Adaptive Online Parameter Identification of Li-Ion Battery Model_PPT

Adaptive Online Parameter Identification of Li-ion Battery Model for Electric Vehicle

機械所系統控制組

R99522843

陳麒文


State of Charge (SOC) Definition

Common Definition:[8]

(1)Coulomb-based state of charge, SOCc

SOC𝑐 t = 𝑄0− 𝐼𝑏(𝜏)𝑑𝜏

𝑡𝑡0

𝑄0 × 100

(2) Voltage-based state of charge, SOCv

SOC𝑣 t =𝑉𝑜𝑐 𝑡 −𝑉𝑏𝑠0

𝑉𝑏𝑠100× 100

(3) Hybrid State of charge [4]

SOCℎ = 𝑤𝑠𝑜𝑐 𝑆𝑂𝐶𝑐 + (1 − 𝑤𝑠𝑜𝑐)(𝑆𝑂𝐶𝑣)

(4)Coulomb-based state of charge based on SOCℎ [3]

SOC𝑐 𝑡 = 𝑆𝑂𝐶ℎ 𝑡 − ∆𝑡 +𝐼𝑡+𝐼𝑡−∆𝑡

𝑞𝑚𝑎𝑥− 𝑞𝑚𝑖𝑛

∆𝑡

2

= 𝑆𝑂𝐶ℎ 𝑡 − ∆𝑡 + 1

𝐶(

𝐼𝑡+𝐼𝑡−∆𝑡

𝑉𝑜𝑐𝑚𝑎𝑥− 𝑉𝑜𝑐𝑚𝑎𝑥 )

State of Health (SOH) Definition [3]

SOH =R𝑛𝑜𝑚𝑖𝑛𝑎𝑙(𝑇, 𝑆𝑂𝐶)

R(𝑇, 𝑆𝑂𝐶)

State of Power (SOP) Definition [3] P𝑚𝑎𝑥 , 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 = 𝐼𝑉 = 𝐼𝑉𝑚𝑖𝑛

P𝑚𝑎𝑥, 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝐼𝑉 = 𝐼𝑉𝑚𝑎𝑥

EQUIVALENT CIRCUIT MODEL OF LI-ION BATTERY General Battery System Model [7][8]

The Rint Model [16]

UL(SOC, SOH, T) = UOC(SOC,SOH,T) - ILRo (4)

The RC Model [2][16]

Fig. 1 General Battery System Model I

𝑉𝑝 = −𝑉𝑝

𝑅𝑑𝐶+

𝑉𝑜𝑐𝑅𝑑𝐶

− 𝐼𝑏𝐶 , 𝑉𝑝 ≤ 𝑉𝑜𝑐 (1)


𝑅𝑐𝐶+

𝑉𝑜𝑐𝑅𝑐𝐶

− 𝐼𝑏𝐶 , 𝑉𝑝 > 𝑉𝑜𝑐 (2)

𝑉𝑏 = 𝑉𝑝 − 𝑅𝑏𝐼𝑏 (3)

Fig. 2 Schematic diagram of the Rint Model

Fig. 3 Schematic diagram of the RC model [2][16]

𝑣𝑏 𝑣𝑐

=

−1

𝐶𝑏(𝑅𝑏 + 𝑅𝑐)

1

𝐶𝑏(𝑅𝑏 + 𝑅𝑐)1

𝐶𝑐(𝑅𝑏 + 𝑅𝑐)

−1

𝐶𝑐(𝑅𝑏 + 𝑅𝑐)

𝑣𝑏𝑣𝑐

+

−𝑅𝑐𝐶𝑏(𝑅𝑏 + 𝑅𝑐)

−𝑅𝑏𝐶𝑐(𝑅𝑏 + 𝑅𝑐)

𝑖

Equation (5)

v = 𝑅𝑐

(𝑅𝑏 + 𝑅𝑐)

𝑅𝑏(𝑅𝑏 + 𝑅𝑐)

𝑣𝑏𝑣𝑐

+ −𝑅 −𝑅𝑏𝑅𝑐

(𝑅𝑏 + 𝑅𝑐)𝑖

Equation (6)

EQUIVALENT CIRCUIT MODEL OF LI-ION BATTERY The Thevenin Model [16]

The PNGV Model [16][17]

The DP(dual polarization) Model [16]

Fig. 4 Schematic diagram for the Thevenin Model

𝑈𝑇ℎ = −

𝑈𝑇ℎ𝑅𝑇ℎ𝐶𝑇ℎ

+ 𝐼𝐿𝐶𝑇ℎ

𝑈𝐿 = 𝑈𝑜𝑐 − 𝑈𝑇ℎ − 𝐼𝐿𝑅𝑜

Equation (7)

𝑈𝑑 = 𝑈𝑜𝑐′ 𝐼𝐿

𝑈𝑃𝑁 = −𝑈𝑃𝑁

𝑅𝑃𝑁𝐶𝑃𝑁+

𝐼𝐿𝐶𝑃𝑁

𝑈𝐿 = 𝑈𝑜𝑐 − 𝑈𝑑 − 𝑈𝑃𝑁 − 𝐼𝐿𝑅𝑜

Equation (8)

Fig. 5 Schematic diagram for the PNGV Model

Fig. 6 Schematic diagram for the DP Model

𝑈𝑝𝑎 = −𝑈𝑝𝑎

𝑅𝑝𝑎𝐶𝑝𝑎+

𝐼𝐿𝐶𝑝𝑎

𝑈𝑝𝑐 = −𝑈𝑝𝑐

𝑅𝑝𝑐𝐶𝑝𝑐+

𝐼𝐿𝐶𝑝𝑐

𝑈𝐿 = 𝑈𝑜𝑐 − 𝑈𝑝𝑎 − 𝑈𝑝𝑐 − 𝐼𝐿𝑅𝑜

Equation (9)

EQUIVALENT CIRCUIT MODEL OF LI-ION BATTERY

The DP(dual polarization) Model [16]

The DP model the composed of three parts:

Open-circuit voltage Uoc

Ro ohmic resistance

Rpa characterizing electrochemical polarization

Rpc characterizing concentration polarization

effective capacitances like Cpa and Cpc

Li-ion Battery System Model [4] V system voltage

VH hysteresis voltage

VOC open-circuit voltage

CD Capatiance

Rct Effective interfacial resistance, ohm

R High frequency resistance, ohm

Fig. 7 Equivalent circuit is used as the model of the battery system


Parametric Model I using General Battery System Model I & System ID

[7]

Assumption 1: The battery voltage 𝑉𝑏 and current 𝐼𝑏 along with their

derivatives 𝑉𝑏 and 𝐼𝑏 are continuous and bounded.

Assumption 2: The open circuit voltage 𝑉𝑜𝑐 is a slowly time varying

signal such that, 𝑉𝑜𝑐 ≈ 0

Assumption 3: 𝑉𝑏 and 𝐼𝑏 are persistently excited s = e + ψ 𝑒 = 𝑉𝑏 − 𝑉𝑟 (24)

R = Rc = Rd


𝑅 𝐶+

𝑉𝑜𝑐

𝑅 𝐶−

𝐼𝑏

𝐶

−𝑅𝐶𝑉𝑏 − 𝑅𝐶𝑅𝑏𝐼𝑏 − 𝑅 + 𝑅𝑏 𝐼𝑏 + 𝑉𝑜𝑐 = 𝑉𝑏

−𝑅𝐶𝑉𝑟 − 𝑅𝐶𝑅𝑏𝐼𝑏 − 𝑅 + 𝑅𝑏 𝐼𝑏 + 𝑉𝑜𝑐

= 𝑉𝑏 + 𝑅𝐶𝜓𝑒 = 𝜃 𝑇𝜙 (26)

𝑉𝑏 = 𝜃𝑇𝜙 − 𝐾𝑑 𝑠 (27)

Choose the following Lyapunov candidate:

V = 1

2*𝑆𝑇𝑅𝐶𝑠 + 𝜙 𝑇Γ−1𝜃 + -> V = 𝑠𝑇𝑌𝑇𝜃 + 𝜃 𝑇Γ−1𝜃 − 𝑠𝑇𝐾𝑑𝑠

𝜃 = −ΓYs leads to V = −𝑠𝑇𝐾𝑑𝑠 ≤ 0


𝑅𝑑𝐶+




𝑅𝑐𝐶+




𝜃1𝜃2𝜃3𝜃4

=

−𝑅𝐶−𝑅𝐶𝑅𝑏

−(𝑅 + 𝑅𝑏)𝑉𝑜𝑐

Parametric Model I using General Battery

System Model I & System ID [7]


Parametric Model II using General Battery System Model I (See

Section II. A.) & System ID [8]

Assumption 3: The values of the terminal, charging, and discharging resistances Rb , Rc , Rd , and C are not known ,

but are assumed to be constant with respect to time.

Consider discharging case

𝑉𝑝 = −𝑉𝑝𝜃2 + 𝜃3 − 𝐼𝑏𝜃4 (32)

𝑉𝑏 = 𝑉𝑝 − 𝐼𝑏𝜃5 (37)

𝑉𝑓 ≜ −𝑏𝑉𝑓 + 𝑏𝑉𝑏 (34)

𝑉𝑏 is unmeasurable

redefine an implementable form of the filter

𝑉𝑓 ≜ 𝑃1 + 𝑏𝑉𝑏 (35) 𝑃1 ≜ −𝑏(𝑃1 + 𝑏𝑉𝑏) (36)

Substituting the time derivative of (37) into (34) yields

𝑉𝑓 ≜ −𝑏𝑉𝑓 + 𝑏,𝑉𝑝 − 𝐼𝑝𝜃5 - (39)

𝑉𝑓 + 𝑏𝑉𝑓 = −b𝑉𝑏𝜃2 + 𝑏𝜃3 − 𝑏𝐼𝑏𝜃4 − 𝑏𝐼𝑏 𝜃5 (40)

𝑉𝑓 ≜ 𝑊(𝐼𝑏 , 𝑉𝑏)𝜃 (41) W = [W1W2 W3 W4]

𝑊1 ≜ −𝑏𝑊1 − 𝑏𝑉𝑏

𝑊2 ≜ −𝑏𝑊2 + 𝑏

𝑊3 ≜ −𝑏𝑊3 − 𝑏𝐼𝑏

𝑊4 ≜ 𝑃2 − 𝑏𝐼𝑏

𝑃2 ≜ −𝑏(𝑃2 − 𝑏𝐼𝑏) (43)


𝑅𝑑𝐶+




𝑅𝑐𝐶+




𝜃2

= 1

𝑅𝑑𝐶

𝜃3 = 𝑉𝑜𝑐𝑅𝑑𝐶

𝜃4 = 1

𝐶

𝜃5 = 𝑅𝑏

𝜃 = −𝑘𝑃𝑙𝑠𝑊

𝑇𝑉𝑓

1 + 𝛾𝑊𝑃𝑙𝑠𝑊𝑇 (47) 𝑃𝑙𝑠 ≜ −𝑘

𝑃𝑙𝑠𝑊𝑇𝑊𝑃𝑙𝑠

1 + 𝛾𝑊𝑇𝑊

Adaptive Online Parameter Identification of Li-ion Battery Model for Electric Vehicle We choose b = 0.2, k = 0.98, k0 = 1000

𝑉𝑜𝑐 𝑉𝑓

𝜃5 𝜃4

𝜃3 𝜃2

ANN Based Model

ANN Based Model

Find Initial Value

ANN Based Model

Parametric Model III using Li-ion Battery System

Model (See Section II. G.) & System ID [4]

determine 𝜕𝜀

𝜕𝑚𝑙 = 0



unweighted total error

Newton’s method was employed to

optimize the forgetting factors:

Where ε′𝑜𝑝𝑡(𝜆) is the Jacobian matrix



ADVANCED MODEL OF LI-ION BATTERY

Battery Pack Modeling (distribution system)

Screening process

accurate selection of cells that have similar electrochemical

characteristics within a group before configuring the battery pack

Electrochemical-Based Battery Model

Fig. 8 Series-parallel connection of unit cells (mSnP)

ADVANCED MODEL OF LI-ION BATTERY

Thanks for Your Attention!

Questions & Answers

ADVANCED MODEL OF LI-ION BATTERY (EXTRA PAGE)

Negative Electrode Reaction Li𝑥𝐶6 ↔ 𝐶6 + 𝑥 Li+ + 𝑥 𝑒−

Positive Electrode Reaction Li𝑦−𝑥𝑀𝑛2𝑂4 + 𝑥 Li+ + 𝑥 𝑒− ↔ Li𝑦𝑀𝑛2𝑂4

Net Reaction Li𝑦−𝑥𝑀𝑛2𝑂4 + Li𝑥𝐶6 ↔ Li𝑦𝑀𝑛2𝑂4 + 𝐶6



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Adaptive Online Parameter Identification of Li-Ion Battery Model_PPT