Method and system for step parameter identification based on electrochemical model
The invention discloses a method for step parameter identification based on an electrochemical model, including: identifying a first type of electrochemical parameters through a reduced-order electrochemical model by utilizing different preset charge-discharge rate data; determining a first type of target electrochemical parameters identified by the reduced-order electrochemical model through extrapolation; the first type of target electrochemical parameters including an approximate value of the first type of electrochemical parameters or the first type of electrochemical parameters at a specific rate; identifying the first type of electrochemical parameters, which includes solid-phase lithium concentration and exchange current, through a full-order electrochemical model by taking the first type of target electrochemical parameters as actual values of the first type of electrochemical parameters of the full-order electrochemical model; and identifying a second type of electrochemical parameters, which includes liquid-phase potential and liquid-phase lithium concentration, through the full-order electrochemical model.
1 . A system for step parameter identification based on an electrochemical model, comprising:
a reduced-order module, configured to identify a first type of electrochemical parameters through a reduced-order electrochemical model by utilizing different preset charge-discharge rate data;
an extrapolation module, configured to determine a first type of target electrochemical parameters identified by the reduced-order electrochemical model through extrapolation; the first type of target electrochemical parameters including an approximate value of the first type of electrochemical parameters or the first type of electrochemical parameters at a specific rate; and
a full-order module, configured to identify the first type of electrochemical parameters through a full-order electrochemical model by taking the first type of target electrochemical parameters as actual values of the first type of electrochemical parameters of the full-order electrochemical model; the first type of electrochemical parameters including solid-phase lithium concentration and exchange current;
wherein the full-order module is further configured to identify a second type of electrochemical parameters through the full-order electrochemical model; the second type of electrochemical parameters including liquid-phase potential and liquid-phase lithium concentration.
2 . The system of claim 1 , wherein the extrapolation module is configured to:
compare change trends of the first type of electrochemical parameters for different preset charge-discharge rate data with successively lower addition rates;
based on the change trends of the first type of electrochemical parameters, obtain the approximate value of the first type of electrochemical parameters or derive the first type of electrochemical parameters at the specific rate through extrapolation or interpolation based on the rate and an identification value of the first type of electrochemical parameters; and
take the approximate value of the first type of electrochemical parameters or the first type of electrochemical parameters at the specific rate as the first type of target electrochemical parameters.
3 . The system of claim 2 , wherein the first type of electrochemical parameters comprises a solid-phase potential, the solid-phase lithium concentration, and the exchange current, and the reduced-order module is configured to:
identify the solid-phase potential by a calculation formula of:
φ s =φ s ( C s /C max );
wherein Ø s is the solid-phase potential, C s is the solid-phase lithium concentration, and C max is a maximum lithium ion concentration in solid-phase material;
identify the solid-phase lithium concentration by a calculation formula of:
∂
c
s
±
(
x
,
r
,
t
)
∂
t
=
1
r
2
∂
∂
r
[
D
S
±
r
2
∂
c
s
±
∂
r
(
x
,
r
,
t
)
]
;
wherein
D
s
±
is a solid-phase diffusion coefficient; and
identify the exchange current by a calculation formula of:
J
n
=
I
app
aFL
;
wherein J n is a solid-liquid exchange current density, I app is an external current density, a is a unit volume surface area, F is a Faraday constant, L is a solution domain spatial scale, x is a Cartesian space coordinate, r is a spherical coordinate, and t is a time coordinate.
4 . The system of claim 3 , wherein the full-order module is configured to:
identify the solid-phase potential by a calculation formula of:
∂
∂
x
[
σ
eff
∂
ϕ
s
±
(
x
,
t
)
∂
x
]
-
a
±
F
j
n
±
(
x
,
t
)
=
0
;
identify the solid-phase lithium concentration by a calculation formula of:
∂
c
s
±
(
x
,
r
,
t
)
∂
t
=
1
r
2
∂
∂
r
[
D
S
±
r
2
∂
c
s
±
∂
r
(
x
,
r
,
t
)
]
;
wherein Ø s is the solid-phase potential, C s is the solid-phase lithium concentration, and σ eff is a solid phase conductivity; and
identify the exchange current by a calculation formula of:
j
n
±
(
x
,
t
)
=
i
0
±
(
x
,
t
)
F
[
exp
(
α
+
F
R
T
η
±
(
x
,
t
)
)
-
exp
(
-
α
-
F
R
T
η
±
(
x
,
t
)
)
]
;
wherein
i
0
∓
Is a reference exchange current density, α is an oxidation-reduction reaction parameter, and η is an overpotential.
5 . The system of claim 4 , wherein the second type of electrochemical parameters comprises the liquid-phase potential and the liquid-phase lithium concentration, and the full-order module is configured to:
identify the liquid-phase potential by a calculation formula of:
∂
Φ
e
∂
x
(
x
,
t
)
=
-
i
e
(
x
,
t
)
[
κ
e
eff
(
C
e
(
x
,
t
)
)
]
+
2
R
T
F
(
1
-
t
+
)
×
[
1
+
∂
ln
f
c
/
a
∂
ln
C
e
]
∂
ln
C
e
(
x
,
t
)
∂
x
;
wherein i e is a liquid-phase current density, C e is the liquid-phase lithium concentration,
K
e
eff
is a liquid-phase conductivity, f c/a is an electrolyte activity coefficient, and t is an electromigration coefficient; and
identify the liquid-phase lithium concentration by a calculation formula of:
∂
C
e
(
x
,
t
)
∂
t
=
∂
∂
x
D
e
eff
[
∂
C
e
(
x
,
t
)
∂
x
]
+
∂
∂
x
(
1
-
t
+
)
i
e
(
x
,
t
)
F
ε
e
;
wherein
D
e
eff
is an effective liquid-phase diffusion coefficient, t + is a positive ion transport number, F is the Faraday constant, typically 96485 Cmol −1 , and ε e is a spatial liquid-phase volume fraction.