Instrumentation & Measurement Magazine 25-7 - 17

and a less strict SOH measure is:
SOH 100 min PF, CF
  
(12)
where SOH = 100% implies a brand new battery, and SOH = 0%
implies a completely used up battery.
It must be noted that all SOH values are computed based
on the assumption that initial values, i.e., P(0) and Q(0), are
known. The implication of this assumption is a significant limitation
factor of BFGs, that a BFG can only compute the SOH of
a 'known' battery.
Remarks about Measuring SOH
Remark 1: The Ohmic resistance of a battery increases by several
hundred % at low temperatures. Hence, PF must always
be computed at the same temperature.
Remark 2: The definition of power in (3) tells us that the power
may differ at different SOC values. Hence, it is also important
to compute PF at a certain SOC.
As the battery ages, the amount of lithium ions decreases
due to various chemical reactions within the battery cell. The
likelihood of self-discharge also increases with aging; this reduces
the battery capacity. The CF is formally defined as:
CF




1
Qk
Q 0


100%
(4)
where Q(0) is the initial capacity of the battery, and Q(k) is the
capacity at time k; similar to before, time k could be either cycle
number or a calendar time unit.
Remark 3: Even though battery capacity does not fluctuate as
wide as the Ohmic resistance, capacity does change with temperature
[10]. Hence, CF must always be computed at the same
temperature.
Remaining Useful Life
As the batteries age, they need to be replaced in critical applications.
For example, an EV with an aged battery may not be able
to achieve its target speed on highways (due to PF), and this is
a serious safety issue. Hence, it is important to predict when a
battery-pack will reach a specific SOH threshold so that battery
replacement can be planned ahead of time.
Based on any of the definitions of SOH in (9)-(12), the SOH
of a brand new battery is 100%.
As the battery ages, the SOH reduces and reaches SOH = 0%
when the battery becomes " dead. " The remaining useful life
(RUL) of a battery is defined as the expected time, in terms of
the number of charge-discharge cycle, a battery-pack will take
until it reaches a certain SOH threshold.
Fig. 4 describes the phenomenon of the RUL in terms of
the predicted number of cycles until the SOH drops to a specific
threshold. Similar to the case of PF and CF estimation, one
can expect the uncertainty of the SOH to increase with battery
aging. For example, in the case of CF, the estimated capacity
October 2022
Fig. 4. The remaining useful life (RUL) of a battery can be extended with the
help of a good BFG algorithm.
becomes less reliable due to age related changes in the OCVSOC
curve.
Similarly, PF estimation is met with increasing uncertainty
due to chemical changes within the battery, such as solid electrolyte
interface formation [7].
Fig. 4 shows such prediction uncertainties of two different
BFGs; the uncertainty of one BFG (shown in blue) has a lower
uncertainty compared to the uncertainty of the other BFG
(shown in red). Fig. 4 demonstrates that having a good BFG is
analogous to extending the life of a battery.
RUL is the amount of time, in terms of the number of cycles,
it takes until the SOH of the battery drops to a predetermined
threshold. The uncertainties of two different battery fuel
gauges (BFGs) are compared to demonstrate the importance of
the BFG in extending the usable life of battery.
Research on Battery Aging
Battery aging is one of the limiting factors of wider EV adaptation.
As of now, replacing an EV battery is costly and time
consuming. Therefore, significant research is being done to
determine newer and better methods to increase the RUL of
a battery.
Search for New Battery Chemistries: There is ongoing research
about finding new battery chemistries that can offer desired
qualities in a rechargeable battery: fast charging without the
risk of thermal runaway and reduced SOH. For example, solid
state batteries have been shown to possess such qualities; however,
solid state batteries remain expensive, and more research
and investment is needed before they can be widely adopted.
Optimal Charging Strategies: Fast charging causes battery
health deterioration. Consider an EV battery that has a capacity
of 300 Ah. In order to charge this battery in 15 minutes, the
charging current must be 1200 A. Such high currents, in addition
to causing heat loss, result in fast decline in SOH. It is
believed that better charging strategies can reduce some of the
detrimental effects of fast charging [6], [14]. Pulse charging is
one such strategy studied by researchers for faster charging of
batteries without severely affecting the health of the battery
IEEE Instrumentation & Measurement Magazine
17
Instrumentation & Measurement Magazine 25-7

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