Determining lithium-metal deposition and related aging in batteries

1 . A device comprising:

a lithium-ion battery; and

a battery-management system configured to:

measure charge states of the lithium-ion battery over a number of charging cycles;

obtain a first expression for lithium-metal-deposition (LMD)-based capacity fade, the first expression based at least on a second expression indicative of total non-LMD-based capacity loss and a third expression indicative of total capacity loss due to LMD; and

determine an LMD state of the lithium-ion battery responsive to a comparison between the measured charge states and the first expression.

2 . The device of claim 1 , wherein the battery-management system is further configured to identify and warn a user of a potentially unsafe condition of the lithium-ion battery responsive to the determined LMD state.

3 . The device of claim 1 , wherein the battery-management system is further configured to estimate a capacity of the lithium-ion battery responsive to LMD state.

4 . The device of claim 1 , wherein the first expression comprises a first sigmoidal rate expression the second expression comprises a second sigmoidal rate expression, and the third expression comprises a third sigmoidal rate expression indicative of total capacity loss due to LMD.

5 . A method of generating an expression for lithium-metal-deposition (LMD)-based capacity fade in a battery, the method comprising:

obtaining a baseline capacity-loss data set for a battery;

responsive to the baseline capacity-loss data set, generating a first expression for baseline capacity loss;

obtaining an LMD-based capacity-loss data set representative of LMD in the battery;

responsive to the LMD-based capacity-loss data set, generating a second expression for LMD-based capacity loss; and

responsive to the first expression and the second expression, generating a third expression indicative of total capacity loss for the battery.

6 . The method of claim 5 , wherein the first expression is a first sigmoidal rate expression, the second expression is a second sigmoidal rate expression, and the third expression is a third sigmoidal rate expression.

7 . The method of claim 6 , wherein:

the first sigmoidal rate expression is indicative of total non-LMD-based capacity loss.

8 . The method of claim 7 , wherein obtaining the second sigmoidal rate expression comprises generating the second sigmoidal rate expression based at least on:

a fourth sigmoidal rate expression indicative of capacity loss due to LMD; and

a fifth sigmoidal rate expression indicative of capacity gain due to LMD reversal.

9 . The method of claim 5 , wherein generating the third expression further comprises generating the third expression further based at least on a model indicative of a fraction of capacity loss attributable to LMD for the battery.

10 . The method of claim 5 , wherein generating the third expression further comprises generating the third expression further based at least on a model indicative of both reversible LMD in the battery and irreversible LMD in the battery.

11 . The method of claim 5 , generating the third expression further comprises generating the third expression further based at least on a model indicative of a surface area of an anode of the battery that is affected by LMD.

12 . The method of claim 11 , wherein the model is further indicative of a depth of the anode affected by LMD.

13 . The method of claim 5 , wherein generating the third expression further comprises generating the third expression further based at least on a model indicative of a surface area of a graphite layer of a lithium-ion battery that is affected by LMD.

14 . The method of claim 13 , wherein the model is further indicative of a depth of the graphite layer affected by LMD.

15 . The method of claim 5 , wherein generating the third expression further comprises generating the third expression further based at least on a lithium-mass-continuity expression.

16 . The method of claim 5 , wherein generating the third expression further comprises generating the third expression further based at least on an analysis of changes that occur in the battery over time as a result of discrete interactions in the battery.

17 . The method of claim 5 , further comprising:

obtaining data samples indicative of capacity of a battery-in-use over a number of complete cycles; and

determining an LMD state of the battery-in-use responsive to a comparison between the data samples and the third expression.

18 . The method of claim 17 , further comprising one or more of:

identifying a potentially unsafe condition of the battery-in-use responsive to the LMD state;

determining a probability of a failure of the battery-in-use responsive to the LMD state;

predicting an end of life of the battery-in-use responsive to the LMD state;

adjusting a charging profile of the battery-in-use responsive to the LMD state;

generating a recommendation indicative of charging instructions for the battery-in-use, the recommendation responsive to the LMD state;

retiring the battery-in-use responsive to the LMD state; or

isolating the battery-in-use responsive to the LMD state.

19 . A method comprising:

obtaining data samples indicative of capacity of a battery over a number of complete cycles;

obtaining charging data indicative of conditions of the number of complete cycles;

obtaining a first expression for lithium-metal-deposition (LMD)-based capacity fade, the first expression based at least on a second expression indicative of total non-LMD-based capacity loss and a third expression indicative of total capacity loss due to LMD; and

determining an LMD state of the battery responsive to a comparison between the data samples, the charging data, and the first expression.

20 . The method of claim 19 , further comprising:

identifying a potentially unsafe condition of lithium dendrite formation on the battery responsive to the LMD state; and

warning a user of the potentially unsafe condition.