Battery DC impedance measurement

Abstract

The state of charge of a rechargeable battery is determined by calculating the DC impedance of the battery. The impedance is calculated by: performing a two different constant current discharges of the battery at a first and second C-rates, respectively; measuring the voltage and current during the interval of each constant current discharge and calculating the amount of charge extracted from the battery up to a point where the battery voltage drops to a threshold value; calculating the state of charge of the battery; and calculating the DC impedance of the battery as a function of the difference between the battery voltages and discharge currents for the two different discharges.

Claims

1. A method of determining a state of charge of a battery comprising steps of: calculating a DC impedance of the battery by: performing a first constant current discharge of the battery at a first C-rate; measuring voltage of the battery and current flowing from the battery during an interval of the first constant current discharge and calculating an amount of charge extracted from the battery up to a point i where the voltage of the battery drops to a first threshold value; calculating a first state of charge as being equal to ((Q.sub.max−Q.sub.i)/Q.sub.max)×100, where Q.sub.max is a total amount of charge extracted from the battery, and where Q.sub.i is the amount of charge extracted at the point i; performing a second constant current discharge of the battery at a second C-rate lower than the first C-rate; measuring the voltage of the battery and current flowing from the battery during an interval of the second constant current discharge and calculating the amount of charge extracted from the battery up to a point j where the voltage of the battery drops to a second threshold value; calculating a second state of charge as being equal to ((Q.sub.max−Q.sub.j)/Q.sub.max)×100, where Q.sub.max is the total amount of charge extracted from the battery, and where Q.sub.j is the amount of charge extracted at the point j; and calculating the DC impedance of the battery, for a given state of charge as being: ((Vbat.sub.second C-rate−Vbat.sub.first C-rate)/(Iload.sub.first C-rate−Iload.sub.second C-rate), where Vbat.sub.second C-rate and Vbat.sub.first C-rate are the voltages of the battery measured at the second C-rate and the first C-rate and based upon the first and second states of charge, respectively, and where Iload.sub.second C-rate and Iload.sub.first C-rate are the current flowing from the battery when discharging at the second C-rate and the first C-rate, respectively.

2. The method of claim 1, wherein the amount of charge extracted from the battery is calculated by recording the current flowing from the battery at intervals throughout the first and second constant current discharges and by multiplying the current flowing from the battery at each interval by a duration of each respective interval.

3. The method of claim 2, further comprising a step of recording in a log the measured currents and times when those currents are measured, and interrogating the log to calculate the amount of charge extracted from the battery during an interval between a pair of times, by multiplying that interval by an average of the corresponding current measurements.

4. The method of claim 2, wherein a total amount of charge extracted is calculated by summing the amounts of charge extracted during each interval.

5. The method of claim 1, wherein the first threshold value comprises a battery voltage of substantially 3.0V.

6. The method of claim 1, further comprising a step of measuring and logging a battery temperature during the first and second constant current discharges.

7. The method of claim 1, wherein the first C-rate is 0.8 C, 0.7 C or 0.3 C, and wherein the second C-rate is 0.1 C or 0.2 C.

8. The method of claim 1, wherein the first and second constant current discharges are performed at substantially a same ambient temperature.

9. The method of claim 8, wherein the ambient temperature is approximately 23-25° C.

10. The method of claim 1, performed using more than two constant current discharges, and by comparing the results across more than one pair of values.

11. The method of claim 1, further comprising a step of providing a log of measured currents, voltages, temperatures and times for each C-rate discharge, plotting the voltage and current as a function of SoC for each C-rate discharge, determining a voltage and current for a specified SoC for each of the C-rate discharges, whereby values of V.sub.high C-rate, V.sub.low C-rate, i.sub.high C-rate and i.sub.low C-rate are used to obtain the DC impedance of the battery at the specified SoC according to the equation:
Z.sub.int(SoC,T)=(Vbat.sub.low C-rate−Vbat.sub.high C-rate)/(Iload.sub.high C-rate−Iload.sub.low C-rate).

12. The method of claim 11, wherein calculation of Z.sub.int (SoC,T) is repeated for different SoC values.

13. The method of claim 11, therein calculation of Z.sub.int (SoC,T) is repeated at different temperatures.

14. The method of claim 11, wherein the DC battery impedance values are stored for later use by a SoC algorithm for correct for variations in the DC battery impedance at different temperatures, voltages and SoC levels.

15. The method of claim 1, further comprising a step of determining a open-circuit voltage VOCV (SoC,T) of the battery using a lower of the C-rate voltages and adding voltage drop due to the DC impedance of the battery according to:
V.sub.OCV(SoC,T)=V.sub.Bat(SoC,T)+Z.sub.int(SoC,T)×I.sub.load.

16. An apparatus, comprising: a circuit configured to determine a state of charge of a rechargeable battery comprising: a discharge circuit configured to discharge the rechargeable battery through a constant current load, a voltmeter configured to measure a voltage of the rechargeable battery, an ammeter configured to measure a discharge current of the rechargeable battery, a temperature sensor configured to measure temperature of the rechargeable battery, a processor comprising an internal clock and configured to select a desired C-rate for discharging the rechargeable battery through the constant current load, monitor and log the voltage, current and temperature at intervals determined by the internal clock, and determine the state of charge of the rechargeable battery according to the method of claim 1.

17. The apparatus of claim 16, further comprising a disconnect circuit configured to disconnect the rechargeable battery from the constant current load when the voltage reaches a threshold cut-off value.

18. The apparatus of claim 16, further comprising a memory for storing a log of one or more of the measured voltages, currents, temperatures and times when the currents, voltages and temperatures are measured.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A preferred embodiment of the invention shall now be described, by way of example only, with reference to the accompanying drawings in which:

(2) FIG. 1 is a schematic showing a system;

(3) FIG. 2 is a schematic graph of current versus time during a constant current charge test; and

(4) FIG. 3 is a schematic graph of voltage and current as a function of SoC for two C-rates.

DETAILED DESCRIPTION OF THE DRAWINGS

(5) In FIG. 1, a rechargeable battery 10 is discharged through a constant current load 12. During the discharge, the battery voltage is measured by a voltmeter 14 and the discharge current is measured by an ammeter 16. The battery 10 comprises a temperature sensor 18, and the system 20 comprises an internal clock 22.

(6) A first C-rate is selected, and the discharge test begins. At intervals determined by the user (or application), and timed by the system clock 22, voltage, current and temperature readings are taken by the voltmeter 14, ammeter 16 and temperature sensor 18, respectively. These values are recorded in a log 24 comprising a table of time 26, temperature 28, voltage 30 and current 32. The discharge continues until the voltage 30 reaches a threshold cut-off value, typically 3.0V.

(7) The log 24 is then interrogated, and the charge extracted from the battery 10 is calculated, as shown in FIG. 2. Here, the current 32 is plotted as a function of time 26, and the charge is simply the area under the curve 34. The total current extracted can be calculated by summing the area under the curve 34 (Q1+Q2+Q3+ . . . Qn).

(8) Next, the voltage 30 and current 32 is plotted as a function of SoC, as shown in FIG. 3.

(9) The test is then repeated at a second C-rate, following the steps above, and the voltage 30 and current 32 values plotted in the graph of FIG. 3.

(10) Now, for a given SoC value, it is possible to read off a corresponding voltage and current for each of the C-rate discharges, as shown in FIG. 3, whereby the values of V.sub.high C-rate 40, V.sub.low C-rate 42, i.sub.high C-rate 44 and i.sub.low C-rate 46 can be seen. These values can then be fed into the equation:
Z.sub.int(SoC,T)=(Vbat.sub.low C-rate−Vbat.sub.high C-rate)/(Iload.sub.high C-rate−Iload.sub.low C-rate)  (Eq. 3)
to obtain the impedance of the battery 10 at that particular SoC value. The calculation can be repeated for different SoC values, and of course, for different temperatures.

(11) The resultant impedance values can be stored for later use by a SoC algorithm to correct for variations in the battery 10 impedance at different temperatures, voltages and SoC levels.

(12) Advantageously, the invention may provide a relatively easy way to obtain the impedance of the battery without having to perform detailed and time-consuming impedance characterization tests (e.g. relaxation tests). Experiments have shown that the calculated impedances, obtained by the invention, are reasonably accurate, and that the impedance calculations can be performed on-system, thereby yielding a more realistic “actual use” values, that could, say, a laboratory-based characterization methodology. In addition, the invention may enable system designers or end users to perform impedance characterization for particular batteries, making it possible to characterize multiple batteries for a single application. Owing to the greater granularity of the invention, a greater number of data points can be obtained, compared to the individual relaxation tests, thereby potentially increasing the accuracy of the characterization process whilst also reducing the cost and time of characterization.