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Increasing Battery Potential: Electrochemical Control Scott Moura Assistant Professor | eCAL Director University of California, Berkeley Satadru Dey, Hector Perez, Saehong Park, Dong Zhang KAIST | Daejeon, Korea Download:

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Increasing Battery Potential: Electrochemical Control

Scott Moura

Assistant Professor | eCAL Director University of California, Berkeley

Satadru Dey, Hector Perez, Saehong Park, Dong Zhang

KAIST | Daejeon, Korea

Download: https://ecal.berkeley.edu/pubs/talks/Moura-KAIST-Batts-Slides.pdf

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 1

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eCAL Battery Controls Team @ UC Berkeley

Current Researchers

  • Prof. Scott Moura | Dr. Satadru Dey | Hector Perez | Saehong Park | Dong Zhang

Supporting Researchers

  • Prof. Xiaosong Hu

| Defne Gun | Changfu Zou | Zach Gima | Preet Gill

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 2

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SLIDE 3

A Golden Era

1985 1990 1995 2000 2005 2010 2015 Year 500 1000 1500 2000 2500 3000 3500

  • No. of Publications

Keyword Search: Battery Systems and Control

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 3

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SLIDE 4

The Battery Problem

Needs: Cheap, high energy/power, fast charge, long life

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 4

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The Battery Problem

Needs: Cheap, high energy/power, fast charge, long life Reality: Expensive, conservatively design/operated, die too quickly

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 4

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The Battery Problem

Needs: Cheap, high energy/power, fast charge, long life Reality: Expensive, conservatively design/operated, die too quickly Some Motivating Facts EV Batts 1000 USD / kWh (2010)∗ 485 USD / kWh (2012)∗ 350 USD / kWh (2015)∗∗ 125 USD / kWh for parity to IC engine Only 50-80% of available capacity is used Range anxiety inhibits adoption Lifetime risks caused by fast charging

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 4

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SLIDE 7

The Battery Problem

Needs: Cheap, high energy/power, fast charge, long life Reality: Expensive, conservatively design/operated, die too quickly

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 4

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The Battery Problem

Needs: Cheap, high energy/power, fast charge, long life Reality: Expensive, conservatively design/operated, die too quickly Some Motivating Facts EV Batts 1000 USD / kWh (2010)∗ 485 USD / kWh (2012)∗ 350 USD / kWh (2015)∗∗ 125 USD / kWh for parity to IC engine Only 50-80% of available capacity is used Range anxiety inhibits adoption Lifetime risks caused by fast charging Two Solutions Design better batteries Make current batteries better (materials science & chemistry) (estimation and control)

∗Source: MIT Technology Review, “The Electric Car is Here to Stay.” (2013) ∗∗Source: Tesla Powerwall. (2015) Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 4

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SLIDE 9

Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 5

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History

Luigi Galvani, 1737-1798, Physicist, Bologna, Italy “Animal electricity” Dubbed “galvanism” First foray into electrophysiology Experiments on frog legs Alessandro Volta, 1745-1827 Physicist, Como, Italy Voltaic Pile Monument to Volta in Como

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 6

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SLIDE 11

Comparison of Lithium Ion (Cathode) Chemistries

Lithium Cobalt Oxide (LiCO2) Lithium Manganese Oxide (LiMn2O4) Lithium Nickel Manganese Cobalt Oxide (LiNiMnCoO2) Lithium Iron Phosphate (LiFePO4) Lithium Nickel Cobalt Aluminum Oxide (LiNiCoAlO2) Lithium Titanate (Li4Ti5O12)

Source: http://batteryuniversity.com/learn/article/types_of_lithium_ion Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 7

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Energy Density

Source: Katherine Harry & Nitash Balsara, UC Berkeley Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 8

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Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 9

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SLIDE 14

Battery Models

Equivalent Circuit Model

(a) OCV-R

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 10

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Battery Models

Equivalent Circuit Model

(a) (b) (c) OCV-R OCV-R-RC Impedance

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 10

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SLIDE 16

Battery Models

Equivalent Circuit Model

(a) (b) (c) OCV-R OCV-R-RC Impedance

Electrochemical Model

Separator Cathode Anode LixC6 Li1-xMO2 Li+ cs

  • (r)

cs

+(r)

css

  • css

+

Electrolyte e- e- ce(x)

  • L
  • L

+ + sep

L

sep

r r x

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 10

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SLIDE 17

Safely Operate Batteries at their Physical Limits

Cell Current Surface concentration Terminal Voltage Overpotential

ECM-based limits of operation ECM-based limits of operation Electrochemical model-based limits of operation

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 11

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ElectroChemical Controller (ECC)

EChem-based State/Param Estimator I(t) V(t), T(t) Battery Cell EChem-based Controller Ir(t) V(t), T(t) ^ ^ + _

Innovations Estimated States & Params

ElectroChemical Controller (ECC)

Measurements

^ x(t), θ(t) ^

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 12

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SLIDE 19

ElectroChemical Controller (ECC)

The State Estimation Problem

EChem-based State/Param Estimator I(t) V(t), T(t) Battery Cell EChem-based Controller Ir(t) V(t), T(t) ^ ^ + _

Innovations Estimated States & Params

ElectroChemical Controller (ECC)

Measurements

^ x(t), θ(t) ^

The State (a.k.a. SOC) Estimation Problem

Given measurements of current I(t), voltage V(t), and temperature T(t), estimate the electrochemical states of interest. Exs: bulk solid phase Li concentration (state-of-charge) surface solid phase Li concentration (state-of-power)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 13

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ElectroChemical Controller (ECC)

The Parameter Estimation Problem

EChem-based State/Param Estimator I(t) V(t), T(t) Battery Cell EChem-based Controller Ir(t) V(t), T(t) ^ ^ + _

Innovations Estimated States & Params

ElectroChemical Controller (ECC)

Measurements

^ x(t), θ(t) ^

The Parameter (a.k.a. SOH) Estimation Problem

Given measurements of current I(t), voltage V(t), and temperature T(t), estimate uncertain parameters related to SOH. Exs: cyclable lithium (capacity fade) volume fraction (capacity fade) solid-electrolyte interface resistance (power fade)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 14

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ElectroChemical Controller (ECC)

The Constrained Control Problem

EChem-based State/Param Estimator I(t) V(t), T(t) Battery Cell EChem-based Controller Ir(t) V(t), T(t) ^ ^ + _

Innovations Estimated States & Params

ElectroChemical Controller (ECC)

Measurements

^ x(t), θ(t) ^

The Constrained Control Problem

Given measurements of current I(t), voltage V(t), and temperature T(t), control current such that critical electrochemical variables are maintained within safe operating constraints. Exs: saturation/depletion of solid phase and electrolyte phase side-reaction overpotentials internal temperature

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 15

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Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 16

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Battery Electrochemistry Model

The Doyle-Fuller-Newman (DFN) Model

Separator Cathode Anode LixC6 Li1-xMO2 Li+ cs

  • (r)

cs

+(r)

css

  • css

+

Electrolyte e- e- ce(x)

  • L
  • L

+ + sep

L

sep

r r x

Key References:

  • K. Thomas, J. Newman, and R. Darling, Advances in Lithium-Ion Batteries. New York, NY USA: Kluwer Academic/Plenum Publishers, 2002, ch. 12:

Mathematical modeling of lithium batteries, pp. 345-392.

  • N. A. Chaturvedi, R. Klein, J. Christensen, J. Ahmed, and A. Kojic, “Algorithms for advanced battery-management systems,” IEEE Control Systems

Magazine, vol. 30, no. 3, pp. 49-68, 2010.

  • J. Newman. (2008) Fortran programs for the simulation of electrochemical systems. [Online]. Available:

http://www.cchem.berkeley.edu/jsngrp/fortran.html Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 17

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Electrochemical Model Equations

well, some of them | Matlab CODE: github.com/scott-moura/fastDFN Description Equation Solid phase Li concentration

∂c±

s

∂t (x, r, t) =

1 r2

∂ ∂r

  • D±

s (c± s )r2 ∂c±

s

∂r (x, r, t)

  • Electrolyte Li

concentration

εe ∂ce

∂t (x, t) = ∂ ∂x

  • Deff

e (ce) ∂ce

∂x (x, t) +

1−t0

c

F

i±

e (x, t)

  • Solid

potential

σeff,± ∂φ±

s

∂x (x, t) = i±

e (x, t) − I(t)

Electrolyte potential

κeff(ce) ∂φe

∂x (x, t) = −ie±(x, t) +

2RT(1−t0

c )κeff(ce)

F

  • 1 +

d ln fc/a d ln ce

  • ∂ ln ce

∂x

(x, t)

Electrolyte ionic current

∂ie± ∂x (x, t) = a±

s Fjn±(x, t)

Molar flux btw phases j±

n (x, t) = 1 F i± 0 (x, t)

  • e

αaF RT η±(x,t) − e− αcF RT η±(x,t)

Temperature

ρcP

dT dt (t) = h

  • T0(t) − T(t)
  • + I(t)V(t) −

0+

0− asFjn(x, t)∆T(x, t)dx

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 18

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Simulations

LiCoO2-C cell | 5C discharge after 30sec

Space, r

c−

s (x, r, t)/c− s,max

Center Surface Space, r

c+

s (x, r, t)/c+ s,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2

Space, x/L

ce(x, t)

0.45 0.5 0.55 0.6 0.65 0.7 0.75

Cathode Separator Anode

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 19

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Model Identification from Experiments

Model Identification Problem

Given measurements of current I(t), voltage V(t), and temperature T(t), identify unknown/uncertain parameters. Challenges: How to design the experiments? How to optimally fit the parameters?

Space, r

c−

s (x, r, t)/c− s,max Center Surface Space, r

c+

s (x, r, t)/c+ s,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 Space, x/L

ce(x, t)

0.45 0.5 0.55 0.6 0.65 0.7 0.75 Cathode Separator Anode

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 20

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Model Identification from Experiments

Generate Feasible Parameter Set Run Test Optimized for Model ID Optimize Parameters Validate on different test

Note: 10-bit A/D converter + 10V ref ⇒ 10mV resolution

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 21

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Model Reduction

ACCURACY SIMPLICITY Integrator Atomistic ECT SPMeT SPMe SPM ECM

Anode Separator Cathode

I(t) cs

  • (r,t)

r Li+ Rs

  • cs

+(r,t)

r Li+ I(t) Rs

+ Electrolyte Solid Li+ Solid Electrolyte

V(t) x ce(x,t) I(t) I(t) Li+ Li+ Li+ 0+ 0- L- 0sepLsepL+ T(t)

Cell 𝑊(𝑢) = ℎ(𝑑𝑡 − (𝑆𝑡 −, 𝑢), 𝑑𝑡 +(𝑆𝑡 +, 𝑢), 𝑑𝑓 −(𝑦, 𝑢), 𝑑𝑓 𝑡𝑓𝑞(𝑦, 𝑢), 𝑑𝑓 +(𝑦, 𝑢), 𝑈(𝑢), 𝐽(𝑢))

V(t) cs

  • (r,t)

r cs

+(r,t)

r Li+ Li+ Anode Separator Cathode Li

+

I(t) I(t) Rs

  • Rs

+

  • --Single Particle Model---

Solid Electrolyte

(b) OCV-R-RC

1/s

Power Energy

Atomistic ECT SPMe SPM ECM Integrator

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 22

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Model Reduction

Methods in literature: Spectral methods Residue grouping Quasilinearization & Padé approximation Principle orthogonal decomposition Single particle model variants and much, much more Very popular and saturated topic Will not discuss further

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 22

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Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 23

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SLIDE 31

Survey of SOC/SOH Estimation Literature

Equivalent Circuit Model (ECM)

(a) (b) (c) OCV-R OCV-R-RC Impedance

Electrochemical Model Separator Cathode Anode LixC6 Li1-xMO2 Li+ cs

  • (r)

cs

+(r)

css

  • css

+

Electrolyte e- e- ce(x)

  • L
  • L

+ + sep

L

sep

r r x

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 24

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SLIDE 32

Survey of SOC/SOH Estimation Literature

Lots of research. What is new? What are the opportunities/challenges? Unprecedented detail w/ EChem models Accurate models Computational challenges Observability/identifiability – i.e. is it possible? Provable convergence – i.e. mathematical certificate Want to capitalize on unprecedented detail of EChem models? We use a reduced EChem model Provable convergence? We mathematically prove estimation error convergence

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 24

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SLIDE 33

Single Particle Model with Electrolyte (SPMe)

Anode Separator Cathode

I(t) cs

  • (r,t)

r Li+ Rs

  • cs

+(r,t)

r Li+ I(t) Rs

+

Electrolyte Solid

Li+ Solid Electrolyte

V(t) x ce(x,t) I(t) I(t) Li+ Li+ Li+ 0+ 0- L- 0sepLsepL+ T(t)

Cell

𝑊(𝑢) = ℎ(𝑑𝑡

− (𝑆𝑡 −, 𝑢), 𝑑𝑡 +(𝑆𝑡 +, 𝑢), 𝑑𝑓 −(𝑦, 𝑢), 𝑑𝑓 𝑡𝑓𝑞(𝑦, 𝑢), 𝑑𝑓 +(𝑦, 𝑢), 𝑈(𝑢), 𝐽(𝑢))

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 25

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SLIDE 34

SPMe - Physical Intuition

Space, r

c−

s (x, r, t)/c− s,max

Center Surface Space, r

c+

s (x, r, t)/c+ s,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2

Space, x/L

ce(x, t)

0.45 0.5 0.55 0.6 0.65 0.7 0.75

Cathode Separator Anode

Approximate solid-phase concentration as uniform in x

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 26

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SLIDE 35

Model Comparison

5 10 15 20 25 30 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Discharged Capacity [Ah/m2] Voltage [V] DFN - (line) SPMe + (plus) SPM ◦ (circle) 0.1C 0.5C 1C 2C 5C

(a)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 27

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SLIDE 36

Model Comparison

−2 2 4 Current [C−rate] 500 1000 1500 2000 2500 3000 3.4 3.6 3.8 4 4.2 Time [sec] Voltage [V] DFN SPMe SPM 150 200 250 300 3.6 3.7 3.8 3.9 4 Voltage [V] 2600 2650 2700 2750 3.6 3.8 4

ZOOM ZOOM

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 27

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SLIDE 37

Causal Structure of SPMe

I(t)

✲ ✲ ✲ ✲

c+

s (r, t)

✲

c+

ss(t)

c−

s (r, t)

✲

c−

ss(t)

c+

e (x, t)

csep

e (x, t)

c−

e (x, t)

✲

c+

e (0+, t)

✲

c−

e (0−, t)

Output

✲

V(t)

Figure: Block diagram of SPMe. Note that the c+

s , c− s , ce subsystems are all (i)

quasilinear parabolic PDEs and (ii) independent of one another.

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 28

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SLIDE 38

Battery Cell

✲ ❄

V(t) Cathode Obs.

ˆ

c+

s (r, t)

Anode Obs.

ˆ

c−

s (r, t)

✻ ˆ

c−

ss

♥ ✻ ❄ ˜

c+

ss

❄ ˆ

c+

ss

✛ ˇ

c+

ss

+ −

I(t)

✲ ✲ ✲ ✲ ✲ ✲

Electrolyte Obs.

ˆ

c+

e (x, t)

ˆ

csep

e (x, t)

ˆ

c−

e (x, t)

✻ ˆ

c+

e (0+)

✻ ˆ

c−

e (0−)

Output Fcn. Inversion

Figure: Block diagram of SPMe Observer.

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 29

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SLIDE 39

Stability Analysis

Theorem 1 - Solid Phase

The anode & cathode solid Li concentration estimates converge asymptotically to the true values. ˆ c±

s (r, t) → c± s (r, t), as t → ∞.

Theorem 2 - Electrolyte Phase

The electrolyte Li concentration estimates converge asymptotically to the true values. ˆ ce(x, t) → ce(x, t), as t → ∞.

Theorem 3 - Output Inversion

The “processed” cathode surface concentration converges exponentially to its true value: ˇ c+

ss(t) → c+ ss(t), as t → ∞.

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 30

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SLIDE 40

Simulation Setup

Truth data from DFN Model Parameters from DUALFOIL LiCoO2 cathode/ graphic anode chemistry. TRUE initial condition: c−

s (r, 0)/c− s,max = 0.8224

OBSERVER initial condition: ˆ c−

s (r, 0)/c− s,max = 0.4

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 31

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SLIDE 41

Constant 1C Discharge Cycle

1 2 Current [C−rate] 0.2 0.4 0.6 0.8 1 Surface Conc. [−] θ − ˆ θ − θ + ˆ θ + ˇ θ + 500 1000 1500 2000 2500 3000 3.4 3.5 3.6 3.7 3.8 3.9 Time [sec] Voltage V ˆ V

(a) (b) (c)

OUTPUT NEARLY NON−INVERTIBLE

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 32

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SLIDE 42

EV Charge/Discharge Cycle: UDDSx2

−4 −2 2 4 Current [C−rate] 0.4 0.5 0.6 0.7 0.8 Surface Conc. [−] θ − ˆ θ − θ + ˆ θ + ˇ θ + 500 1000 1500 2000 2500 3000 3.6 3.8 4 Time [sec] Voltage V ˆ V

(a) (b) (c)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 33

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SLIDE 43

EV Charge/Discharge Cycle: UDDSx2

−0.2 −0.1 0.1 0.2 Surface Conc. Error [−] θ − − ˆ θ − θ + − ˆ θ + θ + − ˇ θ + 500 1000 1500 2000 2500 3000 −20 −10 10 20 Time [sec] Voltage Error [mV] V − ˆ V

(d) (e)

  • S. J. Moura, F

. Bribiesca Argomedo, R. Klein, A. Mirtabatabaei, M. Krstic, “Battery State Estimation for a Single Particle Model with Electrolyte Dynamics,” to appear in IEEE Transactions on Control Systems Technology. DOI: 10.1109/TCST.2016.2571663

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 33

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SLIDE 44

Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 34

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SLIDE 45

Operate Batteries at their Physical Limits

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 35

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SLIDE 46

Battery Charge Protocols: Heuristic

Fast Charging Multi-stage CC + CV (MCC-CV: HighCC-LowCC-CV) [Ansean et al., 2013] Boost charging (CV-CC-CV) [Notten et al., 2005] Constant power constant voltage (CP-CV) [Zhang et al., 2006] Fuzzy logic [Surmann et al., 1996] Neural Networks [Ullah et al., 1996] Grey system theory [Chen et al., 2008] Ant colony system algorithm [Liu et al., 2005] Battery Life Multi-stage CC + CV (MCC-CV: LowCC-HighCC-CV) [Zhang et al., 2006] CC-CV with negative pulse (CC-CV-NP) [Monem et al., 2015]

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 36

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SLIDE 47

Battery Charge Protocols: Optimization & Models

Why so hard?

Accurate models @ high C-rate Numerically solving optimal control problem Existing Studies Linear quadratic formulations [Parvini et al., 2015] State independent electrical parameters [Abdollahi et al., 2015] Piecewise constant time discretization [Methekar et al., 2010] Linear input-output models [Torchio et al., 2015] One step model predictive control formulation [Klein et al., 2010] Reference governor formulation [Perez et al., 2015]

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 37

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SLIDE 48

Our approach

Reduced order models are inaccurate at high C-rates! We use Single Particle Model w/ Electrolyte (SPMe) At high C-rates, temperature matters! We add temperature dynamics, yielding SPMeT Fast charging can accelerate aging! We explicitly constrain internal states for inducing aging mechanisms Solving optimal control problem is numerically intractable We use pseudospectral methods

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 38

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SLIDE 49

Single Particle Model with Electrolyte (SPMe)

Anode Separator Cathode

I(t) cs

  • (r,t)

r Li+ Rs

  • cs

+(r,t)

r Li+ I(t) Rs

+

Electrolyte Solid

Li+ Solid Electrolyte

V(t) x ce(x,t) I(t) I(t) Li+ Li+ Li+ 0+ 0- L- 0sepLsepL+ T(t)

Cell

𝑊(𝑢) = ℎ(𝑑𝑡

− (𝑆𝑡 −, 𝑢), 𝑑𝑡 +(𝑆𝑡 +, 𝑢), 𝑑𝑓 −(𝑦, 𝑢), 𝑑𝑓 𝑡𝑓𝑞(𝑦, 𝑢), 𝑑𝑓 +(𝑦, 𝑢), 𝑈(𝑢), 𝐽(𝑢))

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 39

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SLIDE 50

Add Temperature Dynamics

Jelly Roll T1(t) and Can T2(t) Temperature

C1 dT1 dt (t)

=

1 R12

[T2(t) − T1(t)] + ˙

Q(t) C2 dT2 dt (t)

=

1 R12

[T1(t) − T2(t)] +

1 R2a

[Ta(t) − T2(t)] ˙

Q(t)

=

I(t)

  • V(t) −
  • U+(c+

s ) − U−(c− s )

  • Temperature-dependent Parameters

Ψ(T1) = Ψ(Tref)

  • EΨ

R

  • 1

Tref

− 1

T1

  • , Ψ ∈ {D+

s , D− s , De, κ, k+, k−}

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 40

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SLIDE 51

Single Particle Model w/ Electrolyte & Temperature

𝑑𝑡

−(𝑢)

𝑑𝑓

+(𝑦, 𝑢)

𝑑𝑓

−(𝑦, 𝑢)

𝑑𝑡𝑡

+ (𝑢)

𝑑𝑡𝑡

− (𝑢)

𝑑𝑡

+(𝑠, 𝑢)

𝑑𝑡

−(𝑠, 𝑢)

𝑑𝑓

+(𝑦, 𝑢)

𝑑𝑓

𝑡𝑓𝑞(𝑦, 𝑢)

𝑑𝑓

−(𝑦, 𝑢)

Output

𝑑𝑡

+(𝑢)

Cathode Bulk Anode Bulk

𝑑𝑡

−(𝑠, 𝑢)

𝑑𝑡

+(𝑠, 𝑢)

Temperature

𝑊(𝑢) 𝐽(𝑢) 𝑑𝑓

𝑡𝑓𝑞(𝑦, 𝑢)

𝑈

𝑏𝑤𝑕(𝑢)

𝑈

𝑡(𝑢)

𝑈

𝑑(𝑢)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 41

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SLIDE 52

Optimal Control Problem

Formulation

min

I(t),x(t),tf

tf

t0

1 · dt subject to SPMeT dynamics, boundary conditions, and the following Imin ≤ I(t) ≤ Imax

θ±

min ≤ c± ss(t)

cs,max

≤ θ±

max

ce,min ≤ ce(x, t) ≤ ce,max Tmin ≤ T1,2(t) ≤ Tmax t0 ≤ tf ≤ tmax SOC(t0) = SOC0, SOC(tf) = SOCf

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 42

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SLIDE 53

Pseudospectral Optimal Control

Dynamic programming? Computationally intractable Pontryagin’s minimum principle? Untenable to derive necessary & sufficient conditions Linear Quadratic Regulator? Strong nonlinear dynamics

Pseudospectral Method

Collocation based LGR pseudo-spectral method is ideally suited to solve

  • ptimal control problems with multi-state nonlinearities [Patterson et al.,

2014] [Garg et al., 2011] [Darby et al., 2011] [Garg et al., 2011] [Garg et al., 2010] Previous applications Aerospace and autonomous fight systems [Ross et al., 2012] Road vehicle systems [Limebeer et al., 2014] Energy storage [Hu et al., 2015][Hu et al., 2013]

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 43

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SLIDE 54

Results: Minimum Time Charging

Current Limit Comparison for Imax = 8.5C, 7.25, 6C

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 8 12 Current (C−Rate)

I(t)8.5C I(t)7.25C I(t)6C

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3.5 3.6 3.7 3.8 Voltage (V)

V (t)8.5C V (t)7.25C V (t)6C

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.2 0.4 0.6 0.8 1 SOC

SOC(t)8.5C SOC(t)7.25C SOC(t)6C

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 285 295 305 315 325 Temperature (K) Time (min)

Ts(t)8.5C Ts(t)7.25C Ts(t)6C Tc(t)8.5C Tc(t)7.25C Tc(t)6C

1 2 3 4 5 0.2 0.4 0.6 0.8 Normalized Surf. Conc.

θ−(t)8.5C θ−(t)7.25C θ−(t)6C

1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 Normalized Surf. Conc.

θ+(t)8.5C θ+(t)7.25C θ+(t)6C

1 2 3 4 5 0.5 1 1.5

  • Elec. Conc. (kmol/m

3)

Time (min)

c−

e (0−,t)8.5C

c−

e (0−,t)7.25C

c−

e (0−,t)6C

1 2 3 4 5 0.5 1 1.5 2 2.5 3

  • Elec. Conc. (kmol/m

3)

Time (min)

c+

e (0+,t)8.5C

c+

e (0+,t)7.25C

c+

e (0+,t)6C

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 44

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SLIDE 55

Results: Is CCCV Optimal?

Comparison with CCCV for Imax = 6C

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 4 6 Current (C−Rate) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3.5 3.6 3.7 3.8 Voltage (V) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.2 0.4 0.6 0.8 1 SOC 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 285 295 305 315 325 Temperature (K) Time (min)

I(t)6C I(t)6C,CCCV V (t)6C V (t)6C,CCCV SOC(t)6C SOC(t)6C,CCCV Ts(t)6C Ts(t)6C,CCCV Tc(t)6C Tc(t)6C,CCCV

2 4 6 8 0.2 0.4 0.6 0.8 1 Normalized Surf. Conc. 2 4 6 8 0.5 0.6 0.7 0.8 0.9 1 Normalized Surf. Conc. 2 4 6 8 0.2 0.4 0.6 0.8 1 1.2

  • Elec. Conc. (kmol/m

3)

Time (min) 2 4 6 8 0.5 1 1.5 2 2.5 3

  • Elec. Conc. (kmol/m

3)

Time (min)

θ−(t)5.89C θ−(t)5.89C,CCCV θ+(t)5.89C θ+(t)5.89C,CCCV c−

e (0−,t)5.89C

c−

e (0−,t)5.89C,CCCV

c+

e (0+,t)5.89C

c+

e (0+,t)5.89C,CCCV

  • H. Perez, X. Hu, S. J. Moura, “Optimal Charging of Batteries via a Single Particle

Model with Electrolyte and Thermal Dynamics,” 2016 American Control Conference, Boston, MA, 2016.

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 45

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SLIDE 56

Battery-in-the-Loop Test Facility

Battery Tester Li-ion Cells in Chamber Microcontroller w/ Algorithms

CAN bus Measurements: I , V , T Optimized Charge Cycle Estimates: concentrations,

  • verpotentials, etc.

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 46

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SLIDE 57

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 46

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SLIDE 58

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 46

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SLIDE 59

Outline

1

BACKGROUND & BATTERY ELECTROCHEMISTRY FUNDAMENTALS

2

ESTIMATION AND CONTROL PROBLEM STATEMENTS

3

ELECTROCHEMICAL MODEL

4

STATE ESTIMATION

5

CONSTRAINED OPTIMAL CONTROL

6

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 47

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SLIDE 60

Summary

Background & Electrochemistry Fundamentals SOC Estimation, SOH Estimation, Charge/Discharge Control The DFN Electrochemical Model SOC Estimation Optimally Fast-Safe Charging

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 48

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SLIDE 61

Summary

Background & Electrochemistry Fundamentals SOC Estimation, SOH Estimation, Charge/Discharge Control The DFN Electrochemical Model SOC Estimation Optimally Fast-Safe Charging Applicable control theoretic tools: PDE Control State estimation System identification Nonlinear and adaptive systems Optimal & constrained control

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 48

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SLIDE 62

Summary

Background & Electrochemistry Fundamentals SOC Estimation, SOH Estimation, Charge/Discharge Control The DFN Electrochemical Model SOC Estimation Optimally Fast-Safe Charging

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 49

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SLIDE 63

Summary

Background & Electrochemistry Fundamentals SOC Estimation, SOH Estimation, Charge/Discharge Control The DFN Electrochemical Model SOC Estimation Optimally Fast-Safe Charging Research Topics NOT discussed: Parameter Identification of DFN Parameter Sensitivity Analysis Model Reduction Fault Diagnostics Charge/Discharge Control

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 49

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SLIDE 64

Reading Materials

  • S. J. Moura and H. Perez, “Better Batteries through Electrochemistry and

Controls,” ASME Dynamic Systems and Control Magazine, v 2, n 2, pp. S15-S21, July 2014. (Invited Paper).

  • N. A. Chaturvedi, R. Klein, J. Christensen, J. Ahmed, and A. Kojic, “Algorithms for

advanced battery-management systems,” IEEE Control Systems Magazine, vol. 30, no. 3, pp. 49-68, 2010.

  • H. E. Perez, N. Shahmohammadhamedani, S. J. Moura, “Enhanced Performance
  • f Li-ion Batteries via Modified Reference Governors & Electrochemical Models,”

IEEE/ASME Transactions on Mechatronics, v 20, n 4, pp. 1511-1520, Aug 2015.

  • S. J. Moura, N. A. Chaturvedi, M. Krstic, “Adaptive PDE Observer for Battery

SOC/SOH Estimation via an Electrochemical Model,” ASME Journal of Dynamic Systems, Measurement, and Control, v 136, n 1, pp. 011015-011026, Oct 2013.

  • H. Perez, S. J. Moura, “Sensitivity-Based Interval PDE Observer for Battery SOC

Estimation,” 2015 American Control Conference, Chicago, IL, 2015. Best Student Paper.

  • S. J. Moura, F

. Bribiesca Argomedo, R. Klein, A. Mirtabatabaei, M. Krstic, “Battery State Estimation for a Single Particle Model with Electrolyte Dynamics.”

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 50

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SLIDE 65

VISIT US!

Energy, Controls, and Applications Lab (eCAL) ecal.berkeley.edu smoura@berkeley.edu

Download: https://ecal.berkeley.edu/pubs/talks/Moura-FISITA-Batts-Slides.pdf

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 51

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SLIDE 66

APPENDIX SLIDES

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 52

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SLIDE 67

SPMe Properties

Marginal stability of c+

s , c− s , ce subsystems

Each individual c+

s (r, t), c− s (r, t), and ce(x, t) subsystem is marginally

  • stable. In particular,

each subsystem contains one eigenvalue at the origin the remaining eigenvalues lie on the negative real axis of the complex plane

Conservation of Solid Lithium

The moles of lithium in the solid phase is conserved. Mathematically,

d dt(nLi,s(t)) = 0 where

nLi,s(t) =

  • j∈{+,−}

εj

sLj 4 3π(Rj s)3

Rj

s

4πr2cj

s(r, t)dr

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 53

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SLIDE 68

SPMe Properties

Conservation of Electrolyte Lithium

The moles of lithium in the electrolyte phase is conserved. Mathematically,

d dt(nLi,e(t)) = 0 where

nLi,e(t) =

  • j∈{−,sep,+}

εj

e

Lj

0j cj e(x, 0)dx

This property implies that the equilibrium solution of the ce subsystem with zero current, i.e. I(t) = 0, is given by ce,eq = nLi,e

ε−

e L− + εsep e

Lsep + ε+

e L+ , ∀x ∈ [0−, 0+].

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 53

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SLIDE 69

Invertability Analysis

Question

It is better to invert output function w.r.t. anode OR cathode surface concentration? V(t) =RT

αF sinh−1

  • I(t)

2a+AL+i+

0 (c+ ss)

  • − RT

αF sinh−1

  • I(t)

2a−AL+i−

0 (c− ss)

  • U+(c+

ss) − U−(c− ss) − RtotalI(t) + kconc ln

  • ce(0+)

ce(0−)

  • ,

(1) i±

0 (c± ss) =k±

  • c±

e c± ss(c± s,max − c± ss)

(2) Define: V(t) = h(c+

ss, c− ss, I)

(3) Compute:

∂h ∂c+

ss

(c+

ss, c− ss, I)

AND

∂h ∂c−

ss

(c+

ss, c− ss, I)

(4)

  • ver a range of SOC and I. (Fixed ce)

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 54

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SLIDE 70

OCPs and Output Function Sensitivities

1 2 Anode OCP [V] 3 4 5 Cathode OCP [V] U −(θ −) U +(θ +) 0.2 0.4 0.6 0.8 1 −1 −0.5 0.5 1 1.5 Normalized Surface Concentration, θ ± = c ±

ss/c ± s, max

[×10−6] ∂h/∂c−

ss(θ −)

∂h/∂c+

ss(θ +)

(a) (b) LOW SENSITIVITY

Scott Moura | UC Berkeley ElectroChemical model based Control (ECC) September 29, 2016 | Slide 55