Measuring stored energy capacity is easy. Doing it accurately is a whole different ballgame.
People often think of a battery as an energy-storage device that’s 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 Furthermore, when the battery is agitated with a charge or discharge, the OCV no longer represents the true SoC reading and the battery requires a few hours of rest to regain equilibrium; battery manufacturers recommend 24 hrs.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.
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.
Manual calibration is possible by running the battery down until “low battery” appears. This can be done in the equipment or with a battery analyzer. A full discharge sets the discharge flag and the subsequent recharge fixes the charge flag. Establishing these two markers allows SoC calculation by tracking the distance between the flags. For best results, calibrate a frequently-used device every three months or after 40 partial cycles. If the device applies a periodic deep discharge on its own accord, no additional calibration is required. Figure 2 shows the full-discharge and full-charge flags.
2. Calibration occurs by applying a full charge, discharge and charge. This can be done in the equipment or with a battery analyzer as part of battery maintenance.
What happens if the battery isn’t calibrated regularly? Can such a battery be used with confidence? Most smart battery chargers obey the dictates of the chemical battery rather than the electronic circuit and there are no safety concerns if a battery is out of calibration. The battery will charge fully and function normally but the digital readout may be inaccurate and become a nuisance.
To overcome the need for calibration, modern fuel gauges “learn” by estimating how much energy the battery was able to deliver on the previous discharge. Learning, or trending, may also include charge times because a faded battery charges quicker than a good one. The Adaptive System on Diffusion (ASOD) developed by Cadex Electronics features a learn function that adjusts to battery aging and achieves a capacity estimation of +/-2% across 1000 battery cycles, the typical life span of a battery. SoC estimation is within +/-5%, independent of age and load current. As long as the replacement battery is of same type, the self-learning matrix will gradually adapt to new batteries.
Another method to measure battery SoC is quantum magnetism, which looks at magnetism rather than voltage or current. The negative plate on a discharging lead acid battery changes from lead to lead sulfate, which has a different magnetic susceptibility than lead. A sensor based on a quantum mechanical process reads the magnetic field through a process called tunneling. Figure 3 compares the magnetic field under different SoC conditions. A battery with low charge has a three-fold increase in magnetic susceptibility compared to a full charge.
3. The permeability of the plates increases by a factor of 3 from full charge to empty. Note that (tunneling magneto resistance (TMR) is also known as magnetic tunneling junction (MTJ).
Knowing the precise SoC enhances battery charging, but more importantly, the technology enables diagnostics that include capacity estimation and end-of-life prediction. However, the immediate benefit gravitates toward a better fuel gauge, and this is of special interest for Li-ion with flat discharge curves.
4. Relative magnetic field units provide accurate state-of-charge of lithium- and lead-based batteries.
Figure 4 demonstrates quantum magnetism by showing a steady drop of the relative magnetic field units on discharge and a raise on charge on lithium iron phosphate. There is no rubber-band effect that is common with the voltage method in which discharge lowers the voltage and charge raises it. Quantum magnetism reads SoC while the battery is charged or discharged. The SoC accuracy with Li-ion is +/-5%, lead acid is +/-7%; calibration occurs by applying a full charge. The excitation current to generate the magnetic field is less than 1 mA, and the system is immune to most interference. Q-Mag works with cells encased in foil, aluminum, or stainless steel, but not ferrous metals.
Isidor Buchmann is the founder and CEO of Cadex Electronics Inc. For three decades, Buchmann has studied the behavior of rechargeable batteries in practical, everyday applications, and has written articles and books, including “Batteries in a Portable World.”. Cadex specializes in the design and manufacturing of battery chargers, analyzers and monitoring devices. For more information on batteries, visit www.batteryuniversity.com; product information is on www.cadex.com.