Fuel gauge technology predicts run time in multi-cell portable applications

When it comes to predicting remaining system run time, batteries can become an incredibly misunderstood power source. An increasing number of diverse portable applications require more critical operations to fulfill, such as mobile phones used for account management, portable data log devices that have to remain functional for a full workshift, and medical equipment that must continually monitor critical data without losing integrity.

This article discusses why it is important to calculate the most accurate information possible for remaining capacity of a battery. Unfortunately, today's measurement techniques typically look at a few data points or the battery voltage. Many factors like temperature, the rate of discharge, and age of the battery have a significant influence in the state of charge. A new patent-pending technique will enable designers to predict the state of charge and remaining capacity in lithium-ion (Li-ion) cells within one percent accuracy.

Today's battery capacity monitoring methods
Today's electronics use two methods to determine remaining battery capacity. One is based on current integration, and the second technique is based on voltage measurements. The first method relies on integration of all battery charge and discharge currents to determine how much energy is left. Integrating the current works particularly well when the battery is freshly charged, while the battery capacity at full charge is known.

What seems as a "bullet-proof" approach is successfully implemented in most of today's battery gas gauge ICs. However, the technique is not without problems, particularly because every battery ages and varies in its usage pattern, which often has long periods of inactivity. For instance, if a battery pack is charged and left unused for several days, or never fully charges for several charge and discharge cycles, the self-discharge becomes more evident because of internal chemical reactions taking place. There is no way to measure self-discharge, so it has to be corrected using a pre-defined equation. Different battery models have different self-discharge rates that depend on state of charge, temperature and cycling history of batteries. Exact modeling of self-discharge may take significant time to collect appropriate data and still remains quite imprecise.

Another issue with this method is that the value of total capacity is updated only if full discharge happens immediately after full charge. The average user of a portable device does not ever fully discharge his or her battery, so a battery's actual battery capacity may considerably decrease before its actual value will be updated by the gas gauge IC. This results in the IC overestimating and over-compensating available capacity during these periods, sometimes as much as 50 percent. Even if a gas gauge successfully updates battery capacity at a given temperature and discharge rate, the available capacity varies with changes in the discharge rate and temperature.

Voltage-based methods, a second technique used to monitor a battery pack, are some of the earliest known methods and simply calculate voltage levels across battery terminals. This method is based on the known correlation between a battery voltage and remaining capacity. It seems to be straightforward, but the catch is that the battery voltage correlates in a simple way with capacity only if no load is applied during measurement. When load is applied as what typically occurs when a user is interested in remaining capacity, battery voltage is distorted by the voltage drop due to the battery's internal impedance. Moreover, even when load is removed, relaxation processes inside the battery continue to change the voltage for hours. Correction of the voltage drop based on knowledge of battery impedance is problematic for multiple reasons discussed later.

Battery chemistry and voltage response
The complex electrochemistry of batteries is the chief reason for varied transient voltage responses. Figure 1 (a) depicts basic steps of charge transfer from electrode of Li-ion battery (other batteries have similar steps).

Fig 1

Figure 1: Simple steps of Li-ion battery discharge kinetics (a), Impedance spectra of Li-ion battery with designated areas corresponding to each kinetic step (b).

A charge has to travel through electrochemically active material (anode or cathode) as electrons until the surface of the particle is reached, experiences resistance as it intercalates into particles and then diffuses inside the particles in the form of ions. These chemical steps can be associated with time-constants in battery voltage response. This is described in Figure 1 (b) with the impedance spectrum of the battery. The time-constant range of measured data is from milliseconds to hours.

After applying a load, the voltage will gradually decrease with time at a variable rate, and gradually increase after the load is removed. Figure 2 shows such voltage relaxation after applying a load to Li-ion battery at different states of charge.

Fig 2

Figure 2: Voltage drop and relaxation after applying 1/3C rate load to Li-ion battery in (a) fully charged state and (b) discharged state.

Limitations of voltage-based gas gauge techniques
Assuming the gas gauge IC will correct voltage by subtracting the voltage drop calculated as impedance multiplied by resistance (I*R) from measured voltage value, the gauge can use a corrected voltage reading to obtain the current state of charge (SOC). However, a problem with this approach occurs because actual R depends on SOC. If an average value is used in calculations, an error rate of up to 100 percent may occur in SOC when the battery pack reaches a discharged state, because resistance level there is more then 10 times higher than in charged state.

One way to address this issue is to calculate remaining capacity using a multi-dimensional table of voltages listing different loads depending on the SOC. Resistance strongly depends on temperature, increasing about 1.5 times with every 10 8C temperature decrease. The temperature dependence of resistance has to be included in the table, which makes it four-dimensional.

Effective R will depend on time of load application and determine transient behavior of voltage response. However, when the internal impedance is treated like a simple ohmic resistance without considering the amount of time since the last load change, the calculation will lead to significant errors, even if R(SOC) dependence is determined by a table. Because slope of SOC(V) function depends on SOC, transient error will range from 0.5 in discharged to as high as 14 percent in middle-charged state.

A variation between impedance in different cells causes additional complication. Many brands of new Li-ion battery cells are known to have low-frequency direct current impedance variation of +-15 percent. This impedance variation makes a significant difference in voltage correction at high loads. For example, at common half C rate a typical dc impedance of 2-Ah cells at 0.15½ results in as much as 45mV difference between cells. This corresponds to an estimated SOC error of 20 percent.

Finally, the single most significant impedance-related problem occurs when a cell ages. It is known that increasing impedance is much more significant then decreasing cell capacity. A typical Li-ion battery doubles its dc impedance in 70 cycles, while its no-load capacity decreases in the same period by only two to three percent. If this effect is not considered, a voltage-based algorithm which seems to work for a new battery pack will fail miserably (50 percent error) when the pack reaches only 15 percent of its estimated lifespan of 500 cycles.

Taking battery gas gauging to the next level
TI recently developed a technique that will be used in its next-generation gas gauge solutions for multi-cell battery packs. This new algorithm-based technology combines both current- and voltage-based methods, and uses each method as best appropriate. Due to very precise correlation between open circuit voltage and state-of-charge, the technology gives precise state-of-charge estimation when no load is applied and the battery pack is in a relaxed state. This gives an opportunity to exploit the periods of inactivity, which are present in any battery-powered device, to get an exact "starting position" for state of charge.

The need for self-discharge correction for the inactive periods is eliminated, because when a device is switched on, exact SOC is always known. When devices operate in an active state and load is applied to the battery, current integration takes over. No more need for complex and inexact compensation for voltage drop under load, because coulomb-counting keeps track of SOC changes since the start of operation.

The technique also can be used to update full-charge capacity when there is enough information about percentage of SOC before applying load, SOC after applying load (both from voltage measurement in relaxed state) and the amount of charge passed in-between. Total capacity can easily be determined that directly corresponds to the SOC change at the given charge change. This can be done with small amount of capacity passed, and any start condition (no need for full charge), which can eliminate another weakness of current-integration-based algorithmsÑthe need of special conditions for updating capacity.

In addition to solving the question of SOC by avoiding the effect of cell impedance, the current-integration algorithm is still needed for a different purpose. Total capacity calculated by this method corresponds to "no load" conditions, and defines maximal possible capacity can be extracted from battery. Under a non-zero load, actually available capacity will be lower, because the termination voltage will be reached earlier under load due to IR drop in battery voltage. If impedance dependence of SOC and temperature are known, it is possible to employ simple modeling to determine when termination voltage will be reached at the load and temperature currently observed. However, as mentioned before, impedance is cell-dependent and is rapidly increasing with cell aging and cycling, so it would not be useful to store impedance value in a database.

Taking battery gas gauging to the next level, TI's new algorithm, called Impedance Track technology, sits in the gas gauge to enable real-time impedance measurement and keep the database continually updated. The technology eliminates the problem with impedance variations between cells and cell aging. As seen in Figure 3 the impedance data enables remarkable precision of voltage profile prediction at a given load. In most cases error rate in usable capacity as low as below one percent can be achieved; and most importantly, high accuracy is sustained throughout the entire life of battery pack.

Fig 3

Figure 3: Voltage profile predicted by fuel-gauging algorithm on basis of real-time update of cell impedance in comparison with subsequently measured under typical notebook load experimental data.

Self-adapting technology eases design implementation
Implementation of Impedance Track removes the need to incorporate a pre-determined database describing impedance dependence on SOC and temperature, because all necessary data will be obtained by real-time measurements. The database needed to correct for self-discharge is also eliminated. A database is still included to define the correlation between open circuit voltage and SOC (including temperature). However, the character of this correlation is defined by chemical properties of anode/cathode system, and not by particular battery model design specifics such as electrolyte, separator, thickness of active material, additives etc. Because most battery manufacturers use the same chemistry for active materials (LiCoO2 and graphite), their open circuit dependence remains very closed. Tests on various batteries from different manufacturers prove that generic V(SOC,T) dependence can be used for all of them with a high degree of accuracy. Figure 4 compares no-load voltage profiles for cells made by different manufacturers.
Voltage deviation of Impedance Track database is sufficiently low, with the largest amount of deviation occurring at 5mV, which results in a worst-case SOC error rate of only 1.5 percent. In addition, if a new battery chemistry is introduced into the market, only one new modeling database will be needed, as opposed to hundreds of different databases which are currently used for different battery models. To a portable design engineer, this shaves significant time of the development schedule and simplifies the implementation of TI's gas gauge IC solutions to support a variety of end- equipments.

Fig 4

Figure 4: Voltage dependence on DOD (DOD=one SOC) for Li-ion batteries manufactured by four different makers (a) DOD error calculated if averaged database is used (b), and voltage deviation from average (c).

No reprogramming is necessary, even if the designer adds more Li-ion cells or uses different Li-ion batteries from different manufacturers, allowing the designer to plug-and-play the battery gas gauge onto virtually any multi-cell Li-ion battery pack, while drastically improving its precision and reliability.