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Next-Generation Battery Management Systems Scott Moura Assistant - - PowerPoint PPT Presentation

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Next-Generation Battery Management Systems Scott Moura Assistant Professor | eCAL Director University of California, Berkeley & Tsinghua-Berkeley Shenzhen Institute Presentation to BYD Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018

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SLIDE 1

Next-Generation Battery Management Systems

Scott Moura

Assistant Professor | eCAL Director University of California, Berkeley & Tsinghua-Berkeley Shenzhen Institute

Presentation to BYD

Scott Moura | UC Berkeley Next-Gen BMS July 6, 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

  • Dr. Hongcai

ZHANG Luis CUOTO Ramon CRESPO Mathilde BADOUAL Dylan KATO Emily YOU Teng ZENG

  • Prof. Satadru DEY

Karl WALTER

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 2

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SLIDE 3

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 3

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SLIDE 4

The Battery Problem

CHEAP High Energy & Power Fast Charge Long Lifespan Safe

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 4

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SLIDE 5

The Battery Problem

Samsung Galaxy Note Boeing 787 Dreamliner

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 4

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SLIDE 6

The Battery Problem

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

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 4

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SLIDE 7

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 Next-Gen BMS July 6, 2018 | Slide 4

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SLIDE 8

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 Next-Gen BMS July 6, 2018 | Slide 5

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SLIDE 9

Battery Models

Equivalent Circuit Model

(a) OCV-R

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 6

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SLIDE 10

Battery Models

Equivalent Circuit Model

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

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 6

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SLIDE 11

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 Next-Gen BMS July 6, 2018 | Slide 6

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SLIDE 12

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 Next-Gen BMS July 6, 2018 | Slide 7

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SLIDE 13

Removing the blinders

Image credit: Ilan Gur

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 Next-Gen BMS July 6, 2018 | Slide 8

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SLIDE 14

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 Next-Gen BMS July 6, 2018 | Slide 9

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SLIDE 15

ECC Research Portfolio @ eCAL

Model ID from Experimental Data SOC/SOH Estimator (Gen 1)

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

SOC Estimator (Gen 2a) SOC + Temp Estimator (Gen 2b) SOC + Stress Estimator (Gen 2c) SOC + Multi-Material Estimator (Gen 2d) Reference Governor Fast-Safe Charge

4 6 8 10 12 14 16 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 SOH Decay [%] Charge Time [min] β=1 Time=5.20 min SOH Decay=0.0180% β=0.94 Time=5.23 min SOH Decay=0.0075% β=0.34 Time=5.42 min SOH Decay=0.0045% β=0 Time=15.27 min SOH Decay=0.0027% β=0.04 Time=7.12 min SOH Decay=0.0031%

Fault Diagnostics

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 10

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SLIDE 16

Outline

1

MODEL IDENTIFICATION

2

STATE ESTIMATION

3

OPTIMAL SAFE-FAST CHARGING

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 11

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SLIDE 17

Model Identification from Experiments

Model Identification Problem

Given measurements of current I(t), voltage V(t), and temperature T(t), identify 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 Next-Gen BMS July 6, 2018 | Slide 12

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Current State-of-Art

OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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Current State-of-Art

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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Current State-of-Art

FISHER INFORMATION MATRIX (1) PARAM GROUPING [SCHMIDT 2010] (2) GENETIC ALGORITHM (GA) [FORMAN 2012] MULTI-OBJ. GA [ZHANG 2015] HEURISTIC APPROACH [MARCICKI 2013] ANOVA CONF. INTERVALS [ARENAS 2015]

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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Current State-of-Art

PARAMETER FITTING + INPUT OPTIMIZATION

FISHER INFORMATION MATRIX (1) PARAM GROUPING [SCHMIDT 2010] (2) GENETIC ALGORITHM (GA) [FORMAN 2012] MULTI-OBJ. GA [ZHANG 2015] HEURISTIC APPROACH [MARCICKI 2013] ANOVA CONF. INTERVALS [ARENAS 2015]

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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SLIDE 22

Current State-of-Art

OPTIMIZED SINUSOIDAL INPUT [LIU 2016][ROTHENBERGER 2015]

PARAMETER FITTING + INPUT OPTIMIZATION

FISHER INFORMATION MATRIX (1) PARAM GROUPING [SCHMIDT 2010] (2) GENETIC ALGORITHM (GA) [FORMAN 2012] MULTI-OBJ. GA [ZHANG 2015] HEURISTIC APPROACH [MARCICKI 2013] ANOVA CONF. INTERVALS [ARENAS 2015]

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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SLIDE 23

Current State-of-Art

OPTIMAL EXPERIMENTAL DESIGN (OED) FOR PARAMETERIZATION OPTIMIZED SINUSOIDAL INPUT [LIU 2016][ROTHENBERGER 2015]

PARAMETER FITTING + INPUT OPTIMIZATION

FISHER INFORMATION MATRIX (1) PARAM GROUPING [SCHMIDT 2010] (2) GENETIC ALGORITHM (GA) [FORMAN 2012] MULTI-OBJ. GA [ZHANG 2015] HEURISTIC APPROACH [MARCICKI 2013] ANOVA CONF. INTERVALS [ARENAS 2015]

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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SLIDE 24

Current State-of-Art

OPTIMAL EXPERIMENTAL DESIGN (OED) FOR PARAMETERIZATION OPTIMIZED SINUSOIDAL INPUT [LIU 2016][ROTHENBERGER 2015]

PARAMETER FITTING + INPUT OPTIMIZATION

FISHER INFORMATION MATRIX (1) PARAM GROUPING [SCHMIDT 2010] (2) GENETIC ALGORITHM (GA) [FORMAN 2012] MULTI-OBJ. GA [ZHANG 2015] HEURISTIC APPROACH [MARCICKI 2013] ANOVA CONF. INTERVALS [ARENAS 2015]

PARAMETER FITTING OFFLINE PARAMETER ESTIMATION

Open Research Question

Experiments typically not optimized for parameter identifiability in electrochemical model

  • S. Park, D. Kato, Z. Gima, R. Klein, SJM, “Optimal Input Design for Parameter Identification in an Electrochemical Li-ion

Battery Model,” 2018 American Control Conference, Milwaukee, WI, USA, 2018. ACC Best Student Paper Finalist.

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 13

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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 Next-Gen BMS July 6, 2018 | Slide 14

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SLIDE 26

Understanding Parameter Sensitivity

Anode Particle Radius, R−

s

Anode solid phase conductivity, σ−

200 400 600 800 1000

Time [Sec]

3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9

Voltage [V]

200 400 600 800 1000

Time [Sec]

3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9

Voltage [V]

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 15

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Quantifying Parameter Identifiability

Consider DAE d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) (5) 0 = g(x, z, u; θ) (6) y = h(x, z, u; θ) (7)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 16

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SLIDE 28

Quantifying Parameter Identifiability

Consider DAE d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) (5) 0 = g(x, z, u; θ) (6) y = h(x, z, u; θ) (7) Sensitivity Equations: d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(8) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(9) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(10) where S1 = ∂x

∂θ(θ0), S2 = ∂z ∂θ(θ0), S3 = ∂y ∂θ(θ0)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 16

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Quantifying Parameter Identifiability

Consider DAE d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) (5) 0 = g(x, z, u; θ) (6) y = h(x, z, u; θ) (7) Sensitivity Equations: d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(8) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(9) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(10) where S1 = ∂x

∂θ(θ0), S2 = ∂z ∂θ(θ0), S3 = ∂y ∂θ(θ0)

Define Fisher Information Matrix F ∈ Rnθ×nθ F =

tf

ST

3(t)Q−1S3(t) dt,

(11)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 16

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SLIDE 30

Quantifying Parameter Identifiability

Consider DAE d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) (5) 0 = g(x, z, u; θ) (6) y = h(x, z, u; θ) (7) Sensitivity Equations: d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(8) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(9) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(10) where S1 = ∂x

∂θ(θ0), S2 = ∂z ∂θ(θ0), S3 = ∂y ∂θ(θ0)

Define Fisher Information Matrix F ∈ Rnθ×nθ F =

tf

ST

3(t)Q−1S3(t) dt,

(11) Cramér-Rao Bound characterizes param esti- mation accuracy. α−level confidence ellipsoid:

E =

  • ϑ|(ϑ − ˆ

θ)TF−1(ϑ − ˆ θ) ≤ β

  • (12)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 16

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SLIDE 31

Quantifying Parameter Identifiability

Consider DAE d dt x(t) = f(x, z, u; θ); x(t0) = x0(θ) (5) 0 = g(x, z, u; θ) (6) y = h(x, z, u; θ) (7) Sensitivity Equations: d dt S1(t) = ∂f

∂xS1 + ∂f ∂z S2 + ∂f ∂θ

(8) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(9) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(10) where S1 = ∂x

∂θ(θ0), S2 = ∂z ∂θ(θ0), S3 = ∂y ∂θ(θ0)

Define Fisher Information Matrix F ∈ Rnθ×nθ F =

tf

ST

3(t)Q−1S3(t) dt,

(11) Cramér-Rao Bound characterizes param esti- mation accuracy. α−level confidence ellipsoid:

E =

  • ϑ|(ϑ − ˆ

θ)TF−1(ϑ − ˆ θ) ≤ β

  • (12)

Goal: Minimize (scalarization) of F−1: D-optimality : det(F−1) A-optimality : trace(F−1) E-optimality : λmax(F−1)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 16

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SLIDE 32

Optimal Control Problem for Maximizing Parameter Identifiability

minimize

tf

t=t0

det

  • ST

3(t)Q−1S3(t)

−1

dt (13) 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

(14) 0 = g(x, z, u; θ) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(15) y = h(x, z, u; θ) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(16)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 17

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SLIDE 33

Optimal Control Problem for Maximizing Parameter Identifiability

minimize

tf

t=t0

det

  • ST

3(t)Q−1S3(t)

−1

dt (13) 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

(14) 0 = g(x, z, u; θ) 0 = ∂g

∂x S1 + ∂g ∂z S2 + ∂g ∂θ

(15) y = h(x, z, u; θ) S3(t) = ∂h

∂x S1 + ∂h ∂z S2 + ∂h ∂θ

(16) Elegant formulation! However, computationally intractable: 2 weeks to generate 100 sec of optimized input signals

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 17

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SLIDE 34

Optimal Control Problem for Maximizing Parameter Identifiability

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 18

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SLIDE 35

Optimal Control Problem for Maximizing Parameter Identifiability

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 18

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SLIDE 36

A completely different idea!

Figure: Fixed menu of L inputs, index by j

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 19

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SLIDE 37

A completely 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 Next-Gen BMS July 6, 2018 | Slide 19

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SLIDE 38

A completely 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 750 input profiles in 20 seconds

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 19

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SLIDE 39

Convex OED

Fixed menu of ℓ inputs, indexed by j Execute mj ∈ {0, 1} experiments for input j m1 + m2 + · · · + mℓ = m

✶ ✶

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 20

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SLIDE 40

Convex OED

Fixed menu of ℓ inputs, indexed by j Execute mj ∈ {0, 1} experiments for input j m1 + m2 + · · · + mℓ = m calculate FIM from pre-computed sensitivities ¯ Sj F =

m

  • i=1

SiQ−1

i

ST

i =

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

✶ ✶

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 20

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SLIDE 41

Convex OED

Fixed menu of ℓ inputs, indexed by j Execute mj ∈ {0, 1} experiments for input j m1 + m2 + · · · + mℓ = m calculate FIM from pre-computed sensitivities ¯ Sj F =

m

  • i=1

SiQ−1

i

ST

i =

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

Combinatorial OED minimize F−1 =

 

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

 

−1

subject to mj ≥ 0, m1 + · · · + ml = m mj ∈ {0, 1}

✶ ✶

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 20

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SLIDE 42

Convex OED

Fixed menu of ℓ inputs, indexed by j Execute mj ∈ {0, 1} experiments for input j m1 + m2 + · · · + mℓ = m calculate FIM from pre-computed sensitivities ¯ Sj F =

m

  • i=1

SiQ−1

i

ST

i =

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

Combinatorial OED minimize F−1 =

 

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

 

−1

subject to mj ≥ 0, m1 + · · · + ml = m mj ∈ {0, 1} Let ηj = mj/m be fraction of total experiments to execute of type j. Relax integer constraint F

=

m

ℓ

  • j=1

ηj¯

SjQ−1

j

¯

ST

j

minimize F−1 = 1 m

 

ℓ

  • j=1

ηj¯

SjQ−1

j

¯

ST

j

 

−1

subject to

η 0, ✶Tη = 1 ✶

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 20

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SLIDE 43

Convex OED

Fixed menu of ℓ inputs, indexed by j Execute mj ∈ {0, 1} experiments for input j m1 + m2 + · · · + mℓ = m calculate FIM from pre-computed sensitivities ¯ Sj F =

m

  • i=1

SiQ−1

i

ST

i =

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

Combinatorial OED minimize F−1 =

 

ℓ

  • j=1

mj¯ SjQ−1

j

¯

ST

j

 

−1

subject to mj ≥ 0, m1 + · · · + ml = m mj ∈ {0, 1} Let ηj = mj/m be fraction of total experiments to execute of type j. Relax integer constraint F

=

m

ℓ

  • j=1

ηj¯

SjQ−1

j

¯

ST

j

minimize F−1 = 1 m

 

ℓ

  • j=1

ηj¯

SjQ−1

j

¯

ST

j

 

−1

subject to

η 0, ✶Tη = 1

  • Scalarize. Arrive at convex OED

minimize log det

 

ℓ

  • j=1

ηj¯

SjQ−1

j

¯

ST

j

 

−1

subject to

η 0, ✶Tη = 1

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 20

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SLIDE 44

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 Next-Gen BMS July 6, 2018 | Slide 21

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SLIDE 45

10 20 30 RMSE [mV] DC1 DC2 LA92 SC04 UDDS US06

Nominal Industry OED CVX

  • S. Park, D. Kato, Z. Gima, R. Klein, S. J. Moura, “Optimal Experimental Design for Parameterization of an Electrochemical

Lithium-ion Battery Model,” Journal of the Electrochemical Society, DOI: 10.1149/2.0421807jes

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 22

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SLIDE 46

Objective: J =

tf

  • yexp(t) − ymdl(t; ˆ

θ) 2

dt

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 23

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SLIDE 47

Outline

1

MODEL IDENTIFICATION

2

STATE ESTIMATION

3

OPTIMAL SAFE-FAST CHARGING

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 24

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SLIDE 48

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 Next-Gen BMS July 6, 2018 | Slide 25

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SLIDE 49

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 Next-Gen BMS July 6, 2018 | Slide 25

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SLIDE 50

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 Next-Gen BMS July 6, 2018 | Slide 26

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SLIDE 51

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 Next-Gen BMS July 6, 2018 | Slide 27

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SLIDE 52

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

Next-Gen BMS July 6, 2018 | Slide 28

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SLIDE 53

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 Next-Gen BMS July 6, 2018 | Slide 29

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SLIDE 54

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 Next-Gen BMS July 6, 2018 | Slide 30

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SLIDE 55

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 Next-Gen BMS July 6, 2018 | Slide 30

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SLIDE 56

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 Next-Gen BMS July 6, 2018 | Slide 31

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SLIDE 57

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 Next-Gen BMS July 6, 2018 | Slide 31

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SLIDE 58

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 Next-Gen BMS July 6, 2018 | Slide 32

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SLIDE 59

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 Next-Gen BMS July 6, 2018 | Slide 33

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SLIDE 60

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 Next-Gen BMS July 6, 2018 | Slide 34

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SLIDE 61

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 Next-Gen BMS July 6, 2018 | Slide 35

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SLIDE 62

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 Next-Gen BMS July 6, 2018 | Slide 35

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SLIDE 63

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 Next-Gen BMS July 6, 2018 | Slide 36

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SLIDE 64

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 Next-Gen BMS July 6, 2018 | Slide 37

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SLIDE 65

Outline

1

MODEL IDENTIFICATION

2

STATE ESTIMATION

3

OPTIMAL SAFE-FAST CHARGING

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 38

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SLIDE 66

Operate Batteries at their Physical Limits

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 39

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SLIDE 67

Operate Batteries at their Physical Limits

Commercialized Today iPhone 5S 0.64C Macbook Pro 2015 0.8C Tesla Supercharger 1.4C – 1.8C + USB charger + 60W charger + Model S Defn: (C-rate) Capacity normalized current. C-rate = (current) / (charge capacity).

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 39

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SLIDE 68

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

Problem Statement

Given accurate electrochemical state/parameter estimates (ˆ x, ˆ

θ), govern the input current I(t)

such that the EChem constraints are enforced.

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 39

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SLIDE 69

Operate Batteries at their Physical Limits

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) ^

Problem Statement

Given accurate electrochemical state/parameter estimates (ˆ x, ˆ

θ), govern the input current I(t)

such that the EChem constraints are enforced.

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 39

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SLIDE 70

Constraints

Variable Definition Constraint I(t) Current Power electronics limits c±

s (x, r, t)

Li concentration in solid Saturation/depletion

∂c±

s

∂r (x, r, t)

Li concentration gradient Diffusion-induced stress ce(x, t) Li concentration in electrolyte Saturation/depletion T(t) Temperature High/low temps accel. aging

ηs(x, t)

Side-rxn overpotential Li plating, dendrite formation Each variable, y, must satisfy ymin ≤ y ≤ ymax.

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 40

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SLIDE 71

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 72

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 73

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 74

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 75

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 76

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 77

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 78

Introduction to Reference Governors

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 79

Introduction to Reference Governors

Idea of RG

Given a desired reference rk, generate a modified applied reference vk which guarantees safety, while tracking rk as closely as possible.

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 41

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SLIDE 80

The Algorithm: Modified Reference Governor (MRG)

Battery Cell Ir I V x,z Modified Reference Governor

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 42

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SLIDE 81

The Algorithm: Modified Reference Governor (MRG)

Battery Cell Ir I V x,z Modified Reference Governor

MRG Equations I[k + 1] = β∗[k]Ir[k],

β∗ ∈ [0, 1], β∗[k] = max {β ∈ [0, 1] | (x(t), z(t)) ∈ O}

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 42

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SLIDE 82

The Algorithm: Modified Reference Governor (MRG)

Surface concentration, yj Overpotential, yi y(t) y(t+Ts)

MRG Equations I[k + 1] = β∗[k]Ir[k],

β∗ ∈ [0, 1], β∗[k] = max {β ∈ [0, 1] | (x(t), z(t)) ∈ O}

Admissible Set

O = {(x(t), z(t)) : y(τ) ∈ Y, ∀τ ∈ [t, t + Ts]} ˙

x(t)

=

f(x(t), z(t), βIr)

=

g(x(t), z(t), βIr) y(t)

=

C1x(t) + C2z(t) + D · βIr + E

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 42

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SLIDE 83

Constrained Control of EChem States

1 2 3

Current [C−rate]

I (t) 20 40 60 80 100 120 −0.1 −0.05 0.05 0.1 0.15

Side Rxn Overpotential [V] Time [sec]

ηs(L−, t)

  • H. E. Perez, N. Shahmohammad, S. J. Moura, “Enhanced Performance of Li-ion Batteries via Modified Reference Governors

& Electrochemical Models,” IEEE/ASME Transactions on Mechatronics, Aug 2015. DOI: 10.1109/TMECH.2014.2379695

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 43

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SLIDE 84

Constrained Control of EChem States

1 2 3

Current [C−rate]

I (t) I r(t) 20 40 60 80 100 120 −0.1 −0.05 0.05 0.1 0.15

Side Rxn Overpotential [V] Time [sec]

ηs(L−, t)

  • H. E. Perez, N. Shahmohammad, S. J. Moura, “Enhanced Performance of Li-ion Batteries via Modified Reference Governors

& Electrochemical Models,” IEEE/ASME Transactions on Mechatronics, Aug 2015. DOI: 10.1109/TMECH.2014.2379695

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 43

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SLIDE 85

Application to Charging

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 Next-Gen BMS July 6, 2018 | Slide 44

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SLIDE 86

Application to Charging

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 Next-Gen BMS July 6, 2018 | Slide 44

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SLIDE 87

Application to Charging

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 Next-Gen BMS July 6, 2018 | Slide 44

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SLIDE 88

Application to Charging

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 Next-Gen BMS July 6, 2018 | Slide 44

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SLIDE 89

Application to Charging

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 Next-Gen BMS July 6, 2018 | Slide 44

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SLIDE 90

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 Next-Gen BMS July 6, 2018 | Slide 45

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SLIDE 91

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 45

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SLIDE 92

Battery-in-the-Loop Test Facility

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 45

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SLIDE 93

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 Next-Gen BMS July 6, 2018 | Slide 46

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SLIDE 94

20 40 60 80 100 120 1.8 2 2.2 2.4 2.6 2.8 Capacity [Ah] Half cycle number

Capacity fade

RG vs 1C vs 2C

lChg lDchg RG/1C/2C: l/p/n Cycling ¡/r/o RPT

  • - RG Ref

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 47

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SLIDE 95

20 40 60 80 100 120 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Time [h] Cycle number

RG vs 1C vs 2C

Charge time

lChg RG/1C/2C: l/p/n

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 47

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SLIDE 96

20 40 60 80 100 120 1 1.5 2 2.5 Capacity per charge time [Ah.h-1] Cycle number

RG vs 1C vs 2C

Capacity per charge time

lChg RG/1C/2C: l/p/n

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 47

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SLIDE 97

Outline

1

MODEL IDENTIFICATION

2

STATE ESTIMATION

3

OPTIMAL SAFE-FAST CHARGING

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 48

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SLIDE 98

The Battery Safety Problem

Samsung Galaxy Note Boeing 787 Dreamliner

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 49

slide-99
SLIDE 99

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 50

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SLIDE 100

Battery Fault Diagnostics Problem

Objectives

Detect fault Estimate fault size Boeing 787 Dreamliner

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 51

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SLIDE 101

Battery Fault Diagnostics Problem

Objectives

Detect fault Estimate fault size

Challenges

Few measurements Uncertainty Boeing 787 Dreamliner

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 51

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SLIDE 102

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 Next-Gen BMS July 6, 2018 | Slide 51

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SLIDE 103

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) (17)

∂T ∂r (0, t) =

(18)

∂T ∂r (R, t) =

h k [T∞ − T(R, t)] (19)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 52

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SLIDE 104

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 (17)

∂T ∂r (0, t) =

(18)

∂T ∂r (R, t) =

h k [T∞ − T(R, t)] (19)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 52

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SLIDE 105

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 Next-Gen BMS July 6, 2018 | Slide 53

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SLIDE 106

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 Next-Gen BMS July 6, 2018 | Slide 54

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SLIDE 107

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

Next-Gen BMS July 6, 2018 | Slide 54

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SLIDE 108

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

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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

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Experimental Tests

Commercial LiFeO4 battery cell (A123 26650)

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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

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Outline

1

MODEL IDENTIFICATION

2

STATE ESTIMATION

3

OPTIMAL SAFE-FAST CHARGING

4

FAULT DIAGNOSTICS

5

SUMMARY AND OPPORTUNITIES

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Summary

Model ID from Experimental Data SOC/SOH Estimator (Gen 1)

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

SOC Estimator (Gen 2a) SOC + Temp Estimator (Gen 2b) SOC + Stress Estimator (Gen 2c) SOC + Multi-Material Estimator (Gen 2d) Reference Governor Fast-Safe Charge

4 6 8 10 12 14 16 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 SOH Decay [%] Charge Time [min] β=1 Time=5.20 min SOH Decay=0.0180% β=0.94 Time=5.23 min SOH Decay=0.0075% β=0.34 Time=5.42 min SOH Decay=0.0045% β=0 Time=15.27 min SOH Decay=0.0027% β=0.04 Time=7.12 min SOH Decay=0.0031%

Fault Diagnostics

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VISIT US!

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

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 60

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APPENDIX SLIDES

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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

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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 Bypass optimal control problem by using reference governors

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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] and more... 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]

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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] One step model predictive control formulation [Klein et al., 2010] Piecewise constant time discretization [Methekar et al., 2010] Piecewise constant time discretization w/ Stress [Suthar et al., 2014] Reference governor formulation [Perez et al., 2015] Linear input-output models [Torchio et al., 2015]

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 65

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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 Next-Gen BMS July 6, 2018 | Slide 66

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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 Next-Gen BMS July 6, 2018 | Slide 67

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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 Next-Gen BMS July 6, 2018 | Slide 68

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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

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Parameter Grouping

  • 15
  • 14
  • 13
  • 12
  • 11
  • 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

Sensitivity Magnitude [log scale]

Group 1 Group 2 Group 3 Group 4 R−

s

D−

s

R−

f

σ−

R+

s

D+

s

k−

σ+ ε−

e

ε+

e

εsep

e

κ(·)

ce0 k+ De(·) R+

f

t0

c

d ln fc/a d ln ce (·)

Scott Moura | UC Berkeley Next-Gen BMS July 6, 2018 | Slide 69

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1

Battery model selection

  • Eq. Parameters

Identifiable?

Nominal Parameter Set Battery Parameter ID. Run OCV experiment Non-linear Least-Squares Design Input Library Sensitivity Analysis

No

OED-CVX Programming

Yes

Grouping Parameters Design Optimal Input Experimental Design Parameter Estimation

Is the estimation satisfactory? Parameters Identifiable?

Yes No

Other groups to identify?

Experiment 1 Experiment 2 Experiment n

No Yes Yes

Finalize Parameters

No Parallel approach

Experimental Measurement Error Quantification

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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)

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0 ≤ 𝐷$,&,' ≤ 𝐷̅$ 0 ≤ 𝐷$$,&,' ≤ 𝐷̅$$ η*

$+,&,' = 𝜒* $,&,' − 𝜒/,&,' − 𝑉*$+ > 0

η2

$+,&,' = 𝜒2 $,&,' − 𝜒/,&,' − 𝑉2$+ < 0

ELECTROCHEMICAL MODELING

Current [A/m2] Surface concentration [mol/m3]

Linear constraints: Nonlinear constraints: 13

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  • 1

1 2 C-rate [h-1] 2.5 3 3.5 4 Voltage [V] 11 11.5 12 12.5 13 13.5 14 14.5 25 30 35 Temperature [dC] Time [h]

2C

  • 1

1 2 3 C-rate [h-1] 2.5 3 3.5 4 Voltage [V] 7 7.5 8 8.5 9 9.5 10 25 30 35 Temperature [dC] Time [h]

RG

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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 Next-Gen BMS July 6, 2018 | Slide 74