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Modeling, Identification, & Deep Learning of Batteries Scott Moura Assistant Professor | eCAL Director University of California, Berkeley Energy Resources Engineering Seminar Stanford University Download:

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SLIDE 1

Modeling, Identification, & Deep Learning of Batteries

Scott Moura

Assistant Professor | eCAL Director University of California, Berkeley

Energy Resources Engineering Seminar Stanford University

Download: https://ecal.berkeley.edu/pubs/slides/Moura-StanfordERE-Batts-Slides.pdf

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | 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 Dylan KATO

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 2

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SLIDE 3

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 Modeling, ID, Learning September 18, 2017 | Slide 3

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SLIDE 4

The Battery Problem

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

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 4

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SLIDE 5

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 Battery Modeling, ID, Learning September 18, 2017 | Slide 4

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SLIDE 6

The Battery Problem

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

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | 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 Battery Modeling, ID, Learning September 18, 2017 | Slide 4

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SLIDE 8

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 Battery Modeling, ID, Learning September 18, 2017 | Slide 4

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SLIDE 9

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 Modeling, ID, Learning September 18, 2017 | Slide 5

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SLIDE 10

Outline

1

BACKGROUND

2

ELECTROCHEMICAL MODEL

3

MODEL IDENTIFICATION

4

DEEP LEARNING

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 6

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SLIDE 11

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 Modeling, ID, Learning September 18, 2017 | Slide 7

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SLIDE 12

Battery Models

Equivalent Circuit Model

(a) OCV-R

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 8

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SLIDE 13

Battery Models

Equivalent Circuit Model

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

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 8

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SLIDE 14

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 Modeling, ID, Learning September 18, 2017 | Slide 8

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SLIDE 15

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 Modeling, ID, Learning September 18, 2017 | Slide 9

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SLIDE 16

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 Modeling, ID, Learning September 18, 2017 | Slide 10

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SLIDE 17

Outline

1

BACKGROUND

2

ELECTROCHEMICAL MODEL

3

MODEL IDENTIFICATION

4

DEEP LEARNING

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 11

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SLIDE 18

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 Battery Modeling, ID, Learning September 18, 2017 | Slide 12

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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 Modeling, ID, Learning September 18, 2017 | Slide 13

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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 Modeling, ID, Learning September 18, 2017 | Slide 13

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SLIDE 21

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 Modeling, ID, Learning September 18, 2017 | Slide 13

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SLIDE 22

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 Modeling, ID, Learning September 18, 2017 | Slide 13

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SLIDE 23

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 Modeling, ID, Learning September 18, 2017 | Slide 13

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SLIDE 24

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 Modeling, ID, Learning September 18, 2017 | Slide 14

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SLIDE 25

Outline

1

BACKGROUND

2

ELECTROCHEMICAL MODEL

3

MODEL IDENTIFICATION

4

DEEP LEARNING

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 15

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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 Battery Modeling, ID, Learning September 18, 2017 | Slide 16

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Current State-of-Art

Literature Review (Schmidt 2010) Fisher info, param grouping (Forman 2012) Fisher info, genetic algorithm (Marcicki 2013) SPMe, heuristic approach (Arenas 2014) ANOVA confidence intervals (Zhang 2015) Multi-obj GA (voltage & temp) (Alavi 2015) identifiability analysis (Rothenberger 2015) ECM, sinusoidal input (Liu 2016) ECM & SPM, sinusoidal input and more?

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 17

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SLIDE 28

Current State-of-Art

Literature Review (Schmidt 2010) Fisher info, param grouping (Forman 2012) Fisher info, genetic algorithm (Marcicki 2013) SPMe, heuristic approach (Arenas 2014) ANOVA confidence intervals (Zhang 2015) Multi-obj GA (voltage & temp) (Alavi 2015) identifiability analysis (Rothenberger 2015) ECM, sinusoidal input (Liu 2016) ECM & SPM, sinusoidal input and more?

Key Takeaway

Experiments are not optimized for parameter identifiability

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 17

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SLIDE 29

Optimal Control Approach

Canonical Optimal Control Problem (OCP)

minimize

tf

t=t0

L(x, u)dt + Φ(x(tf)) (1) subject to: d dt x(t) = f(x, u); x(t0) = x0 (2) xmin ≤ x(t) ≤ xmax (3) umin ≤ u(t) ≤ umax (4) x(t): state; u(t): controlled input

d dt x(t) = f(x, u);

x(t0) = x0

Numerical Solution Methods

Dynamic programming Quasilinearization Direct shooting Spectral methods Collocation methods many more...

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 18

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SLIDE 30

Optimal Control Problem for Maximizing Parameter Identifiability

minimize

tf

t=t0

det

  • ST

3(t)Q−1S3(t)

  • dt

(5) subject to: d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(6) 0 = g(x, z, u; θ) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(7) y = h(x, z, u; θ) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(8)

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 19

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SLIDE 31

Optimal Control Problem for Maximizing Parameter Identifiability

minimize

tf

t=t0

det

  • ST

3(t)Q−1S3(t)

  • dt

(5) subject to: d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(6) 0 = g(x, z, u; θ) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(7) y = h(x, z, u; θ) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(8) Elegant formulation! However, the OCP proved to be computationally intractable: 2 weeks to generate 100 sec of optimized input signals

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 19

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SLIDE 32

Optimal Control Problem for Maximizing Parameter Identifiability

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 20

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SLIDE 33

Optimal Control Problem for Maximizing Parameter Identifiability

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 20

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SLIDE 34

A different idea!

Figure: Fixed menu of L inputs, index by j

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 21

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SLIDE 35

A different idea!

Figure: Fixed menu of L inputs, index by j

Convex OED

Pre-compute all sensitivities Sj on menu minimizeη log det

 

L

  • j=0

ηjSjQ−1ST

j

 

−1

subject to:

ηj ≥ 0,

L

  • j=0

ηj = 1

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 21

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SLIDE 36

A different idea!

Figure: Fixed menu of L inputs, index by j

Convex OED

Pre-compute all sensitivities Sj on menu minimizeη log det

 

L

  • j=0

ηjSjQ−1ST

j

 

−1

subject to:

ηj ≥ 0,

L

  • j=0

ηj = 1

Convex program → polynomial complexity Optimize 783 input profiles in 20 seconds

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 21

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SLIDE 37

Input Library 783 input profiles

Pulses Sinusoids Dynamic drive cycles

112+ hours of experiments Compute sensitivities via cluster computing Selected 12 for OED Parameters of Interest

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 22

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SLIDE 38

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 23

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SLIDE 39

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 Battery Modeling, ID, Learning September 18, 2017 | Slide 24

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SLIDE 40

Outline

1

BACKGROUND

2

ELECTROCHEMICAL MODEL

3

MODEL IDENTIFICATION

4

DEEP LEARNING

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 25

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SLIDE 41

Should we believe the Newman model?

Micro-scale effects of porous electrodes [Arunachalam, Onori, Battiato] Degradation mechanisms Non-uniformity etc.

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 26

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SLIDE 42

Black Box White Box

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 27

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SLIDE 43

Hybrid Modeling

Model the residual between (data) measurements and (first principle) models via Deep Learning

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 28

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SLIDE 44

Research Objective

Enhance the predictive accuracy of electrochemical models via deep neural nets Battery Cell Anode | Cathode | Output Elman Network w/ Learning

+ _ + +

Electrochemical Model : SPM Deep Neural Network: Recurrent NN Hybrid Model : SPM + RNN

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 29

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SLIDE 45

Deep Neural Networks

Figure adopted from Michael Nielsen

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 30

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SLIDE 46

Feedforward vs Recurrent Neural Networks

Figure adopted from Grigory Sapunov

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 31

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SLIDE 47

Elman Network

x(k) = f(W1 · x(k − 1) + W2 · u(k)) y(k) = g(W3 · x(k)) Jeff Elman (UCSD)

Output Layer Hidden Layer “Context” Layer Input Layer u(k) x(k-1) x(k) y(k) W1 W2 W3

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 32

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SLIDE 48

Single Particle Model (SPM)

Diffusion of Li in solid phase:

∂c−

s

∂t (r, t) = D−

s

r2

∂ ∂r

  • r2 ∂2c−

s

∂r2 (r, t)

  • ∂c+

s

∂t (r, t) = D+

s

r2

∂ ∂r

  • r2 ∂2c+

s

∂r2 (r, t)

  • Boundary conditions:

∂c−

s

∂r (R−

s , t) = −ρ−I(t)

∂c+

s

∂r (R+

s , t) = ρ+I(t)

Voltage Output Function: V(t) = h(c−

ss(t), c+ ss(t), I(t))

V(t) cs

  • (r,t)

r cs

+(r,t)

r Li+ Li+

Anode Separator Cathode Li

+

I(t) I(t) V(t) = h(c -(R -,t), c +(R +,t), I(t)) Rs

  • Rs

+

  • --Single Particle Model---

Solid Electrolyte

Definitions States: lithium concentration c±

s (r, t)

Input: current I(t)

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 33

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SLIDE 49

Learning Algorithm

Recall Elman Network: x(k) = f(W1 · x(k − 1) + W2 · u(k)) y(k) = g(W3 · x(k)) Loss Function: minimize J(k); J(k) = 1 2e(k)2 = 1 2 [yd(k) − y(k)]2 Learning Algorithm:

W1(k + 1) = W1(k) − η(k) · ∂J(k) ∂W1 W2(k + 1) = W2(k) − η(k) · ∂J(k) ∂W2 W3(k + 1) = W3(k) − η(k) · ∂J(k) ∂W3

Assumptions: activation functions: f(z) = tanh(z), g(z) = z Elman1: W3 is a free matrix of parameters Elman2: W3 = W3 is a fixed matrix of parameters

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 34

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SLIDE 50

Stability Analysis

Theorem: Convergent Learning

Consider the Elman Network with Elman2 learning. Then W1 → W⋆

1, W2 → W⋆ 2 as k → ∞ if

learning rate η(k) satisfies 0 ≤ η(k) ≤ 2/

  • αx(k − 1)T + u(k)2W

T 3γ(k)T

Proof Sketch

1

Define weight error ˜

Wi = Wi − W⋆

i , and formulate error dynamics. Hint: Use Mean Value Thm

2

Consider Lyapunov functional: V(k) = ˜

W1(k)2

F + ˜

W22

F

3

Show that ∆V = V(k + 1) − V(k) ≤ 0

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 35

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SLIDE 51

Battery Cell Anode | Cathode | Output Elman Network w/ Learning

+ _ + +

Electrochemical Model : SPM Deep Neural Network: Recurrent NN Hybrid Model : SPM + RNN

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 36

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SLIDE 52

RMS Voltage Error | Training Results

1C discharge 2C discharge 5C discharge Sine wave UDDS 20 40 60 80 100 120

Root Mean Square Voltage Error [mV]

SPM (60) SPMe (90) SPM+Elman1 (64) SPM+Elman2 (64)

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 37

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SLIDE 53

RMS Voltage Error | Test Results, trained on UDDS

1C discharge 2C discharge 5C discharge Sine wave 20 40 60 80 100 120

Root Mean Square Voltage Error [mV]

SPM (60) SPMe (90) SPM+Elman1 (64) SPM+Elman2 (64)

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 38

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SLIDE 54

Cumulative Distribution of Absolute Voltage Error on UDDS

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Absolute voltage error [V]

0.2 0.4 0.6 0.8 1

CDF

SPM SPMe SPM+Elman 1 SPM+Elman 2

19.4 mV 14.0 mV 26.0 mV 36.0 mV

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 39

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SLIDE 55

Outline

1

BACKGROUND

2

ELECTROCHEMICAL MODEL

3

MODEL IDENTIFICATION

4

DEEP LEARNING

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 40

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SLIDE 56

Summary

Background & Electrochemistry Fundamentals Electrochemical-based models can enhance monitoring & performance! Optimal Experiment Design for Parameter Identifiability (Dim Sum) Hybrid Modeling w/ Elman Networks (Deep Neural Nets)

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 41

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SLIDE 57

Summary

Background & Electrochemistry Fundamentals Electrochemical-based models can enhance monitoring & performance! Optimal Experiment Design for Parameter Identifiability (Dim Sum) Hybrid Modeling w/ Elman Networks (Deep Neural Nets) Research Topics NOT discussed: Model Reduction State-of-Charge Estimation State-of-Health Estimation Optimal Fast-Safe Charging Fault Diagnostics

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 41

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SLIDE 58

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

  • S. Park, D. Zhang, SJM, “Hybrid Electrochemical Modeling with Recurrent Neural Networks for Li-ion

Batteries,” 2017 American Control Conference. DOI: 10.23919/ACC.2017.7963533

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 42

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SLIDE 59

VISIT US!

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

Download: https://ecal.berkeley.edu/pubs/slides/Moura-StanfordERE-Batts-Slides.pdf

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 43

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SLIDE 60

APPENDIX SLIDES

Scott Moura | UC Berkeley Battery Modeling, ID, Learning September 18, 2017 | Slide 44

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SLIDE 61

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 Modeling, ID, Learning September 18, 2017 | Slide 45