Method of estimating surface ion density
The present teachings are directed toward machine implemented method for estimating the ion density of the surface of either positive or negative electrode of a battery. The machine-implemented method includes dividing each electrode into N layers of active electrode material, determining the ion density variable for each one of the N layers of the active electrode, and determining the ion density of the electrode surface. In the presently disclosed method, the ion density variable of each of the N layers of the active electrode changes as a function of the difference between the respective ion density variables of adjacent N layers, and the ion density of the electrode surface changes as a function of the battery current and the difference between the respective ion density variables of adjacent N layers. The present method is particularly applicable to Li-ion batteries.
1. A machine implemented method for estimating the ion density of the surface of either positive or negative electrode of a battery, the machine-implemented method comprising:
dividing each electrode into N layers of active electrode material;
determining a battery current applied to the electrode of the battery;
determining the ion density variable for each one of the N layers of the active electrode material; and
determining the ion density of the electrode surface, and
wherein the ion density variable of each of the N layers of the active electrode material comprises a function of the difference between the respective ion density variables of adjacent N layers, and
wherein the ion density of the electrode surface comprises a function of the battery current and the difference between the respective ion density variables of adjacent N layers.
2. The machine implemented method according to claim 1 , wherein the ion density of the electrode surface comprises the ion density variable of the 0 th layer of active electrode material.
3. The machine implemented method according to claim 1 , wherein the ion density of the 0 th layer of active electrode material comprises the solution to the following equation:
C
0
j
(
k
+
1
)
=
C
0
j
(
k
)
-
D
diffj
(
C
0
j
(
k
)
-
C
1
j
(
k
)
)
+
NT
c
3600
I
b
(
k
)
.
4. The machine implemented method according to claim 1 , wherein the ion density variable for each of the 1 st through the N−2 th layer of active electrode material comprises the respective solutions to the following equation:
C ij ( k+ 1)= C ij ( k )+ D diff j ( C i−1j ( k )− C 1j ( k ))− D diff j ( C ij ( k )− C i+1j ( k )
for i equal to 1 to N−2.
5. The machine implemented method according to claim 1 , wherein the ion density variable of the N−1 th layer of active electrode material comprises the solution to the following equation:
C N−1j ( k+ 1)= C N−1j ( k )+ D diff j ( C N−2j ( k )− C N−1j ( k )).
6. The machine implemented method according to claim 1 , wherein the battery comprises a lithium ion battery.
7. A battery charging device for a battery comprising:
a battery;
a battery charger for charging the battery; and
a charging control means comprising a machine implemented method for estimating the ion density of the surface of either positive or negative electrode of the battery, the machine-implemented method comprising:
dividing each electrode into N layers of active electrode material;
determining a battery current applied to the electrode of the battery;
determining the ion density variable for each one of the N layers of the active electrode material; and
determining the ion density of the electrode surface, and
wherein the ion density variable of each of the N layers of the active electrode material comprises a function of the difference between the respective ion density variables of adjacent N layers, and
wherein the ion density of the electrode surface comprises a function of the battery current and the difference between the respective ion density variables of adjacent N layers.
8. A battery charging device for a battery according to claim 7 , wherein the battery charger for charging the battery comprises a generator.
9. A battery charging device for a battery according to claim 7 , wherein the battery charger for charging the battery comprises a generator for a hybrid electric vehicle.