in Hybrid Electric Vehicle (PHEV)

We have random power demand (driver pedal position)

Add a second depletable energy store!

Examples of PHEVs

Toyota Prius PHEV

Ford Fusion Energi

Chevrolet Volt

Fisker Karma

Two Depletable Energy Stores

Battery/

Mechanical

Energy

Chemical

Energy

Engine

Wheel+

Ptank ωeng Teng=Peng

Pdemand

ωM/G1 TM/G1+

ωM/G2 TM/G2

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 internalcombustion engine.

PHEV Optimal Energy Management

Objective Function:

minu(k),k=0···kf

kf∑k=0

[Fuel Consumption(k) + Emissions(k)]

Constraints:

subject to: x(k + 1) = f(x(k),u(k),w(k)),

SOC(k) ≥ SOCmin, ∀ k = 0, · · · , kf

Charge Depletion-Charge Sustenance vs. Blending

500 1000 1500 2000 2500 3000

Timec(s)

ChargecdepletingcandcchargecsustainingDynamiccprogramming

ChargecdepletingChargecsustaining

Optimal

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

Use Real-time Traffic Data

Traffic Data

Energy Management

Feedback

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 2015. DOI: 10.1109/TCST.2014.2361294

Approaching Optimal Performance

DP CDCS Static@T Static@S Dyn.@T Dyn.@S50

Standard2Deviation

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 2015. DOI: 10.1109/TCST.2014.2361294

Electric Vehicle (EV)

We have random power demand (driver pedal position)

Remove it! Replace with a battery & motor!

Examples of EVs

Nissan Leaf

Ford Focus EV

Tesla Model S & Roadster

Renault Zoe

Vehicle-to-Grid (V2G) or Vehicle Grid Integration (VGI)

Plug-in electric vehicles (PEVs) communicate with the grid to providemutually beneficial services, such as demand response through throttled

charging, or selling power to the grid.

Government Initiatives

CA Vehicle-Grid Integration Roadmap

– 1.5M zero emission vehicles in CA by 2025

“Electric vehicle charging creates a reciprocal re-lationship between battery-powered cars and thepower grid in a way that produces mutual ben-efits. Without compromising the driving habitsof consumers, incentives should be pursued asa way to aggregate vehicle charging to developvaluable grid services.”

China Ministry of Science & Technology

– 5 million new energy vehicles on China’s roadsby end of 2020

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 2016.

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!

Outline

Problem Statement

Objective: Optimize power flow of engine & battery to satisfy demand.Given:

Power demand time-seriesHEV powertrain model parameters

0 5 10 15 200

Speed [m

0 5 10 15 20−30

Time [min]

and [kW

0 5 10 15 200

Speed [m

0 5 10 15 20−30

Time [min]

and [kW

Power Demand for a Toyota Prius undergoing UDDS cycle

Modeling - I

Engine Vehicle

Ba-ery

Power Balance Peng(k) + Pbatt(k) = Pdem(k), ∀ k = 0, · · · ,N− 1

Battery dynamics E(k + 1) = E(k)− Pbatt(k) ∆t, ∀ k = 0, · · · ,N− 1

E(0) = E0

Net-zero batt energy

Modeling - I

Engine Vehicle

Ba-ery

E(0) = E0

Net-zero batt energy

Modeling - I

Engine Vehicle

Ba-ery

E(0) = E0

Net-zero batt energy E(N) = E(0)

Modeling - I

Engine Vehicle

Ba-ery

E(0) = E0

Net-zero batt energy 0.95 E(0) ≤ E(N) ≤ 1.05 E(0)

Modeling - II

Engine Vehicle

Ba-ery

Batt energy lims Emin ≤ E(k) ≤ Emax, ∀ k = 0, · · · ,NBatt pwr lims Pmin

batt ≤ Pbatt(k) ≤ Pmaxbatt , ∀ k = 0, · · · ,N− 1

Eng pwr lims 0 ≤ Peng(k) ≤ Pmaxeng , ∀ k = 0, · · · ,N− 1

min. fuel consumption J =∑N−1

k=0 α · Peng(k) ∆t

Modeling - II

Engine Vehicle

Ba-ery

Batt energy lims Emin ≤ E(k) ≤ Emax, ∀ k = 0, · · · ,NBatt pwr lims Pmin

batt ≤ Pbatt(k) ≤ Pmaxbatt , ∀ k = 0, · · · ,N− 1

Eng pwr lims 0 ≤ Peng(k) ≤ Pmaxeng , ∀ k = 0, · · · ,N− 1

min. fuel consumption J =∑N−1

k=0 α · Peng(k) ∆t

Optimization Formulation

minPbatt(k),Peng(k),E(k)

J =N−1∑k=0

α · Peng(k) ∆t (1)

with equality constraints

Peng(k) + Pbatt(k) = Pdem(k), ∀ k = 0, · · · ,N− 1 (2)

E(k + 1) = E(k)− Pbatt(k) ∆t, ∀ k = 0, · · · ,N− 1 (3)

E(0) = E0 (4)

and inequality constraints

0.95 E(0) ≤ E(N) ≤ 1.05 E(0), (5)

Emin ≤ E(k) ≤ Emax, ∀ k = 0, · · · ,N (6)

Pminbatt ≤ Pbatt(k) ≤ Pmax

batt , ∀ k = 0, · · · ,N− 1 (7)

0 ≤ Peng(k) ≤ Pmaxeng , ∀ k = 0, · · · ,N− 1 (8)

Optimization Formulation - reduced

minPbatt(k),E(k)

J =N−1∑k=0

α∆t · (Pdem(k)− Pbatt(k)) (9)

E(k + 1) = E(k)− Pbatt(k) ∆t, ∀ k = 0, · · · ,N− 1 (10)

E(0) = E0 (11)

0.95 E(0) ≤ E(N) ≤ 1.05 E(0), (12)

Emin ≤ E(k) ≤ Emax, ∀ k = 0, · · · ,N (13)

Pminbatt ≤ Pbatt(k) ≤ Pmax

batt , ∀ k = 0, · · · ,N− 1 (14)

0 ≤ Pdem(k)− Pbatt(k) ≤ Pmaxeng , ∀ k = 0, · · · ,N− 1 (15)

LP Formulation

minimizex cTx (16)

subject to: Ax ≤ b (17)

Aeqx = beq (18)

where the decision variable is given by

x = [Pbatt(0), Pbatt(1), · · · , Pbatt(N− 1),E(0),E(1), · · · ,E(N− 1),E(N)]T (19)

2N + 1 decision variables

Problem Data

UDDS drive cycle: N = 1369 time steps⇒ 2,739 optimization vars

∆t = 1 sec

α = 0.1 g/(s-kW)

E0 = 0.6 kWh = 2.16 MJ = 50%

Emin = 1.296 MJ = 30%, Emax = 3.024 MJ = 70%

Pminbatt = -15 kW, Pmax

batt = +15 kW

Pmaxeng = 35 kW

Results

0 5 10 15 200

ons. [g

0 5 10 15 200.35

Battery

0 5 10 15 20−20

Time [min]

Batt Power

Eng Power

Batt Limits

Optimal Energy Management Problem

Power Flow Network

Supply = DemandPower Flow dynamics

& constraints

S1 S2 SNS

Generators Demand

Storage

Applications• USElectricPowerGrid• DistributiongridonUCB

campus• Microgrid inKenyanvillage• Commercialbuildingwith

solar&storage• Ahybridvehicle(e.g.Prius)• Asolarcar/aircraft• Awirelesssensornode

withenergyharvesting

Figure: Setup for the energy management problem

Outline

Problem Statement

Objective: Optimize charge schedule to minimize electricity costGiven:

Time-varying price signalEV battery model parameters

00:00 04:00 08:00 12:00 16:00 20:00 24:000

Time of Day

icity C

Hypothetical time-varying electricity price

Modeling - I

+ _Voc

Integrator SOC(k + 1) = SOC(k) + ∆tQcap

I(k), k = 0, · · · ,N− 1

SOC(0) = SOC0

Kirchoff’s voltage law V(k) = Voc + RI(k), k = 0, · · · ,N

Electric Power P(k) = I(k)V(k) = VocI(k) + RI2(k), k = 0, · · · ,N

Charging cost J =∑N−1

k=0 c(k)[Voc · I(k) + R · I2(k)

Modeling - I

+ _Voc

I(k), k = 0, · · · ,N− 1

SOC(0) = SOC0

k=0 c(k)[Voc · I(k) + R · I2(k)

Modeling - I

+ _Voc

I(k), k = 0, · · · ,N− 1

SOC(0) = SOC0

k=0 c(k)[Voc · I(k) + R · I2(k)

Modeling - I

+ _Voc

I(k), k = 0, · · · ,N− 1

SOC(0) = SOC0

k=0 c(k)[Voc · I(k) + R · I2(k)

Modeling - II

+ _Voc

SOC lims SOCmin ≤ SOC(k) ≤ SOCmax, k = 0, · · · ,NCurrent lims 0 ≤ I(k) ≤ Imax, k = 0, · · · ,N− 1

Final SOC SOC(N) ≥ EQcapVoc

+ SOCmin

Modeling - II

+ _Voc

SOC lims SOCmin ≤ SOC(k) ≤ SOCmax, k = 0, · · · ,NCurrent lims 0 ≤ I(k) ≤ Imax, k = 0, · · · ,N− 1

Final SOC SOC(N) ≥ EQcapVoc

+ SOCmin

Optimization Formulation

minI(k),SOC(k)

J =N−1∑k=0

c(k)∆t VocI(k) + c(k)∆tR I2(k) (20)

SOC(k + 1) = SOC(k) +∆t

QcapI(k), k = 0, · · · ,N− 1 (21)

SOC(0) = SOC0 (22)

SOCmin ≤ SOC(k) ≤ SOCmax, k = 0, · · · ,N (23)

0 ≤ I(k) ≤ Imax, k = 0, · · · ,N− 1 (24)

SOC(N) ≥ E

QcapVoc+ SOCmin (25)

QP Formulation

minimizex1

2xTQx + RTx (26)

subject to: Ax ≤ b (27)

Aeqx = beq (28)

where decision variable is

x = [I(0), I(1), · · · , I(N− 1),SOC(0),SOC(1), · · · ,SOC(N− 1),SOC(N)]T (29)

2N + 1 decision variables

Problem Data

Given time-varying price: N = 96 time steps⇒ 193 optimization vars

∆t = 15 min

Qcap = 13.8 A-hr, Voc = 363V, R = 1.1 Ohms

SOC0 = 0.2

SOCmin = 0.1, SOCmax = 0.9

Imax = 9.66 A

E = 14.4 MJ

assume PEV plugged-in 16:00 - 24:00

Results

0 5 10 15 200

c(k ) [cents/kW h ]

P (k ) [kW ]

00:00 04:00 08:00 12:00 16:00 20:00 24:000

Battery

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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