Method and system for target-based electric field decoupling for electrochemical model
The invention discloses method and system for target-based electric field decoupling for an electrochemical model. The method includes selecting one endpoint of a negative/positive electrode region as a starting point and the other endpoint as an end point; providing a trial solution of solid-phase and liquid-phase potentials of the starting point empirically, obtaining solid-phase/liquid-phase current of the end point according to the trial solution; obtaining a tentative solution that satisfies boundary value conditions by iterative approximation; designating the tentative solution satisfying the boundary value conditions as a deterministic solution of the solid phase potential and the liquid phase potential of the starting point; and obtaining the microscopic physical quantity of any spatial point in the positive electrode region/negative electrode region in the electric field based on the deterministic solution of the solid phase/liquid phase current, the solid phase and liquid phase potentials at the starting point.
1 . A method for target-based electric field decoupling for an electrochemical model of a lithium ion battery, comprising:
selecting a negative electrode region or a positive electrode region of the electrochemical model of the lithium ion battery as a calculation region, and marking one endpoint of the calculation region as a starting point and the other endpoint as an end point;
selecting a solid phase current or a liquid phase current as an observed quantity;
acquiring the observed quantity of the starting point at a present time;
initializing a solid-phase potential and a liquid-phase potential of the starting point at the present time by using a trial solution;
based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time, obtaining the observed quantity of the end point at the present time according to an electrochemical reaction process of the electrochemical model;
determining whether an error between the observed quantity of the end point at the present time and a target value of the end point is within an error range;
when the error is not within the error range, updating the trial solution according to a preset rule, initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time using another trial solution, obtaining the observed quantity of the end point at the present time according to said another trial solution, determining whether the error between the observed quantity of the end point at the present time and the target value of the observed quantity is within the error range, and repeating the process until the error is within the error range;
when the error is within the error range, using the trial solution as a deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time; and
obtaining microscopic physical quantities of each spatial point in the calculation region at the present time according to the observed quantity of the starting point at the present time and the deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time,
wherein said initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using the trial solution comprises:
initializing the solid-phase potential of the starting point at the present time to the deterministic solution of the solid-phase potential of the starting point at a previous time, and initializing the liquid-phase potential of the starting point at the present time to the deterministic solution of the liquid-phase potential of the starting point at the previous time.
2 . The method of claim 1 ,
when the starting point is an endpoint proximal to a current collector, the solid-phase current of the starting point at the present time is equal to an external current at the present time, and the target value of the solid-phase current of the end point at the present time is 0;
when the starting point is an endpoint distal to the current collector, the solid phase current of the starting point at the present time is equal to 0, and the target value of the solid phase current of the end point at the present time is the external current at the present time.
3 . The method of claim 1 , wherein said obtaining the observed quantity of the end point at the present time based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time comprises:
based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time, calculating the observed quantity, the solid-phase potential and the liquid-phase potential of a next spatial point at the present time along the x axis at a preset pace; and
calculating the observed quantity, the solid-phase potential and the liquid-phase potential of another next spatial point at the present time according to the observed quantity, the solid-phase potential and the liquid-phase potential of the next spatial point at the present time, and repeating the processes until the observed quantity, the solid-phase potential and the liquid-phase potential of the end point at the present time are obtained.
4 . The method of claim 3 , wherein said calculating the observed quantity, the solid-phase potential and the liquid-phase potential of the next spatial point at the present time based on the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point comprises:
based on the solid phase potential and the liquid phase potential of the starting point at the present time, obtaining an overpotential of the starting point at the present time by a formula of:
η( x,t )=φ s ( x,t )−φ e ( x,t )−ocv( x,t );
wherein η is the overpotential, φ s is the solid phase potential, φ e is the liquid phase potential, ocv is an electrode steady state open circuit voltage related to a lithium ion concentration on surfaces of solid phase particles;
based on the overpotential of the starting point at the present time, obtaining an exchange current density of the starting point at the present time by a formula of:
j
n
(
x
,
t
)
=
1
F
j
0
(
x
,
t
)
[
exp
(
α
+
F
R
T
η
(
x
,
t
)
)
-
exp
(
-
α
-
F
R
T
η
(
x
,
t
)
)
]
;
wherein α + and α − are transfer coefficients, F is a Faraday constant, R is a molar gas constant, T is an absolute temperature of the battery, and j 0 is the exchanging current density for an electrode reaction in an equilibrium state;
based on the exchange current density of the starting point at the present time, calculating the observed quantity of the next spatial point at the present time by using a difference method or a Runge-Kutta method;
based on the observed quantity of the starting point at the present time, obtaining a partial derivative of the solid-phase potential of the starting point at the present time by a formula of:
∂
ϕ
s
∂
x
(
x
,
t
)
=
-
i
s
(
x
,
t
)
k
wherein i s is the solid phase current, k is a solid phase conductivity;
calculating the solid phase potential of the next spatial point by using the difference method or the Runge-Kutta method based on the partial derivative of the solid phase potential of the starting point at the present time;
obtaining a partial derivative of the liquid phase potential of the starting point at the present time according to a formula of:
∂
ϕ
e
∂
x
(
x
,
t
)
=
-
i
e
(
x
,
t
)
σ
*
ε
b
r
u
g
+
2
R
T
F
(
1
-
t
c
)
∂
ln
c
e
∂
x
(
x
,
t
)
wherein i e is the liquid phase current, t c is the point mobility, c e is a liquid phase lithium ion concentration, σ is a liquid phase conductivity, ε is a liquid phase volume fraction, brug is a porous media coefficient; and
calculating the liquid phase potential of the next spatial point by using the difference method or the Runge-Kutta method based on the partial derivative of the liquid phase potential of the starting point at the present time.
5 . The method of claim 1 , wherein said updating the trial solution according to the preset rule comprises:
x
k
+
1
=
x
k
+
g
-
i
k
i
k
-
i
k
-
1
(
x
k
-
x
k
-
1
)
wherein x k is the kth trial solution, i k is the observed quantity of the end point at the present time obtained by adopting the k-th trial solution, and g is the target value of the observed quantity of the end point at the present time.
6 . The method of claim 1 , wherein after said obtaining microscopic physical quantities of each spatial point in the calculation region at the present time, the method further comprises:
performing an early warning diagnosis on the lithium ion battery according to the microscopic physical quantities.
7 . The method of claim 6 , wherein the microscopic physical quantities include the overpotential; and wherein said performing the early warning diagnosis on the lithium ion battery based on the microscopic physical quantities comprises:
when the overpotential of at least one spatial point is smaller than a first potential threshold value, the lithium ion battery is considered to have SEI film thickening;
when the overpotential of at least one spatial point is smaller than a second potential threshold, the lithium ion battery is considered to have lithium dendrite growth; and
when the overpotential of at least one spatial point is higher than a third potential threshold, the lithium ion battery is considered to have electrolyte decomposition.
8 . The method of claim 6 , wherein the microscopic physical quantities include the liquid phase current; and wherein said performing the early warning diagnosis on the lithium ion battery based on the microscopic physical quantities comprises when the liquid phase current of at least one spatial point is higher than a first current threshold, the lithium ion battery is considered to have an internal short circuit.
9 . A system for target-based electric field decoupling for an electrochemical model of a lithium ion battery, wherein a negative electrode region or a positive electrode region of the electrochemical model of the lithium ion battery is selected as a calculation region, and one endpoint of the calculation region is marked as a starting point and the other endpoint is marked as an end point, and a solid phase current or a liquid phase current is selected as an observed quantity, the system comprising:
an acquisition module, configured to acquire the observed quantity of the starting point at a present time;
a setting module, configured to initialize a solid-phase potential and a liquid-phase potential of the starting point at the present time by using a trial solution, wherein said initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using the trial solution comprises:
initializing the solid-phase potential of the starting point at the present time to the deterministic solution of the solid-phase potential of the starting point at a previous time, and initializing the liquid-phase potential of the starting point at the present time to the deterministic solution of the liquid-phase potential of the starting point at the previous time;
a calculation module configured to
obtain the observed quantity of the end point at the present time according to the observed quantity, the solid-phase potential and the liquid-phase potential of the starting point at the present time and the electrochemical reaction process of the electrochemical model;
determine whether an error between the observed quantity of the end point at the present time and a target value of the end point is within an error range;
when the error is not within the error range, update the trial solution according to a preset rule, initializing the solid-phase potential and the liquid-phase potential of the starting point at the present time by using another trial solution, obtain the observed quantity of the end point at the present time according to said another trial solution, determine whether the error between the observed quantity of the end point at the present time and the target value of the observed quantity is within the error range, and repeat the process until the error is within the error range;
when the error is within the error range, the trial solution is used as a deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time; and
a microscopic quantity updating module, configured to obtain the microscopic physical quantities of each spatial point in the calculation region at the present time according to the observed quantity of the starting point at the present time and the deterministic solution of the solid-phase potential and the liquid-phase potential of the starting point at the present time.