Real Time Estimation of the State of Health of Dynamic Power Profiles Application to Li-Ion Batteries
Lithium-ion batteries show very good performance regarding their energy density . For this reason, they are considered as a promising technology for electrical energy storage. However, the performance of lithium-ion batteries weakens with time and usage  their available energy decreases. In other words, the batteries become unsuitable for the applications for which they were originally specified.
Two classes of indicators that allow the tracking of battery aging can broadly be distinguished.
1. The first type can readily be embedded in a system in order to analyze the actual power solicitation profile, but indicators of this type mostly focus on the irreversible loss of battery capacity :
SoHc (t=t1)= Capacity t=t1 / Capacity t=0 (1)
In practice, knowledge about capacity aging is insufficient for system management because additional information about the voltage profile is necessary to arrive at the available energy, which is the actually useful information [ 4].
2. Other indicators are mostly diagnostic methods which do not take into account the real time usage profile of the battery. Such diagnostics always present a trade-off between the time and material necessary to perform the test, and its precision, especially for applications with high constraints like electric vehicles. The objective of this work is to develop a tracking algorithm for the development of power and energy performance with the following characteristics:
SoHE (t=t1)= Energy t=t1 / Energy t=0 (2)
- Updated using the actual power solicitation
- Readily embedded in a real time system
- Compatible with a State-of-Energy indicator (SoE)
Several A123System batteries  are cycled under 9 experimental conditions with different ambient temperatures (0°C, 25°C and 45°C) and discharge power (1*Pn,3*Pn and 5*Pn) (cf. Figure 1).
The resulting surfaces of the SoHEhave been traced at the different temperatures as illustrated in Figure 2 for 45°C.
This approach allows predicting the SoHE in real time as a function of the discharge power profile, the cumulated discharged energy and the temperature. The SoHE at the end of an investigation period is estimated from the discharge power, the temperature during the period and the initial SoHE as shown in Figure 3 .
The algorithm consists of three steps :
- Treatment of the power profile
- Consult the SoHE surface
- Estimation of the SoHE at the beginning of the next period
Results and conclusion:
Table 1 lists the deviation of the experimentally measured SoHE from the SoHEestimated using the tracking algorithm after applying multiple cycles of the dynamic power profile show in Figure 4 at a fixed temperature of 45°C.
Extreme temperatures (0 ° C and 45 ° C) and high power ( 5*Pn ) strongly favor the loss of energy performance of batteries, i.e. reduction of the SoHE. Applied to the power profile presented in Figure 4, the difference between the real and the estimated SoHE proves to be less than 1%, which is a satisfactory result. These results can be combined with the method developed in  and used to update the SoE .
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