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Lithium-ion cell fuel gauging with Dallas Semiconductor devices

Posted: 10 Apr 2001     Print Version  Bookmark and Share



1 of 9 091200 INTRODUCTION Determining the remaining charge of a Lithium-Ion cell accurately under real world conditions requires much more than just coulomb counting alone. The DS2438's integrated current accumulator (ICA) provides an accurate measurement of cell capacity under known conditions, however in applications where temperature and discharge rates vary and the cell's capacity degrades with aging, the DS2438's ICA needs to be adjusted to achieve the desired accuracy. This document shows how the fuel-gauging concept of the DS2438 can be expanded to insure greater accuracy under extreme operating conditions. This is accomplished by characterizing cell capacity over temperature and rate and controlling the coulomb count in software. This process is not limited to just the DS2438 or a specific type of Lithium- Ion cell. Any Dallas Semiconductor Battery Management device with a coulomb counter, temperature converter and 15 bytes of user EEPROM, such as the DS2760 High Precision Li-Ion Battery Monitor is capable of performing high accuracy fuel gauging on any type of Lithium-Ion cell. LITHIUM-ION CELL BEHAVIOR To understand why coulomb counting alone is not sufficient for high accuracy fuel gauging it is helpful to see how its environment affects a Lithium-Ion cell's charge capacity. The cell in the examples below is a 1200 mAH rated 4/3A cylindrical. It was charged by a two step method, first by a constant 1C rate until the cell voltage reached 4.2 volts, then by a constant voltage until the charge current fell below C/20 or 60 mA. At this point it was considered fully charged. It was discharged either at a high current rate of 1C or a low current rate of 0.2C. The cell was considered to be fully discharged when its voltage fell below 2.5 volts. TEMPERATURE & DISCHARGE RATE The capacity of the Lithium-Ion cell varies greatly depending on the temperature and discharge rate. Figure 2 shows its charge capacity in milliamp-hours as temperature and discharge rate are changed. The "Full" line on the chart is the point at which the cell is considered fully charged by using the above charging method at the corresponding temperature. The "High Current Empty" line is the point at which the cell is considered fully discharged by a 1C rate at each temperature. The "Low Current Empty" line was plotted in the same manner using a discharge rate of 0.2C. Application Note 131 Lithium-Ion Cell Fuel Gauging with Dallas Semiconductor Devices ) 2000 Dallas Semiconductor HOST PROCESSOR DS2438 DS2760 Voltage, Current, and Temperature Measurements. Cell Characterization Data. Accurate Capacity Estimation. Figure 1: System Diagram BATTERY: 59% APPLICATION NOTE 131 2 of 9 The capacity of the cell at a given rate and temperature is the difference from the "Full" line and the corresponding "Empty" line. Because both the empty and full points change over temperature and rate, every point on the chart is relative to every other point. For example, if a cell was fully charged at a temperature of 800C and then fully discharged at the low current rate at -200C, the amount of charge able to be removed would be the difference between the full value at 800C (1340 mAH) and the low current empty value at -200C (250 mAH) or 1090 mAH. If the cell was then fully recharged at -200C, only the difference between the full and empty values at -200C or 860 mAH could be returned to the cell. Only the immediate temperature and rate are needed to determine relative full and empty points. A cell that is discharged partially at temperature 1 and rate 1, then discharged completely at temperature 2 and rate 2 will be considered empty at a point based on temperature 2 and rate 2. Similarly, the cell above could be fully discharged at the high current rate yet is able to be further discharged at the low current rate by the number of milliamp-hours between the two "Empty" points that correspond to the present cell temperature. Because of this, it is only necessary to keep track of the present cell temperature and discharge rate when determining remaining capacity. CELL AGING As a Lithium-Ion cell ages it loses its ability to store charge. Figure 3 shows the effects of repeatedly charging and discharging the cell at room temperature. By maintaining an ongoing coulomb count of the charge on the cell it can be shown that aging affects the "Full" point only. The "Empty" points remain unchanged. To account for this, the formulas for calculating remaining capacity must be capable of dynamically changing over time to remain accurate. OTHER CONDITIONS Most other conditions have little or no effect on charge capacity. Lithium-Ion cells are extremely efficient when charging; very little energy is lost to heat during the cycle unlike other cell chemistries. The self- discharge of a Lithium-Ion cell is extremely low to the point where it is difficult to even measure. Since all these conditions combined affect the coulomb count result less than the accuracy of the measurement device does, they are ignored completely in the fuel gauging equations. Cell Capacity over Temperature (mAH) 0 200 400 600 800 1000 1200 1400 -20 -10 0 10 20 30 40 50 60 70 80 Temperature (0C) Capacity(mAH) Full Line defined as 4.2V High Current Emtpy Line defined as 2.5V Low Current Empty Line defined as 2.5V Figure 2 APPLICATION NOTE 131 3 of 9 CALCULATING REMAINING CAPACITY From the charts above it is easy to see how a coulomb counting only method can become very inaccurate under real world conditions. This section shows how coulomb counting combined with characterization of the expected "Empty" and "Full" points can maintain an accurate estimation of remaining cell capacity. STANDARD ASSUMPTIONS For the algorithms to function accurately while minimizing computational complexity and parametric data storage, certain assumptions are made. First it is assumed that similar charging efficiencies and termination limits are applied universally to the application. It is also assumed in this example that there are a finite number of repeatable discharge efficiencies encountered, each being well bounded. The cell must always be considered fully discharged at the same voltage level, 2.5 volts for example. Charge efficiency and pack self-discharge are assumed negligible in this application and are ignored. CELL CHARACTERIZATION The fuel gauging equations work by comparing the DS2438's ICA value with expected "Empty" and "Full" values for that cell type which are stored in the DS2438's user EEPROM. This data is generated by characterization of the cell type over the expected temperature range and current consumption of the application. This information is subsequently stored in a pack resident memory for the algorithms to later extract and modify. Figure 4 shows the system used to collect the characterization data. Information should be gathered on several packs so that average or typical values can be stored in every production pack. For best accuracy, the data should be collected on assembled packs containing the production circuit as opposed to individual cells. Cell Capacity over Lifetime (mAH) 0 200 400 600 800 1000 1200 1400 0 100 200 300 400 500 600 700 800 900 1000 Age (Cycles) Capacity(mAH) Full Line defined as 4.2V High Current Emtpy Line defined as 2.5V Low Current Empty Line defined as 2.5V Figure 3 APPLICATION NOTE 131 4 of 9 To collect the data, the cell pack is fully charged at each temperature and fully discharged at each rate at each temperature. Figure 5 shows the ICA reading of the DS2438 as full charge data and active current discharge data is collected from 00C to 400C. This process would then be extended to collect the standby current discharge data over the same temperature range. All collected data points are arranged in Table 1 below. Since only the difference between points is important, the absolute values of the data do not matter, they have been normalized to lowest value (standby current empty at 400C). This reduces the amount of data needing to be stored since Standby Empty 400C is now always 0. Table 1: Cell Characterization Data 00C 100C 200C 300C 400C FULL (mAH) 554 561 578 582 588 STANDBY EMPTY (mAH) 65 42 19 11 0 ACTIVE EMPTY (mAH) 124 90 65 50 44 Cell Pack Environmental Chamber System Controller GPIB Bus Precision Source Measurement Unit Figure 4: Cell Characterization System Capacity Characterization over Temperature 0 100 200 300 400 500 600 700 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Time (s) ICA(mAH) Active Current Empty Points at each Temperature (mAH). Full Points at each Temperature (mAH). ICA Reading Cell Temperature Figure 5 APPLICATION NOTE 131 5 of 9 The characterization data is then stored in two pages of the DS2438's EEPROM memory. Because values larger than 25510 require more than 1 byte of memory to store, the amount of data is reduced by storing only the first value and then recording the incremental differences between temperatures. A memory map of the DS2438 data store is shown in table 2 below. Table 2: DS2438 Memory Map Page 3 Page 4 0 STANDBY EMPTY to 200C 1 FULL at 00C STANDBY EMPTY to 300C 2 FULL to 100C ACTIVE EMPTY to 00C 3 FULL to 200C ACTIVE EMPTY to 100C 4 FULL to 300C ACTIVE EMPTY to 200C 5 FULL to 400C ACTIVE EMPTY to 300C 6 STANDBY EMPTY to 00C ACTIVE EMPTY at 400C 7 STANDBY EMPTY to 100C Unused The first 6 bytes of page 3 contain the cell's measured FULL point at the different temperatures across the range. Bytes 0-1 are the capacity of the cell at 00C; the next four bytes are values of the increase in capacity from the previous temperature. For example if a given cell's capacity was 554 mAH at 00C and 561 mAH at 100C then bytes 0-1 would contain 55410 (0x022Ah) and byte 2 would contain 710 (0x07h). The next nine bytes hold the STANDBY EMPTY and ACTIVE EMPTY information stored in the same manner as the FULL values. EMPTY values are incremented in the opposite direction starting at 400C because it is the lowest value. STANDBY EMPTY at 400C is not included since it is always 010. Table 3 shows the actual information stored in the DS2438 using the characterization data contained in Table 1 above. Table 3: Memory map of cell data stored in DS2438 0 1 2 3 4 5 6 7 Page 3 0x02h 0x2Ah 0x07h 0x11h 0x04h 0x06h 0x17h 0x17h FULL STANDBY EMPTY Page 4 0x08h 0x0Bh 0x22h 0x19h 0x0Fh 0x06h 0x2Ch X STANDBY EMPTY ACTIVE EMPTY THE EQUATIONS After characterization of the cell pack is complete, calculating remaining capacity is very simple. The characterization data is used to find cell full and empty points based on temperature and discharge rate, and the DS2438's integrated current accumulator is compared against those values to express remaining capacity as a percentage. Upon power-up, the characterization data should be read from the DS2438 and stored in host RAM. When the host decides to update its remaining capacity indicator, it begins the process by reading the cell temperature and the DS2438's ICA. The present full value for the cell is then calculated by linearly interpolating between the FULL characterization data points using the cell temperature. For example, the cell full point at 280C is calculated by: Full Value (280C) = (FULL 200C) + ((28-20)/10) W (FULL 300C - FULL 200C) APPLICATION NOTE 131 6 of 9 The empty point is calculated in exactly the same method, except a determination must be made to use the ACTIVE or STANDBY characterization data based on the current activation state of the system. Capacity can then be calculated by determining the location of the ICA between empty and full points as a percentage. The formulas are summarized below: Full Value = FULL[Temperature] Empty Value = STANDBY EMPTY[Temperature] or ACTIVE EMPTY[Temperature] Capacity = ((ICA - Empty Value) / (Full Value - Empty Value)) W 100% No estimation of remaining capacity is perfect. To prevent a long-term accumulation of error the ICA register should be reset to the corresponding EMPTY value each time the cell is fully drained. Likewise, each time the cell is fully charged, the corresponding FULL value should be changed to match the ICA. By permanently adjusting the full point based on actual operation, the pack is able to adjust for cells that are different from the "typical" characterization data and adjusts as the cell ages and deteriorates. At End of Discharge: ICA = Empty Value At End of Full Charge: FULL[Temperature] = ICA DISPLAYING THE INFORMATION The equations above report remaining capacity as a percentage between calculated empty and full points. This might not be appropriate for every application. For example, a cell might be discharged to a level below ACTIVE EMPTY but above STANDBY EMPTY. If the remaining capacity percentage was based off the STANDBY EMPTY point it would show some capacity left even though the cell would not be able to support an active current at that time. This could be very confusing for the end user. The way the host processor presents the capacity data is unique to each application and not covered by standard fuel gauging equations. REMAINING ENERGY CALCULATION For some applications estimating the remaining energy is very important. For example if the circuit had constant power dissipation where the active current increased and the cell voltage dropped, remaining time would not be related directly to remaining charge. A good estimation of remaining energy can be easily calculated with a voltage reading from the DS2438 however. Recall the energy equation: Energy (J) = Volts W Current W time Which can be rewritten in terms of remaining energy: Remaining Energy (J) = 3.6 W Remaining mAH W RAV Where: Remaining mAH are the remaining milliamp-hours calculated by the above equations. 3.6 is the conversion factor from milliamp-hours to amp-seconds. RAV is the remaining average voltage of the cell explained below. APPLICATION NOTE 131 7 of 9 The upper plot on Figure 6 shows a typical cell discharge curve. The average remaining cell voltage can be approximated at any time by finding the average between the cell voltage currently, and the cell voltage when empty (2.5 volts typically). RAV = (Voltage + 2.5) / 2 The remaining energy calculation can now be summarized as: Remaining Energy (J) = 3.6 W Remaining mAH W (Voltage + 2.5) / 2 Where: Remaining mAH are the remaining milliamp-hours calculated by the fuel gauging equations. Voltage is present cell voltage measured by the DS2438. 3.6 is the conversion factor from milliamp-hours to amp-seconds. The second plot on Figure 6 shows the accuracy for this cell when predicting remaining energy with this method. The more linear a cell's discharge curve is, the more accurate this method will be. The less linear the cell, the less accurate the calculation. In either case, the calculation becomes more accurate where it is most important: as the cell voltage approaches the empty point. EXAMPLE APPLICATION For the following example a DS2438 demo board was used to monitor a 520 mAH prismatic Li+ cell. For information on the DS2438 demo board refer to the DS2438K datasheet. A Keithley 2304A DVM/power supply simulated the charger and load for the cell and a Tenney environmental chamber was used to control cell temperature. The cell characterization information and actual data stored in the DS2438 are the same as in the Cell Characterization section above. They are repeated in Tables 4 & 5 below for convenience. The controlling software was written in Visual Basic and sections of the code dealing directly with fuel gauging are presented at the end of this paper. Li+ Discharge Curve & Remaining Energy Calculation Error 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 0 500 1000 1500 2000 2500 3000 Time (s) Voltage(V) 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% CalculationError(%) Energy Calculation Error Accuracy Improves as cell voltage drops Cell Voltage over 1.2C Discharge Cycle Figure 6 APPLICATION NOTE 131 8 of 9 Table 4: Cell Characterization Data 00C 100C 200C 300C 400C FULL (mAH) 554 561 578 582 588 STANDBY EMPTY (mAH) 65 42 19 11 0 ACTIVE EMPTY (mAH) 124 90 65 50 44 Table 5: Memory map of cell data stored in DS2438 0 1 2 3 4 5 6 7 Page 3 0x02h 0x2Ah 0x07h 0x11h 0x04h 0x06h 0x17h 0x17h FULL S. EMPTY Page 4 0x08h 0x0Bh 0x22h 0x19h 0x0Fh 0x06h 0x2Ch X S. EMPTY ACTIVE EMPTY The cell was subjected to twenty partial charge-discharge cycles over a variety of temperatures from 00C to 400C. This test was designed to prove the accuracy of the fuel gauging equations under conditions which are far more extreme than would generally be encountered in a standard commercial application. Figure 8 shows the integrated current accumulator's relationship to the dynamically calculated empty and full points over the duration of the test. The cell temperature is shown at the bottom of the graph. The X-axis Update Cycle units refer to each time the remaining capacity was updated, approximately every 15 seconds. The worst case error occurred during the first charge (around update cycle 1000) and was approximately 3%. The fuel gauge algorithms permanently adjusted the full point based on that error and the second time a charge occurred at the same temperature (around update cycle 5500) the ICA matched the expected full level almost exactly. Cell Pack Tenney Environmental Chamber System Controller GPIB Bus Keithly 2304A Figure 7: Example Application System DS2438 DemoBoard 520mAHLi+ Prismatic PAC - DQ PAC + APPLICATION NOTE 131 9 of 9 The software then calculates the remaining capacity as a percentage of the difference between the empty and full points. Figure 9 below shows the actual fuel gauge output from the data shown above. SUMMARY Considering cell behavior over temperature and discharge rate when calculating remaining cell capacity provides superior accuracy to coulomb counting alone. Dallas Semiconductor's fuel gauging equations can be applied to any Lithium-Ion cell type and any Dallas Semiconductor coulomb counting device while using a minimum of host processor cycles. They also adjust for cell to cell differences and cell aging, becoming more accurate over time. Fuel Gauging Example (%) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 0 1000 2000 3000 4000 5000 6000 Update Cycles (~15 seconds each) RemainingCapcity(%) Cell Capacity Values adjusted after a complete charge ICA Reset to 0 after a complete discharge. Figure 9 Fuel Gauging Example (mAH) 0 100 200 300 400 500 600 700 800 0 1000 2000 3000 4000 5000 6000 Update Cycles (~15 seconds each) RemainingCapacity(mAH) Full Point Dynamically Adjusted Based on Temperature and Previous Cycles. Empty Point Dynamically Adjusted Based on Rate and Temperature. Remaining Capacity (ICA Register). Cell Temperature. Figure 8

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