Battery state of charge estimation based on reduced order electrochemical models
A vehicle may include a battery having positive and negative electrodes. The vehicle may also include a controller programmed to charge and discharge the battery according to a state of charge that is based on an effective surface lithium-ion concentration of one of the electrodes, and an effective surface lithium-ion concentration of the other of the electrodes derived from a center-to-surface lithium-ion concentration profile of the one of the electrodes. The effective surface lithium-ion concentration of the other of the electrodes may be derived via a relationship mapping the center-to-surface lithium-ion concentration profile of the one of the electrodes to the effective surface lithium-ion concentration of the other of the electrodes.
1. A vehicle comprising:
a battery including positive and negative electrodes; and
a controller programmed to charge and discharge the battery according to a state of charge that is based on an effective surface lithium-ion concentration of one of the electrodes, and an effective surface lithium-ion concentration of the other of the electrodes derived from a center-to-surface lithium-ion concentration profile of the one of the electrodes.
2. The vehicle of claim 1 , wherein the effective surface lithium-ion concentration of the other of the electrodes is derived via a relationship mapping the center-to-surface lithium-ion concentration profile of the one of the electrodes to the effective surface lithium-ion concentration of the other of the electrodes.
3. The vehicle of claim 2 , wherein the relationship is non-linear.
4. The vehicle of claim 1 , wherein the effective surface lithium-ion concentration of the one of the electrodes is based on a measured current input and measured voltage output of the battery.
5. A controller comprising:
input channels configured to receive current input and voltage output associated with a battery pack having two electrodes;
output channels configured to provide charge and discharge commands for the battery pack; and
control logic programmed to generate the commands according to a state of charge of the battery pack that is based on an effective surface lithium-ion concentration of one of the electrodes derived from the current input and voltage output, and an effective surface lithium-ion concentration of the other of the electrodes derived from a center-to-surface lithium-ion concentration profile of the one of the electrodes.
6. The controller of claim 5 , wherein the effective surface lithium-ion concentration of the other of the electrodes is derived via a relationship mapping the center-to-surface lithium-ion concentration profile of the one of the electrodes to the effective surface lithium-ion concentration of the other of the electrodes.
7. The controller of claim 6 , wherein the relationship is non-linear.
8. The controller of claim 5 , wherein the effective surface lithium-ion concentration of the one of the electrodes is based on a measured current input and measured voltage output of the battery pack.
9. A vehicle power system comprising:
a controller programmed to charge and discharge a battery according to a state of charge that is based on an effective surface lithium-ion concentration of an electrode of the battery derived from current input and voltage output associated with the battery, and an effective surface lithium-ion concentration of an other of the electrodes of the battery derived from a center-to-surface lithium-ion concentration profile of the electrode.
10. The vehicle power system of claim 9 , wherein the effective surface lithium-ion concentration of the other of the electrodes is derived via a relationship mapping the center-to-surface lithium-ion concentration profile of the electrode to the effective surface lithium-ion concentration of the other of the electrodes.
11. The vehicle power system of claim 10 , wherein the relationship is non-linear.
12. The vehicle power system of claim 9 , wherein the effective surface lithium-ion concentration of the electrode is based on a measured current input and measured voltage output of the battery.