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Analysing battery fuel gauges

Posted: 05 Mar 2012     Print Version  Bookmark and Share

Keywords:energy-storage device  open-circuit voltage  battery fuel gauge 

People usually have the idea that a battery is an energy-storage device that is similar to a fuel tank dispensing liquid fuel. For simplicity reasons, this is somewhat accurate. However, measuring stored energy from an electrochemical device is far more complex. The battery fuel gauge is generally poorly understood, particularly in the medical field.

While an ordinary fuel gauge measures liquid flow from a tank of known size, a battery fuel gauge has unconfirmed definitions and only reveals the open-circuit voltage (OCV), a reflection of state-of-charge (SoC). The specified ampere-hour (Ah) rating remains only true for the short time when the battery is new. In essence, a battery is a shrinking vessel that takes on less energy with each charge, and the marked Ah rating is no more than a reference of what the battery should hold. A battery can't guarantee a quantified amount of energy because prevailing conditions restrict delivery. These are mostly unknown to the user and include battery capacity, load currents, and operating temperature. Considering these limitations, one can appreciate why battery fuel gauges can be inaccurate.

The most simplistic method to measure state-of-charge is reading voltage, but this is inaccurate. Batteries within a given chemistry have dissimilar architectures and deliver unique voltage profiles. Temperature also plays a role; heat raises the voltage while a cold ambient lowers it. Furthermore, when the battery is agitated with a charge or discharge, the OCV no longer represents the true SoC reading and the battery requires a few hours of rest to regain equilibrium; battery manufacturers recommend 24 hrs. The largest challenge, however, is the flat discharge voltage curve on nickel- and lithium-based batteries. There is also the load current that pulls the voltage down during discharge.

Advanced fuel gauges measure SoC by coulomb counting, the theory that goes back 250 years when Charles-Augustin de Coulomb first established the "Coulomb Rule." It works on the principle of measuring in and out flowing currents. Figure 1 illustrates the principle graphically.

Figure 1: The stored energy represents state-of-charge; a circuit measures the in-and-out flowing current.

Coulomb counting should be flawless, but it experiences errors as well. For example, if a battery was charged for one hour at 1 A, the same amount of energy should be available on discharge. But this isn't the case. Inefficiencies in charge acceptance, especially towards the end of charge, as well as losses during discharge and storage, reduce the total energy delivered and skew the readings. The available energy is always less than what had been fed into the battery. For example, the energy cycle (charging and then discharging) of the Li-ion batteries in the Tesla Roadster car is about 86% efficient.

A common error in fuel gauge design is assuming that the battery will stay the same. Such an oversight renders the readings inaccurate after about two years. If, for example, the capacity decreases to 50% over time, the fuel gauge will still show 100% SoC on full charge but the run time will be half. For a mobile phone or laptop user, this fuel gauge error may only be a mild inconvenience. However, the problem becomes acute with medical instruments or an electric drive train that depends on precise predictions to reach the destination.

A fuel gauge based on coulomb counting needs periodic calibration, also known as capacity re-learning. Calibration corrects the tracking error that develops between the chemical and digital battery on charge and discharge cycles. The correction could be omitted if the battery received a periodic full discharge at a constant current followed by a full charge. The battery would reset with each full cycle and the tracking error would be kept at less than 1% per cycle. In real life however, a battery may be discharged for a few minutes with a load signature that's difficult to capture, then partially recharged and stored with varying levels of self-discharge depending on temperature and age.

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