Dynamic Pricing of Battery. Warranties

San Francisco
New York
Chicago
Houston
Time
Capacity

Factors
Battery capacity decreases over time and the main factor that affects the rate of battery degradation is the ambient temperature. The effect of temperature on degradation has been well studied and modeled as a stress factor that accelerates the ongoing degradation process. Degradation processes are accelerated by Temperature Stress Model "S(T)" and SOC (state of charge) Stress Model S(σ).
We couldn’t find a reliable approach to measure S(σ) stress factor which takes specific gravity as inputs to aid in assessing the state of charge, so we decided to use temperature stress factors.

Temperature Stress factor S(T)
We used a research paper and found that the stress factor for temperature is derived from the Arrhenius equation, which models the temperature dependence of the rate of a chemical reaction:
value of the temperature stress coefficient kT and values of the reference temperature Tref are defined in the research paper.

S(T) modelling
We use the temperature in the city of San Francisco to model temperature stress factor S(T).
In the graph we can observe:
temperature distribution
S(T) distribution
used to simulate factor values
and capacity decline.