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Estimation and Fault Diagnostics of Battery PDE Models Scott Moura - - PowerPoint PPT Presentation

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Estimation and Fault Diagnostics of Battery PDE Models Scott Moura Assistant Professor | eCAL Director University of California, Berkeley Rensselaer Polytechnic Institute (RPI) Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, &

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SLIDE 1

Estimation and Fault Diagnostics of Battery PDE Models

Scott Moura

Assistant Professor | eCAL Director University of California, Berkeley

Rensselaer Polytechnic Institute (RPI)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 1

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SLIDE 2

Eric MUNSING Sangjae BAE

  • Dr. Chao

SUN Laurel DUNN Saehong PARK Dong ZHANG Bertrand TRAVACCA

  • Dr. Hector

PEREZ ZHOU Zhe Zach GIMA Hongcai ZHANG Jianchao Li Luis CUOTO Ramon CRESPO Mathilde BADOUAL Dylan KATO Emily YOU Teng ZENG

  • Prof. Satadru DEY

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 2

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SLIDE 3

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 3

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SLIDE 4

A Golden Era

1985 1990 1995 2000 2005 2010 2015

Year

1000 2000 3000

  • No. of Publications

Keyword Search: Battery Systems and Control

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 4

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SLIDE 5

Decline Costs

  • B. Nykvist and M. Nilsson, “Rapidly falling costs of battery packs for electric vehicles,” Nature Climate Change, Mar 2015.

DOI: 10.1038/NCLIMATE2564

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 5

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SLIDE 6

The Battery Problem

CHEAP High Energy & Power Fast Charge Long Lifespan Safe

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 6

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SLIDE 7

The Battery Problem

Samsung Galaxy Note Boeing 787 Dreamliner

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 6

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SLIDE 8

The Battery Problem

Two Solutions Design better batteries Make current batteries better (materials science & chemistry) (estimation and control)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 6

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SLIDE 9

The Battery Problem

Two Solutions Design better batteries Make current batteries better (materials science & chemistry) (estimation and control) Objective: Develop a battery management system that enhances performance and safety. Present BMS* Advanced BMS

*BMS: Battery-Management System

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 6

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SLIDE 10

On-Going Research Goals

Increase usable energy capacity by 20% Decrease charge times by factor of 5X Increase battery life time by 50% Decrease fault detection time by factor of 10X

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 7

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SLIDE 11

Outline

1

BACKGROUND & PROBLEM STATEMENTS

2

ELECTROCHEMICAL MODEL

3

STATE ESTIMATION

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 8

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SLIDE 12

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 9

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SLIDE 13

Lithium-ion Batteries

Negative plate rxn: LixC6 ⇔ C6 + xLi+ + xe− Positive plate rxn: Li1−xMO2 + xLi+ + xe− ⇔ LiMO2

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 10

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SLIDE 14

Battery Models

Equivalent Circuit Model

(a) OCV-R

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 11

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SLIDE 15

Battery Models

Equivalent Circuit Model

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

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 11

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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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 11

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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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 12

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SLIDE 18

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 13

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SLIDE 19

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 14

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SLIDE 20

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 14

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SLIDE 21

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 14

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SLIDE 22

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 14

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SLIDE 23

What are we protecting against?

Cobalt Oxide Graphite

Electrolyte Stability

Electrolyte Oxidation

Potential (E) vs. Li

Electrolyte Reduction (Kinetically limited) Lithium Plating (Dendrites) Electrode “Breathing” (Stress/Cracking)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 14

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SLIDE 24

Removing the blinders

Electrolyte oxidation / reduction Lithium Plating (Dendrites) Electrode stress/cracking Internal cell defects Thermal runaway

What we are protecting against What we currently monitor

Temperature Voltage Current

Inside every cell Groups of cells

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 15

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SLIDE 25

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 16

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SLIDE 26

ECC Research Portfolio @ eCAL

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 17

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SLIDE 27

Outline

1

BACKGROUND & PROBLEM STATEMENTS

2

ELECTROCHEMICAL MODEL

3

STATE ESTIMATION

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 18

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SLIDE 28

Electrochemical Model Equations

well, some of them | Open Source 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 19

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SLIDE 29

Electrochemical Model Equations

well, some of them | Open Source 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)

  • (PDE in 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)

  • (PDE in r, 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 19

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SLIDE 30

Electrochemical Model Equations

well, some of them | Open Source 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) (ODE in x)

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) (ODE in x)

Electrolyte ionic current

∂ie± ∂x (x, t) = a±

s Fjn±(x, t) (ODE in x)

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 19

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SLIDE 31

Electrochemical Model Equations

well, some of them | Open Source 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)

(nonlinear AE) 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 19

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SLIDE 32

Electrochemical Model Equations

well, some of them | Open Source 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 (ODE in t)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 19

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SLIDE 33

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 20

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SLIDE 34

Outline

1

BACKGROUND & PROBLEM STATEMENTS

2

ELECTROCHEMICAL MODEL

3

STATE ESTIMATION

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 21

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SLIDE 35

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 22

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SLIDE 36

Survey of SOC/SOH Estimation Literature

What is new? What are the opportunities/challenges? EChem models provide unprecedented detail 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 22

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SLIDE 37

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 23

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SLIDE 38

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 24

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SLIDE 39

SPMe Equations

Subsystem Partial Differential Equation (PDEs) Boundary Conditions Solid phase Li diffusion

∂c±

s

∂t (r, t) =

1 r2 ∂

∂r

  • D±

s (c± s ) · r2 ∂c±

s

∂r (r, t)

  • ∂c±

s

∂r (0, t) = 0, ∂c±

s

∂r (R±

s , t) =

±1

D±

s Fa±L± I(t)

Electrolyte Li diffusion

∂ce ∂t (x, t) = ∂ ∂x

  • Deff

e (ce) ∂ce

∂x (x, t)

  • ∓

1−t0

c

ε±

e FL± I(t)

∂c−

e

∂x (0−, t) = ∂c+

e

∂x (0+, t) = 0

Output Equation: V(t)

=

RT

αF sinh−1

  • −I(t)

2a+L+¯ i+

0 (t)

  • − RT

αF sinh−1

  • I(t)

2a−L−¯ i−

0 (t)

  • +U+(c+

s (R+ s , t)) − U−(c− s (R− s , t)) −

  • R+

f

a+L+ + R−

f

a−L−

  • I(t)

+L+ + 2Lsep + L−

2κ I(t) + kconc(t)

  • ln ce(0+, t) − ln ce(0−, t)
  • Scott Moura | UC Berkeley

Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 25

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SLIDE 40

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 26

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SLIDE 41

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 27

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SLIDE 42

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 27

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SLIDE 43

SPMe Conservation Properties

Conservation of Solid Lithium

Moles of solid phase Li are 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 28

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SLIDE 44

SPMe Conservation Properties

Conservation of Solid Lithium

Moles of solid phase Li are 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

Conservation of Electrolyte Lithium

Moles of electrolyte phase Li are conserved. Mathematically,

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

nLi,e(t) =

  • j∈{−,sep,+}

εj

e

Lj

0j cj e(x, 0)dx

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 28

slide-45
SLIDE 45

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 29

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SLIDE 46

Stability Analysis

Theorem 1 - Solid Phase

Assume nLi,s is known. Then 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

Assume nLi,e is known. Then electrolyte Li concentration estimates converge asymptotically to the true values. ˆ ce(x, t) → ce(x, t), as t → ∞.

Theorem 3 - Output Inversion

Assume −∞ < ∂V/∂c+

ss < 0. Then the “processed” cathode surface concentration converges

exponentially to its true value: ˇ c+

ss(t) → c+ ss(t), as t → ∞.

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 30

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SLIDE 47

Test with Experimental Data

Experimental voltage & current data obtained from our battery-in-the-loop facility Data used to fit full-order EChem model parameters offline “Truth data” generated from experimentally validated full-order EChem model 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 31

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SLIDE 48

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 32

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SLIDE 49

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

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 32

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SLIDE 50

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)

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

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 33

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SLIDE 51

Interval PDE Observer under Parametric Uncertainty

Problem Statement: Map parameter uncertainty θ ∈

  • θ, θ
  • to interval state estimates

ˆ

c(r, t) ∈

  • ˆ

c(r, t), ˆ c(r, t)

  • where c(r, t) is governed by PDE.

Diffusion PDE Diffusion PDE Copy + Output Inj. Sensitivity PDEs Interval Estimator

  • H. Perez, SJM, “Sensitivity-Based Interval PDE Observer for Battery SOC

Estimation,” 2015 American Control Conference, Chicago, IL, 2015. O. Hugo Schuck Best Paper & ACC Best Student Paper Awards

10 20 30 40 50 −4 −2 2 4 6 Current [C−rate] 10 20 30 40 50 1 2 x 10

4

Sensitivity 10 20 30 40 50 0.2 0.4 0.6 0.8 1 Bulk SOC 10 20 30 40 50 3.2 3.3 3.4 Time [min] Voltage S1(1, t) S2(1, t) S3(1, t) S4(1, t) SOC(t) ˆ SOC(t) ˆ SOC(t) ˆ SOC(t) V (t) ˆ V (t) ˆ V (t) ˆ V (t) 3.7 3.8 3.9 3.23 3.24 3.25 3.26 3.27 V (t) ˆ V (t) ˆ V (t) ˆ V (t) 3.5 4 4.5 0.45 0.5 0.55 0.6 SOC(t) ˆ SOC(t) ˆ SOC(t) ˆ SOC(t)

(a) (b) (c) (d)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 34

slide-52
SLIDE 52

Outline

1

BACKGROUND & PROBLEM STATEMENTS

2

ELECTROCHEMICAL MODEL

3

STATE ESTIMATION

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 35

slide-53
SLIDE 53

The Battery Safety Problem

Samsung Galaxy Note Boeing 787 Dreamliner

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 36

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SLIDE 54

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 37

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SLIDE 55

Battery Fault Diagnostics Problem

Objectives

Detect fault Estimate fault size Boeing 787 Dreamliner

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 38

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SLIDE 56

Battery Fault Diagnostics Problem

Objectives

Detect fault Estimate fault size

Challenges

Few measurements Uncertainty Boeing 787 Dreamliner

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 38

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SLIDE 57

Battery Fault Diagnostics Problem

Objectives

Detect fault Estimate fault size

Challenges

Few measurements Uncertainty

State-of-Art

Industry: Limit check measurements Published Literature: Sensor faults,

  • ver charge/discharge

Boeing 787 Dreamliner

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 38

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SLIDE 58

Battery Thermal Model

Figure: Radial heat transfer model of cylindrical cell

β ∂T ∂t (r, t) = ∂2T ∂r2 (r, t) +

  • 1

r

∂T ∂r (r, t) + 1

k

˙

Q(t) (1)

∂T ∂r (0, t) =

(2)

∂T ∂r (R, t) =

h k [T∞ − T(R, t)] (3)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 39

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SLIDE 59

Battery Thermal Model

Figure: Radial heat transfer model of cylindrical cell

β ∂T ∂t (r, t) = ∂2T ∂r2 (r, t) +

  • 1

r

∂T ∂r (r, t) + 1

k

˙

Q(t)+∆Q (1)

∂T ∂r (0, t) =

(2)

∂T ∂r (R, t) =

h k [T∞ − T(R, t)] (3)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 39

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SLIDE 60

Diagnostic Scheme

Objective

Detect and estimate thermal fault size Robust Observer: Estimates dis- tributed temperature, under faulty & healthy conditions Diagnostic Observer: Detects and es- timates fault size

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 40

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SLIDE 61

Observer Structure: Copy of the System + Feedback

System Model:

∂T ∂t (x, t) = ∂2T ∂x2 (x, t) + 1

k

˙

Q(t) +

  • i

θi · ψi(x, t)

Thermal Fault

∂T ∂x (0, t) =

0;

∂T ∂x (1, t) = h

k [T∞ − T(1, t)]

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 41

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SLIDE 62

Observer Structure: Copy of the System + Feedback

System Model:

∂T ∂t (x, t) = ∂2T ∂x2 (x, t) + 1

k

˙

Q(t) +

  • i

θi · ψi(x, t)

Thermal Fault

∂T ∂x (0, t) =

0;

∂T ∂x (1, t) = h

k [T∞ − T(1, t)] Robust Observer:

∂ˆ

T1

∂t (x, t) = ∂2ˆ

T1

∂x2 (x, t) + 1

k

˙

Q(t) + p1(x)

  • T(1, t) − ˆ

T1(1, t)

  • ∂ˆ

T1

∂x (0, t) =

0;

∂ˆ

T1

∂x (1, t) = h

k [T∞ − T(1, t)] + p10

  • T(1, t) − ˆ

T1(1, t)

  • Scott Moura | UC Berkeley

Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 41

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SLIDE 63

Observer Structure: Copy of the System + Feedback

System Model:

∂T ∂t (x, t) = ∂2T ∂x2 (x, t) + 1

k

˙

Q(t) +

  • i

θi · ψi(x, t)

Thermal Fault

∂T ∂x (0, t) =

0;

∂T ∂x (1, t) = h

k [T∞ − T(1, t)] Robust Observer:

∂ˆ

T1

∂t (x, t) = ∂2ˆ

T1

∂x2 (x, t) + 1

k

˙

Q(t) + p1(x)

  • T(1, t) − ˆ

T1(1, t)

  • ∂ˆ

T1

∂x (0, t) =

0;

∂ˆ

T1

∂x (1, t) = h

k [T∞ − T(1, t)] + p10

  • T(1, t) − ˆ

T1(1, t)

  • Diagnostic Observer:

∂ˆ

T2

∂t (x, t) = ∂2ˆ

T2

∂x2 (x, t) + 1

k

˙

Q(t) + ˆ

θ(t)Tψ(x, t) + p2 ˆ

T1(x, t) − ˆ T2(x, t)

  • ∂ˆ

T2

∂x (0, t) =

0;

∂ˆ

T2

∂x (1, t) = h

k [T∞ − T(1, t)] d dt

ˆ θi(t) =

1 p3,i

1 ψi(x, t) ˆ

T1(x, t) − ˆ T2(x, t)

  • dx

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 41

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SLIDE 64

Diagnostic Scheme: Design and Theoretical Convergence Analysis

Key Design Steps

1

Backstepping transformation to get target error system

2

Analyze the target error system using Lyapunov stability theory

3

Utilize Lyapunov-based adaptive observer design to estimate θ

Theorem (Convergence Analysis)

Asymptotically, estimation errors T(x, t) − ˆ T1(x, t)H1 → ǫ1,

  • θ − ˆ

θ(t)

  • → ǫ2 as t → ∞

Bounds ǫ1, ǫ2 can be made arbitrarily small by choosing p1(x), p10, p2, p3,i appropriately

  • S. Dey, H. Perez, SJM, “Model-based Battery Thermal Fault Diagnostics: Algorithms, Analysis and Experiments,” IEEE

Transactions on Control Systems Technology. DOI: 10.1109/TCST.2017.2776218

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 42

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SLIDE 65

Experimental Tests

Commercial LiFeO4 battery cell (A123 26650)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 43

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SLIDE 66

Experimental Tests

Robust Observer estimates surface temperature under all conditions [estimation error within 0.2 deg C] Diagnostic Observer detects and estimates the fault [estimation error within 15%] Fault detection time 5 sec

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 44

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SLIDE 67

Outline

1

BACKGROUND & PROBLEM STATEMENTS

2

ELECTROCHEMICAL MODEL

3

STATE ESTIMATION

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 45

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SLIDE 68

Summary

Background & Electrochemistry Fundamentals State-of-Charge Estimation Thermal Fault Diagnostics

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 46

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SLIDE 69

Summary

Background & Electrochemistry Fundamentals State-of-Charge Estimation Thermal Fault Diagnostics Research Topics NOT discussed: Model Reduction Optimal Experiment Design for Parameter Identifiability State-of-Health Estimation Optimal Fast-Safe Charging

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 46

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SLIDE 70

0.5 1

Current [C−rate]

CCCV MRG 3.6 3.8 4 4.2 4.4

Voltage [V]

0.6 0.8 1

SOC

5 10 15 20 25 30 35 40 45 0.1 0.2

Side Rxn Overpotential [V] Time [min]

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 47

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SLIDE 71

0.5 1

Current [C−rate]

CCCV MRG 3.6 3.8 4 4.2 4.4

Voltage [V]

0.6 0.8 1

SOC

5 10 15 20 25 30 35 40 45 0.1 0.2

Side Rxn Overpotential [V] Time [min] Exceed 4.2V “limit”

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 47

slide-72
SLIDE 72

0.5 1

Current [C−rate]

CCCV MRG 3.6 3.8 4 4.2 4.4

Voltage [V]

0.6 0.8 1

SOC

5 10 15 20 25 30 35 40 45 0.1 0.2

Side Rxn Overpotential [V] Time [min] Eliminate conservatism, Operate near limit Exceed 4.2V “limit”

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 47

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SLIDE 73

0.5 1

Current [C−rate]

CCCV MRG 3.6 3.8 4 4.2 4.4

Voltage [V]

0.6 0.8 1

SOC

5 10 15 20 25 30 35 40 45 0.1 0.2

Side Rxn Overpotential [V] Time [min] Eliminate conservatism, Operate near limit Exceed 4.2V “limit” 5% more charge capacity

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 47

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SLIDE 74

0.5 1

Current [C−rate]

CCCV MRG 3.6 3.8 4 4.2 4.4

Voltage [V]

0.6 0.8 1

SOC

5 10 15 20 25 30 35 40 45 0.1 0.2

Side Rxn Overpotential [V] Time [min] Eliminate conservatism, Operate near limit Exceed 4.2V “limit” 5% more charge capacity 20% reduction in 0-95% SOC charge time

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 47

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SLIDE 75

VISIT US!

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

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 48

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SLIDE 76

APPENDIX SLIDES

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 49

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SLIDE 77

Model Reduction

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

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 50

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SLIDE 78

Operate Batteries at their Physical Limits

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 51

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SLIDE 79

Operate Batteries at their Physical Limits

Commercialized Today iPhone 5S 0.64C Macbook Pro 2015 0.8C Tesla Supercharger 2.0C + USB charger + 60W charger + Model S 60 Defn: (C-rate) Capacity normalized current. C-rate = (current) / (charge capacity).

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 51

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SLIDE 80

Battery Charge Protocols: Optimization & Models

Why so hard?

Accurate models @ high C-rate Numerically solving optimal control problem

What we do

Use models with accuracy @ high C-rates Include thermal dynamics Constrain states to limit aging

  • Adv. numerical methods: pseudo-spectral optimal control

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 52

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SLIDE 81

Optimal Control Problem

Formulation

min

I(t),x(t),tf

tf

t0

1 · dt subject to EChem-T 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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 53

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SLIDE 82

Results: Minimum Time Charging | Ride constraints, in some order

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

  • H. Perez, S. Dey, X. Hu, SJM, “Optimal Charging of Li-Ion Batteries via a Single Particle Model with Electrolyte and

Thermal Dynamics,” Journal of the Electrochemical Society. DOI: 10.1149/2.1301707jes

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 54

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SLIDE 83

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 Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 55

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SLIDE 84

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 55

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SLIDE 85

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 55

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SLIDE 86

What about Q?

minimizeη log det

 

L

  • j=0

ηjSjQ−1ST

j

 

−1

Measured voltage for 10 experimental trials

294.5 295 295.5 296

Time

3.63 3.64 3.65 3.66 3.67 3.68 3.69

Voltage

1375 1380 1385 1390

Time

3.803 3.804 3.805 3.806 3.807 3.808

Voltage

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 56

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SLIDE 87

What about Q?

Regression Models for Q

50 100 150 200 250 300 Intensit

y Metric

  • 0.005

0.005 0.01 0.015 0.02 0.025 0.03 Q (sqrt of average variance)

fitting data curve fit drive cycles

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 56

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SLIDE 88

Fit on Testing Data

500 1000 1500 2000

Time [sec]

  • 1.5
  • 1
  • 0.5

Current [C-rates]

500 1000 1500 2000

Time [sec]

3.4 3.6 3.8 4

Voltage [V]

Experiment Simulation (proposal) Simulation (conventional)

200 400 600 800 1000 1200

Time [sec]

  • 5

5

Current [C-rates]

200 400 600 800 1000 1200

Time [sec]

3 3.5 4

Voltage [V]

Experiment Simulation (proposal) Simulation (conventional)

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 57

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SLIDE 89

Q: How to select the threshold?

A: Derive dynamic thresholds based on sensitivity equations.

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 58

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SLIDE 90

Reading Materials

SJM and H. Perez, “Better Batteries through Electrochemistry and Controls,” ASME Dynamic Systems and Control Magazine, July 2014.

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

battery-management systems,” IEEE Control Systems Magazine, 2010.

  • H. E. Perez, N. Shahmohammadhamedani, SJM, “Enhanced Performance of Li-ion Batteries via Modified

Reference Governors & Electrochemical Models,” IEEE/ASME Transactions on Mechatronics, Aug 2015. SJM, 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, Oct 2013.

  • H. Perez, SJM, “Sensitivity-Based Interval PDE Observer for Battery SOC Estimation,” 2015 American

Control Conference, Chicago, IL, 2015. O. Hugo Schuck Best Paper & ACC Best Student Paper. SJM, F . Bribiesca Argomedo, R. Klein, A. Mirtabatabaei, M. Krstic, “Battery State Estimation for a Single Particle Model with Electrolyte Dynamics,” IEEE Transactions on Control Systems Technology, Mar 2017

  • H. Perez, X. Hu, SJM, “Optimal Charging of Li-Ion Batteries via a Single Particle Model with Electrolyte

and Thermal Dynamics,” Journal of the Electrochemical Society. DOI: 10.1149/2.1301707jes

Scott Moura | UC Berkeley Battery ID, Fault Diagnostics, & Control March 28, 2018 | Slide 59