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Battery Capacity Monitoring Accuracy and Implementation ABSTRACT This topic gives a systematic overview of battery-capacity monitoring in portable devices. It gives definitions for battery state-of-charge (SOC) at different rates of discharge and temperature and describes how gas-gauge indication accuracy can be measured. Three common SOC-monitoring methods—voltage correlation, current integration, and Impedance Track™—are discussed along with their common hardware implementations. Implementation of capacity-indication circuits embedded in the battery or in the device is analyzed in relation to these three methods.

Battery state-of-charge (SOC) indication has evolved in recent years from being a simple warning to the user of impending power depletion to providing information to the system for more complex tasks such as soft shutdown to prevent data loss. This is a natural development that accompanies the spread of data-processing devices into the markets for handheld and portable products. Using SOC indication for preventing data loss gives a completely different meaning to “gas-gauge accuracy.” With this type of use, a capacity-estimation error is not only misleading but results in reduced usable runtime available to the end user. Indeed, if devices shut down because of early indication of zero capacity, the leftover energy will never be extracted from the battery. This means that using a capacity indicator with a 10% accuracy error is the same as using a battery with 10% less capacity. Lower-capacity cells cost substantially less, so every percent of accuracy can be related to battery cost. This overview will provide sufficient information for choosing the optimal battery-monitoring method and hardware implementation that will satisfy the accuracy needs of a particular device and work reliably under its usage profile. II. DEFINING SOC AND ITS ACCURACY

vendors of gas-gauge ICs might define SOC differently, so device operation has to be adjusted accordingly, or an IC with a suitable definition needs to be selected. The simplest definition is based on the maximum possible discharge capacity that can be achieved at a low rate of discharge, Qmax. To find Qmax (see Fig. 1), the battery is fully charged, then discharged at a low rate (such as C/20) until the minimum voltage defined by the battery manufacturer (typically 3 V per cell) or the minimum system voltage is reached. To determine remaining battery capacity, SOC monitoring simply measures any discharge, Qpassed, since the last full charge to determine the present capacity. SOC is then defined as SOC (%) =

Q max − Q passed Q max

(1)

•100.

4.5

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I. INTRODUCTION

4.0

Present Point Qpassed

3.5

Termination Voltage or End-of-Discharge Voltage (EDV) 3.0

Using the SOC indication to affect device operation requires a definition of SOC that is most relevant for the device’s purposes. Such a definition is not as obvious as it appears. Different

0

1

2

3 Capacity – Ah

4

5

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Fig. 1. SOC definition for low rate of discharge.

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SOC (%) =

Q use − Q passed Q use

The simplest and most adequate error measurement is to find the difference between the SOC reported by the gas gauge and the true SOC. True SOC is defined as SOC true (%) =

FCC true − Q true •100. FCC true

(3)

Here Qtrue is the integrated charge found by using a calibrated reference device, and FCCtrue is the integrated charge consumed at the moment when the termination voltage is reached at a given rate. Because FCCtrue becomes available only at the end of discharge, the error analysis can also be done only then, based on the logged data. Voltage versus true and reported SOC can be plotted to indicate the error graphically, like the example in Fig. 3a. The error itself is shown in Fig. 3b.

(2)

•100

13

The same equation needs to be used for the case where temperature changes significantly. At low temperatures R is much higher, so higher IR drop across the battery internal resistance will reduce Quse compared to Qmax. The importance of accuracy has already been mentioned. But what is accuracy and how is it defined? Different accuracy claims can be found in the documentation for different gas-gauging solutions. Each claim has to be considered together with the definition of error measurement. For example, accuracy of current integration itself does not necessarily reflect the error in the SOC, to which other factors such as the charge/ discharge rate and temperature contribute.

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This definition based on “full capacity” is simple, but it is suitable only for very lowdischarge-rate applications where the internal resistance of the battery does not noticeably change the cell voltage. The situation is different for high-discharge-rate applications, illustrated by Fig. 2, in which the IR drop causes the battery voltage to be much lower, so the termination voltage is reached earlier. This means that the capacity available until the termination point is reached will be less than Qmax. This actual application capacity, Quse < Q max, is called “usable capacity.” It also affects SOC estimation because, at the termination-voltage point, the SOC needs to be zero regardless of the rate of discharge. So the SOC definition changes from that in Equation (1) to one that is relative to Quse:

Reported SOC

11

True SOC 10

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a. Discharge voltage versus reported and true SOC values. 3.0

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b. Difference between the true and reported SOC values.

6

Fig. 2. SOC definition for arbitrary rate of discharge.

0

Fig. 3. SOC versus voltage and SOC error.

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It is important to note that accuracy is dependent on parameter updates and the conditions under which they will (or will not) happen in the case of a particular device’s usage pattern. Such relationships will be discussed for each particular gas-gauging method. Most of the older methods depended on parameter updates at the end of discharge (which will not happen at all in many of today’s devices because of hibernation to save data), or close to the end of discharge (which will happen very rarely). Error increase in the absence of updates is an important characteristic that needs to be kept in mind. SOC can also be defined in terms of energy. Indeed, most electronic devices require constant power for their operation; so, as battery voltage decreases during discharge, current will increase, and the same amount of charge will result in less runtime at the end of discharge. Remaining power is therefore a better indication for runtime estimation than remaining charge. SOC can be defined in terms of power with an equation similar to that expressed in terms of charge: SOCp (%) =

E use − E •100, E use

(4)

where Euse is usable energy measured by integrating the voltage and current along the discharge curve at a given discharge power load until the termination voltage is reached, and E is the charge integrated from the beginning of discharge until the present moment. The Smart-Battery Specifications (SBS) for laptop gas-gauges allow both energy and capacity to be reported. However, many gas gauges do not report a truly integrated energy level and instead simply multiply milliampere-hours by an average voltage such as 3.6 V per cell, which does not reflect changes of current with changing cell voltage and changes at different rates of discharge.

III. VOLTAGE-BASED SOC MONITORING Some of the earliest methods for determining the SOC require only measuring the voltage across the battery terminals. These methods are based on the known correlation between battery voltage and remaining capacity. It seems to be straightforward, but the battery voltage correlates in a simple way with capacity only if no load or a very light load is applied during measurement. When a load is applied, as it is in most cases when the user is interested in the capacity, battery voltage is distorted by the voltage drop that is due to internal impedance of the battery. Moreover, even when the load is removed, relaxation processes inside the battery continue to change the voltage for hours. Correction of the voltage drop based on the knowledge of battery impedance is possible using the formula V = OCV + I • R(SOC,T), where OCV is the battery’s open-circuit voltage, but several issues affect accuracy. The main sources of error are as follows: • Relaxation effect—Voltage keeps changing after application/removal of the load. • Cell-to-cell variations—The database is created for the average cell, but tests show that the internal resistance (R) varies by about 15%, even in the same lot. • Internal resistance changes with aging— Even though 1-kHz impedance of batteries is quite stable with aging, the low-frequency resistance that affects IR drop during constant current increases greatly with age, usually from 50 to 70% during each 100 cycles (or an aging time that is equivalent in terms of capacity loss).

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The effect of all contributions to error is summarized in Fig. 4. Note that at different SOCs, the relationship between SOC error and voltage error is not fixed. That is because the flat portions of the battery-voltage curve have a higher SOC error even if the voltage error is the same.

15 Relaxation Error Cell-to-Cell Variation Total Error

13.13 SOC Error – %

11.25

A. Hardware Implementation of Voltage-Based Battery Monitor Simple voltage-correlation methods are often implemented on the host microcontroller of a device that uses an embedded battery. Such implementations use a simple ADC to measure voltage with an error of 20 to 40 mV. For the common LiCoO2-based Li-ion battery, this measurement transforms into an SOC error of 20 to 40% in the flat region of the voltage curve. To increase the accuracy of a voltage-based implementation, external voltage monitors can be used that report accurate voltage measurements to the host via single-wire communication such as SDQ or HDQ. One example of such an implementation is the TI bq2023 voltage monitor. In addition to voltage information, it provides current and temperature information that can be used to implement IR compensation to improve accuracy. The bq2023 allows voltage correlation to be combined with current integration as described later. Fig. 5 shows an example application diagram that includes a battery-monitor IC.

9.38 7.5 5.63 3.75 1.88 0

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a. Contributions of relaxation effect and cell-to-cell variations to SOC error. 100 300 Cycles 200 Cycles 100 Cycles 0 Cycles

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b. Overall SOC error change with aging. Fig. 4. Typical examples of SOC error. J1

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IV. Current-Integration Method The current-integration method of determining the SOC relies on the robust idea that if all battery charge and discharge currents are integrated, the remaining coulomb metric capacity is a known value. Integrating the current works particularly well when the initial battery capacity is known and the coulomb metric efficiency is 100% (i.e., when all the coulombs that go into the battery stay in the battery during charging and all decreases in battery capacity are due to an external discharge current). This seemingly bulletproof approach is modified by predicting self-discharge and batterycharging efficiencies, and is then successfully used in most currently employed battery gas gauges. However, these modifications to the charge-integration method are principally estimates that may produce errors in particular usage patterns such as long periods of inactivity or a highly variable discharge current. If the battery is charged and left unused for several days or is just never fully charged for several charge and discharge cycles, the self-discharge due to internal chemical reactions becomes noticeable. There is no way to measure the self-discharge current, so it has to be corrected with a predefined equation. Because different battery models have different self-discharge rates that depend on the SOC, temperature, and cycling history of the batteries, exact modeling of self-discharge requires timeconsuming effort in data collection and still remains quite imprecise. Although not restricted to coulomb counting, another problem is that the value of total capacity is updated only if a nearly full discharge occurs very soon after a full charge. If full-discharge events are rare or comparatively rare, a considerable decrease of actually available capacity can commence before the gas gauge updates its value. This will result in overestimation of available capacity during these periods. In some applications (such as laptops), the operating system will terminate the discharge at about 3% remaining capacity, so a system learning opportunity for updating the total capacity will never occur. To solve this problem, voltage modeling can be used that allows the system to predict the total capacity at voltage thresholds

higher than minimal voltage. For example, in the TI bq2060 gas gauge, fixed-voltage thresholds that correspond to remaining capacities of 7% and 3% are used, as shown in Fig. 6a. This method works well if discharge is always taking place at the same rate and temperature. The problem with all these changing conditions can be seen in Fig 6b. When the voltage threshold is calculated for current I1, learning correctly occurs at 7% SOC. When the current changes to I2, the same voltage threshold corresponds to about 30% SOC; but the gas gauge will assume the remaining capacity is still 7%, underestimating the SOC by 23%! To solve this problem, newer gas gauges like the bq2060 are using compensated end-of-discharge voltage (EDV) thresholds, or CEDVs. The voltage threshold for 7% SOC is expressed by the internal function V(7%, T, I) = OCV(7%,T) + IR(7%, T). 4.5

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b. With adjustable-rate thresholds. Fig. 6. Capacity learning before termination voltage is reached.

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Parameters of this function are battery-specific and have to be generated by testing each battery at different rates and temperatures. When such data has been collected for several voltage profiles, correction parameters can be calculated with automatic tools that are available. This improves the accuracy under variable-discharge-rate conditions for a new battery. The resistance function R(7%,T) remains static; but actual cell resistance changes with aging, so the CEDV function eventually will be out of date and error will increase. Newer devices such as TI’s bq2084 have a correction factor that can increase resistance R with an increasing number of cycles. This constitutes some improvement, but because battery aging is unpredictable and depends on other factors such as temperature, time, and charging conditions, the number of cycles is not a perfectly accurate way to adjust resistance. A. Hardware Implementation of CurrentIntegration Gas Gauges Current integration is typically done by measuring voltage drop across a sense resistor (R1), as shown in the example implementation in Fig. 7 on the next page. The accuracy of current measurement and integration plays a critical role in the implementation of current-integration gas gauges. Sources of integration error include gain error, granularity error, offset error, clock error, and sampling error. The gain of the integrating ADC is typically calibrated at board level to account for sense-resistor tolerance. To reduce power losses on sense resistors, small values of 5 to 20 mΩ are typically used. With such a small value, the resistance of board traces plays a significant role, so it is important to provide Kelvin (two-wire) connection from both sides of the sense resistor directly to the ADC input. The sense resistor can become hot during active device operation, so it is recommended that only resistors with a low thermal coefficient be used. Due to a very small voltage drop across the sense resistor, noise from other components on the board can contribute significant distortion. Because of that, a filter

circuit (C16, C18, C19, R15, and R16) is recommended. The ADC used for current integration should have sufficient resolution to reduce granularity error (the bq2084 uses a 16-bit ADC). Sampling error can degrade accuracy if the sampling rate of the ADC is not sufficient to capture all load pulses. Oversampling, integrating, sigma-delta converters or voltage-to-frequency converters can provide adequate integration for most applications. While simple current integration requires only a crude voltage measurement to detect end of discharge, the schemes that allow learning without reaching EDV or CEDV require a maximal voltage-error limit of 20 to 40 mV to accurately detect the learning threshold. Adjustable thresholds and other sophisticated logic require the use of a microcontroller as part of the capacity indicator. It is also preferable to have programmable memory onboard so that thresholds calculated specifically for a particular battery model can be programmed during production. Programmable memory also allows increased flexibility for supporting various safety settings, cell-balancing settings, etc. V. COMBINED VOLTAGE CORRELATION AND CURRENT INTEGRATION—IMPEDANCE TRACK™ METHOD To improve the accuracy of remaining capacity predictions, a combination of voltage measurement and current integration can be used. Although the EDV and CEDV methods use this combination near the end of discharge, applying them at all SOCs provides important benefits, especially for those batteries whose capacities vary greatly with discharge rate and temperature. Each battery can be characterized with an OCV-versus-SOC data table. Due to the very precise correlation between the OCV and the SOC, the voltage-measuring method allows for a precise SOC estimation when no load is applied and the battery is in a relaxed state. This provides an opportunity to exploit the periods of inactivity,

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Fig. 7. Example of current-integration gas-gauge implementation (bq2084), including an analog frontend (bq29312A) and protection FETs.

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Q max =

∆Q , SOC1 − SOC2

(5)

Since battery OCV tables are often available from manufacturers for common battery chemistries, the battery-pack designer does not need to perform any testing or data collection. When the chemistry of a particular battery is unknown, a selection table or a simple selection test can be used to identify the correct chemistry. While the SOC has been determined without considering the effect of cell impedance, the latter is still important for determining total capacity for the rate of discharge. The total capacity determined by this method corresponds to no-load conditions—e.g., the maximum possible capacity that can be extracted. Under a nonzero load, capacity will be less due to the IR drop that causes the termination voltage to be reached earlier under load. If the cell-impedance dependencies on SOC and temperature are known, it is possible to employ simple modeling to determine when termination voltage will be reached at the given load and temperature. However, as mentioned

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which are present in most battery-powered devices, to get an exact starting point for the SOC, as shown in Fig. 8. Since the self-discharge contribution is reflected in the OCV, the need for self-discharge estimation for the periods of inactivity is eliminated. In addition, the inaccuracies from measuring very light loads, similar to the inaccuracies presented by the battery-pack electronics and system leakage paths, are eliminated. The process to precisely determine the present SOC is to make periodic voltage measurements while the device is off. When the device is switched on, current integration begins. This method can also reduce the battery pack’s idle current because measurements are made periodically. Can OCV measurement and current integration be used also to update full-charge capacity? Indeed, when we know the SOC before applying a load and we precisely measure the capacity added or removed, we can determine the SOC after the load is removed as shown in Fig 9. This method can be used whenever the initial SOC and the measured capacity added or removed are known to be accurate. The battery chemical capacity, Qmax, is given by

Measurement Points

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before, impedance is cell-dependent and increases rapidly with cell aging and cycling, so it would not be sufficient to just store it in a database. To solve this problem, one approach is realtime impedance measurement, which can keep a database continuously updated. Impedance is determined by comparing OCV for a given SOC from an OCV table with presently measured voltage as shown in Fig. 10a. The resulting dependence of impedance on SOC is shown in Fig. 10b. Such real-time impedance updates eliminate impedance variations that occur between cells and with cell aging. As shown in Fig. 11, real-time cell-impedance updates enable remarkable precision of voltage-profile predictions at given loads compared to measured voltage profiles with typical laptop loads. In most cases a usable-capacity estimation error below 1% can be achieved; and, most importantly, high accuracy is sustained throughout the entire life of the battery pack. 13

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Fig. 11. Voltage profile predicted by gas-gauging algorithm compared to measured voltage. A. Hardware Implementation of Impedance Track Algorithm Hardware implementation of the Impedance Track algorithm is similar to that for coulombcounting gas gauges. Special attention needs to be given to the voltage accuracy of the measurement system, because a worst-case voltage error of 1 mV in the flat portion of the voltage curve translates to a 1% SOC error. Calibration routines are included as part of the device firmware for all Impedance Track devices. Current-integration error is less important because current-measurement errors are compensated by updating resistance tables and Qmax. While absolute measurement of milliamperehours will still be affected by measurement error, relative values such as SOC and remaining runtime will be unaffected. This is especially important for applications that have long periods of inactivity where offset error becomes significant. The charge-integration error accumulated due to the ADC offset is canceled through new SOC estimation from the OCV measurement, which allows hardware requirements to relax and reduces cost. For example, a smaller sense resistor can be used without changing the ADC. In some applications, current-gain calibration can be eliminated completely. The Impedance Track algorithm can run on microcontrollers similar to those used to implement the CEDV gas-gauging algorithms described earlier. Flash memory is required to enable support of different battery chemistries, as

Fig. 10. Real-time impedance measurement. Workbook 2-9

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OCV tables will change if, for example, instead of LiCoO2 a different cathode material is used. Examples of Impedance Track gas gauges are TI’s bq20z80, bq20z90, and bq20z70.

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VI. CHALLENGES OF HOST-SIDE GAUGING Most of the discussion so far has assumed that the battery-capacity monitor can be continuously connected to the battery. While many low-cost applications have simplified battery-pack circuitry to provide basic functions such as short-circuit protection, many applications have a host processor that could provide sufficient processing power to handle capacity monitoring. What issues would arise in using a host processor? One issue is the need for firmware development that includes a capacity-monitoring algorithm. Host-processor development teams may not have any experience with capacity monitoring and battery behavior. The learning curve can often be prohibitive, especially if many different battery models have to be used and data acquisition is required for each model. Another issue is that any accurate measurement has to be interrupt-driven, and adding interrupts to the main firmware can often interfere with the primary host activities. These issues force consolidation of firmware development, which often creates a development nightmare. However, the problems can be easily resolved by using a separate IC for all the interrupt-intensive monitoring work. Measurement accuracy can also be an issue. While it is possible in principle to measure current and voltage with the general-purpose ADCs present on host processors, typical accuracy of such devices allows only about 25% SOC measurement error even without any methodrelated errors. Added errors from battery aging often make such measurement too inaccurate for data-processing applications like PDAs or highend phones where soft shutdown is used to preserve the data. Use of an external monitoring IC, such as the bq2023, that communicates over a single-wire interface with the host and reports accurate measurements can ensure measurement accuracy and provide firmware-development support from the IC developer.

Regardless of host-processor implementation, choosing the capacity-monitoring method is also critical for this application. Current-integration data can be lost if the battery is disconnected from the monitor. This makes a direct currentintegration method possible only if the host itself can initialize capacity data to a reasonable value after disconnect. Overall, voltage-correlation methods (while being inherently less accurate due to IR-drop uncertainty) are more suitable for this application because the SOC can be re-initialized after reconnection of the battery. The Impedance Track algorithm is especially suitable because it combines the high accuracy of current-integration gauges with the ability of voltage-based algorithms to be initialized to the correct SOC after battery reconnection. More complex issues arise if more than one battery has to be used with one device. In this case, even if the SOC is correctly initialized, other battery-specific information such as cell impedance and total capacity will still be uncertain (assuming that only cells with the same chemistry are allowed). SOC can be relearned during normal use, but if battery packs are interchanged on a regular basis, the overall accuracy will be affected. Placing flash memory within battery packs allows storage of all cellspecific information or at least identification information sufficient to determine which of the two existing packs is currently inserted. Even in the absence of such identification, gas gauges can employ some fast measurement techniques that will allow identification. However, the number of battery packs routinely used with one device is limited by the memory dedicated to store all pack information in the host. VII. SUMMARY Current-integration and voltage-correlation methods for monitoring battery capacity have been reviewed. Voltage-correlation methods are simpler to implement and are suitable for hostside implementation, but they have lower accuracy due to various error terms associated

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with cell-impedance compensation. Currentintegration methods are accurate and can be successful in applications that have a full discharge for recalibrating capacity. In the design of such monitoring devices, care has to be taken to provide accurate current-integration data. For devices where a full discharge is not possible or rare, additional voltage-based prelearning methods have to be used to update full capacity without full discharge. These methods do require cell-specific data collection and more sophisticated hardware, including a microcontroller. Methods such as Impedance Track that combine voltage-correlation and current-integration methods provide the benefits of both while eliminating the effect of aging on accuracy. Data collection by the batterypack manufacturer is also eliminated, which shortens design time.

Impedance Track is a trademark of Texas Instruments.

Workbook 2-11

Topic 2

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