Fuel-Gauging: Dynamic Loads and Predicting Time-to-Empty on Lithium and other rechargeable batteries – part 2

In Part 1, I had defined the problem in predicting TTE (time-to-empty) when a fuel gauge sees a dynamic load. In this sequel I will explain how modern fuel gauges that use the lookup-table and coulomb counting method deal with this problem.

Dynamic load

To define the problem, we need to first understand what a dynamic load is. A static load is one wherein the current or power demand is constant. On the other hand, a dynamic load has one or more of the following characteristics.

1.?A time-varying characteristic: The power (or current) drawn from the battery is not constant. It can increase or decrease depending on the system’s needs. Dynamic loads cause the battery to provide varying currents (or voltages) depending on the instantaneous power required. This fluctuation may be fast or slow and can be influenced by factors such as the application’s processing demands, environmental conditions, or user behavior. For example, mobile phones may experience spikes in power demand when performing gaming or video streaming and lower demand during idle times or when talking without using the speakers and the screen off.

2.?Energy Storage and Discharge: If the system where the battery is used has regen capabilities like in hybrid cars or EVs, the load on the battery constantly changes and in certain cases the battery may even be recharged during use.

3.?Impact on Battery Life and Performance: A dynamic load typically causes higher stress on the battery than a steady, static load, especially if the battery needs to supply power quickly or at high rates. Frequent or deep discharge cycles, rapid charging, or transient higher than peak power demand can accelerate battery aging and reduce its overall lifespan. This is particularly seen if the peak demand persists beyond a transient time. At intervals approaching greater than a few seconds, such demand can be considered DC demand that negatively impacts battery terminal voltage and thereby may cause shutdown if not handled adequately.

The facts at hand

To deal with estimating time-to-empty and RSOC we can work with a few known parameters

We know that the method used here to estimate capacity is based on an OCV lookup table. This OCV look up table specifies the battery’s open circuit voltage that is taken at several known points of periodic relaxation as it is discharged from a fully charged state.

If at any point during discharge the battery enters a relaxed state and reaches an OCV that is between VMAX and VMIN, then using that voltage, a direct estimation of the state of charge of the battery can be reached.

Secondly, we also know that we use the method of coulomb counting. In this method we can determine how much charge has been delivered by the battery to the load. If this load rate approaches a nominal no-load value, then the RSOC can be directly estimated as Qmax-Qpass/Qmax % where Qmax is the chemical capacity of the battery and Qpass is the passed charge. Since real life loads are much higher than the nominal no-load rate this equivalence cannot be directly used.

To deal with this problem a few approximations or calculations must be made

1. Load and the loaded/unloaded battery terminal voltage must be modeled

2.?The relationship between the maximum capacity of the battery and temperature must be captured.

3.?The capacity decay due to aging must be captured.

4.?Finally, the peak demand must also be modeled to report remaining usable life.

These relations will be discussed in the third part of the series. For now, assume that these relations have been found. With this if,

Since we have established that we are using coulomb counting

However, we have also established that the load in this case is a varying load. Therefore

where

However, this leaves a further issue, it is possible that the time to empty prediction can change rather quickly as the denominator in the TTE equation changes. This means that the user might see increasing time or rapidly decreasing time to empty values in their application. To suppress these rapid changes, smoothing becomes necessary. This can be done in multiple ways.

For loads with a known skew that doesn’t deviate much from the average, it is possible to model the loaded voltage as the RSOC approaches 0% such that the OCV anchor points are spaced closer. This would mean that under known loads, an interpolated loaded voltage can be determined. With coulomb counting this method can increase the accuracy of the predicted RSOC.

Accuracy can be further increased using an exponential moving average of the load current. If

In many gauges the true values of remaining capacity, full charge capacity, state of charge and time to empty are tracked separately. The values reported to the user are smoothed using methods like those presented above to improve the user experience. However, both smoothed and true values converge when the gauge determines the actual capacity to be zero.

The third part of the series will discuss briefly how load, temperature, aging, and predictive load modeling can be used to better report RSOC and TTE.

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