WO2003067735A1 - Method and apparatus using a circuit model to evaluate cell/battery parameters - Google Patents
Method and apparatus using a circuit model to evaluate cell/battery parameters Download PDFInfo
- Publication number
- WO2003067735A1 WO2003067735A1 PCT/US2003/003606 US0303606W WO03067735A1 WO 2003067735 A1 WO2003067735 A1 WO 2003067735A1 US 0303606 W US0303606 W US 0303606W WO 03067735 A1 WO03067735 A1 WO 03067735A1
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- Prior art keywords
- battery
- cell
- charge
- time
- varying electrical
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Classifications
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M10/00—Secondary cells; Manufacture thereof
- H01M10/42—Methods or arrangements for servicing or maintenance of secondary cells or secondary half-cells
- H01M10/48—Accumulators combined with arrangements for measuring, testing or indicating the condition of cells, e.g. the level or density of the electrolyte
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
- G01R31/379—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator for lead-acid batteries
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/389—Measuring internal impedance, internal conductance or related variables
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/10—Energy storage using batteries
Definitions
- TSC Total storage capacity
- ASC absolute stored charge
- SOC state-of-charge
- ACC absolute cranking current
- FCCC fully charged cranking current
- SOH state-of-health
- Total storage capacity denotes- the total amount of charge that a fully charged battery can supply under specified discharge conditions.
- ASC Absolute stored charge
- ampere-hours or reserve capacity minutes denotes the amount of charge that a battery can supply in its current charge state. As a battery is discharged, its ASC decreases — much like the level of liquid in a fuel tank.
- SOC State-of-charge
- Relative stored charge is the ratio of a battery' s ASC to its TSC — generally expressed as a percentage.
- a battery's SOC indicates whether charging is advisable and identifies the point at which charging should be discontinued.
- ACC Absolute cranking current
- FCCC Full charged cranking current
- SOH state-of-health
- voltage correction methods are not very accurate.
- Patent 3,984,762 to Dowgiallo purports to determine SOC from the phase angle of the complex impedance at a single frequency.
- Randin et al. assert that SOC can be determined from the argument (i.e., phase angle) of the difference between complex impedances measured at two different frequencies.
- Bounaga in U.S. Patent 5,650,937, reportedly determines SOC from measurements of the imaginary part of the complex impedance at a single frequency.
- Basell et al. purport to determine SOC from the rate of change of impedance with frequency in U.S. Patent 5,717,336. Ding et al., in U.S.
- Patent 6,094,033 broadly assert that SOC can be determined from a battery' s "impedance response, which can include series and parallel equivalent circuit parameters, i.e., resistance, capacitance, and phase angle, among others".
- impedance response which can include series and parallel equivalent circuit parameters, i.e., resistance, capacitance, and phase angle, among others.
- techniques purporting to determine SOC from the transient response to an applied pulsed voltage and/or current are disclosed by Andrieu and Poignant in U. S. Patent 5,530,361 and by Simon in French Patent Application FR 2,749,396A. The fact that none of these metiods has g ' m wide acceptance, ⁇ iowever, suggests that they may not be altogether satisfactory methods for determining SOC.
- SUMMARY OF THE INVENTION Testing apparatus senses the time-varying electrical response of an electrochemical cell/battery to time-varying electrical excitation.
- the cell/battery may, or may not, be in service.
- Computation circuitry responsive to the time-varying electrical response evaluates elements of a unique circuit model representation of the cell/battery. Performance parameters and physical parameters are computed from these element values . Computed performance parameters include, but are not limited to, ' “total storage capacity”, “absolute stored charge”, “state-of-charge”, “absolute cranking current”, “fully charged cranking current”, and "state-of-health".
- Computed physical parameters include, but are not limited to, "exchange current”, “maximum exchange current”, “charge transfer conductance”, “maximum charge transfer conductance”, “double layer capacitance”, and “maximum double layer capacitance”. Computed parameters are either displayed to the user, employed to initiate an alarm, or used to control a process such as charging the cell/battery.
- FIG. 1 is a block diagram of apparatus for evaluating performance parameters and physical parameters of an electrochemical cell or battery in accordance with one embodiment of the present invention.
- FIG. 2 depicts a generic 2n-element small signal circuit model representation of an electrochemical cell or battery employed in the present invention.
- FIG. 3 depicts the six-element small signal circuit model representation of a particular fully ⁇ charged 12V VRA battery determined from complex immittance measurements at 5 Hz, 50 Hz, and 500 Hz.
- FIG. 4 is a plot of the variation of the three subcircuit time-constants defined in FIG. 3 as charge is removed from the battery.
- FIG. 5 is a plot of values of the. three conductances defined in FIG. 3 as charge is removed from the battery.
- FIG. 6 is plot of values of capacitances C2 and C3 defined in FIG. 3 as charge is removed from the battery.
- FIG. 7 is a plot of the "exchange current" I Q derived from “charge transfer conductance" G3 of FIG. 5 as charge is removed from the battery.
- FIG. 8 is a plot of the "state-of-charge” SOC derived from “charge transfer conductance” G3 of FIG. 5 and “double layer capacitance” C2 of FIG. 6 as charge is removed from the battery.
- FIG. 9 is a plot of the "absolute stored charge” ASC determined from “double layer capacitance” C2 of FIG. 6 as charge is removed from the battery.
- FIG. 10 is a plot of the "total storage capacity" TSC derived from “charge transfer conductance” G3 of FIG. 5 and “double layer capacitance” C2 of FIG. 6 as charge is removed from the battery.
- FIG. 12 is a plot of the function used to correct the "absolute cranking current" ACC for "state- of-charge” SOC to obtain the "fully charged cranking current” FCCC of FIG 13.
- FIG. 13 is a plot of the corrected "fully charged cranking current" FCCC as charge is removed from the battery.
- FIG. 14 is a diagram of the "commonly accepted” circuit model showing the placement of a “charge transfer resistance” and “double layer capacitance” in parallel with one another.
- FIG. 16 is a block diagram of apparatus for evaluating performance and physical parameters of an electrochemical cell or battery wherein an external source produces time-varying electrical excitation.
- FIG. 1 discloses a block diagram of apparatus 5 for evaluating performance parameters and/or physical parameters according to one embodiment of the present invention.
- Measuring circuitry 10 electrically couples to cell/battery 20 at positive terminal 15 and negative terminal 25 by means of current-carrying contacts A and B and voltage-sensing contacts C and D. Cell/battery 20 may, or may not, be in service. Under control of microcontroller circuitry 30 via control path 35, measuring circuitry 10 passes periodic time-varying excitation current i(t) through contacts A and B and senses periodic time-varying response voltage v(t) across contacts C and D.
- Amplification and analog to digital conversion circuitry contained within measuring circuitry 10 formulates digital representations of i(t) and v(t) samples and communicates them to microcontroller circuitry 30 via data path 40.
- microcontroller circuitry 30 computes real and imaginary parts of complex immittance either, impedance Z or admittance Y — at a measuring frequency f ⁇ ; where f k is a discrete frequency contained in the periodic waveforms of i(t) and v(t) .
- Microcontroller circuitry 30 commands measuring circuitry 10 to repeat these measurements at each one of n discrete measuring frequencies, where n is an integer number equal to or greater than 3.
- Microcontroller circuitry 30 can employ algorithms disclosed in U. S. Patents 6,037,777 and 6,222,369 to numerically combine the 2n experimental quantities to evaluate the 2n elements of the circuit model representation of the cell/battery disclosed in FIG. 2.
- This unique circuit model comprises a single series R-L subcircuit in series with a plurality, n-1, of parallel G-C subcircuits.
- Microcontroller circuitry 30 computes one or more performance and/or physical parameters of cell/battery 20 from values of one or more elements of this circuit model representation of FIG. 2. Additionally, microcontroller circuitry 30 can compare one or more computed parameters with battery rating information inputted by a user on input device 45 to determine the battery's "state-of-health" SOH. Finally, microcontroller circuitry 30 can output appropriate performance or physical parameters to a user on display 50, and/or apply one or more computed parameters to initiate an alarm 55 or to control a process 60 such as charging of the battery.
- the experimental battery was a VR A (valve-regulated lead-acid) automotive battery of spiral-grid construction that was rated 700 CCA, 95 minutes reserve capacity, and 50 Ah capacity @ 20 hour rate.
- the three measurement frequencies were 5, 50, and 500 Hz.
- the three subcircuits are characterized by three very different time constants.
- the three subcircuits represent quite different physical processes that can be differentiated from one another by their time constants .
- CCA cold-cranking amps
- Series inductance LI describes energy storage in the battery' s surrounding magnetic field, with no electrochemical component to LI yet observed.
- Both the parallel G2-C2 subcircuit and the parallel G3—C3 subcircuit are believed to be linearized representations of nonlinear electrochemical processes occurring at the negative electrode surfaces. These two subcircuits together describe the response of negative electrode surfaces to changes in an externally applied electrochemical overpotential .
- Electrochemical overpotential at an electrode surface consists of two parts: an electrical overpotential and a chemical overpotential.
- the electrical part arises from electrical forces on charged particles, and the chemical part arises from concentration differences.
- the faster G2-C2 subcircuit responds to the electrical part of an electrochemical overpotential and the slower G3-C3 subcircuit responds to the chemical part.
- These two subcircuits add in series in the circuit model of FIG. 3 because the electrical overpotential and the chemical overpotential add together to form the electrochemical overpotential. Voltages (potentials) add in series.
- FIGS. 4, 5, and 6 display the results of three-frequency immittance measurements performed on the battery whose model is depicted in FIG. 3 during a discharge sequence.
- the battery was initially charged, allowed to reach equilibrium, and was then repeatedly discharged at an approximate 8-hr rate in increments of approximately 3 ampere-hours. The battery was permitted to rest for 2.5 hours after each discharge period before the three-frequency immittance measurements were taken.
- FIG. 4 is a plot of the variation of the three time constants defined in FIG. 3 as charge is removed from the battery. One notes that the time constants remain widely separated as charge is removed, and that the longest of the three, ⁇ 3 , is nearly independent of state-of-charge .
- Gl l/Rl
- G2 G2
- G3 becomes small near full charge as well as near full discharge.
- G3 sets G3 apart from Gl and G2 , both of which reach maxima at full charge.
- Such unusual behavior can be explained by assuming that G3 describes faradaic processes occurring at the negative electrode surfaces and considering the kinetics of such processes.
- i is the current in the external circuit (assumed positive in the "charge” direction) while if and ij, are "forward” and “backward” ionic "reaction” currents, respectively, in the electrolyte.
- Voltage V3 in equation (1) is believed to be the chemical component of the electrochemical overpotential (positive for "charge” and negative for “discharge”) at the negative electrode surfaces .
- the chemical overpotential, V3 drives the two ionic reaction currents.
- the opposite is true.
- N ⁇ Np b +Np b so 4 i- s the total number of negative-
- Np ⁇ b is the number of such
- Equation (4) can therefore be written
- G3 4 •G3 max •(SOC)•(1-SOC) (6)
- FIG. 6 discloses the variation of capacitance C2 and capacitance C3 as charge is removed from the battery.
- Time constant ⁇ 3 is believed closely related to the reaction time of faradaic processes at the negative electrode surfaces (See U.S. Patents 6,137,269 and 6,294,697).
- Capacitance C2 in FIG. 6 is observed to vary in an entirely different manner from C3 as charge ⁇ is removed.
- C2 assumes its largest value with zero amp-hours removed and simply decreases monotonically as charge is removed from the battery. Such behavior suggests that the G2-C2 subcircuit is responsive to the nonfaradaic or electrical component of an electrochemical overpotential at the negative-electrode surfaces. In this interpretation, capacitance C2 represents the negative-electrode's ionic "double layer capacitance" . - a physical parameter of considerable interest.
- Equation (7) indicates that physical parameter C2 j relates to battery size and condition
- Equation . (4) indicates that physical parameter G3 max relates to size and condition
- Equations (6) , (7) , and (8) can be combined algebraically to provide separate expressions for SOC , C2 j ⁇ , and G3 max in terms of ⁇ , C2 , and G3.
- the results are-
- FIG. 8 displays performance parameter SOC (in percent) calculated from equation (9) by using the experimental G3 and C2 data disclosed in FIGS. 5 and 6. Note that combining G3 and C2 data to determine SOC resolves the multi-value ambiguity of equation (6) .
- the "state-of-charge" determined in this manner varies from a maximum value of 93.6%, with zero ampere- hours removed from the battery, to a minimum value of 4.1% with 45.2 ampere-hours removed. The observed, nearly linear, variation of SOC with ampere-hours removed provides excellent corroboration of the theory.
- TSC K cs - ⁇ C2 + ⁇ - (G3/C2) ⁇ (14)
- cs is a "charge storage" constant that depends upon the battery type, and upon the units of charge storage (i.e., ampere-hours @ an 8 hr rate, ampere- hours @ a 20 hr 'rate, reserve capacity minutes, coulombs, etc.) I find that for batteries of the type under consideration herein, and with ASC and TSC expressed in ampere-hours @ an 8 hr rate, K cs sll.3.
- the performance parameter "state-of-charge” SOC that is defined physically in terms of numbers of reaction sites by equation (5) , is actually the ratio of the two performance parameters "absolute stored charge” ASC and “total storage capacity” TSC .
- FIG. 9 displays performance parameter "absolute stored charge” ASC (in ampere-hours) calculated from equation (13) using the experimental C2 data disclosed in FIG. 6.
- the "absolute stored charge” determined in this manner varies from a maximum value of 47.2 ampere-hours, with zero ampere-hours removed from the battery, to a minimum value of 1.9 ampere-hours with 45.2 ampere-hours removed.
- “absolute stored charge” ASC decreases as the battery discharges - much like the level of liquid in a fuel tank. Accordingly, ASC would comprise an excellent “electric fuel gauge” readout.
- FIG. 11 displays performance parameter ACC determined from equation (16) by using the Gl data of FIG. 5. One sees that ACC decreases significantly as charge is removed from the battery.
- FCCC For batteries that are less than fully charged, the performance parameter "fully charged cranking current" FCCC can be . determined by correcting the ACC according to -
- FCCC ACC •F(SOC) (17)
- FIG. 12 discloses an e perically determined F(SOC) for correcting the ACC of batteries of the type under consideration. This function can be expressed mathematically as -
- FIG. 13 displays performance parameter FCCC obtained by correcting the data of FIG. 11 according to equation (17) using the correction factor defined by equation (18) (FIG. 12) .
- the first method is to compare the computed "total storage capacity” TSC with an appropriate user-inputted capacity rating such as the battery's rated “ampere- hour capacity” or rated “reserve capacity” in minutes.
- the second method is to compare the computed "fully charged cranking current” FCCC with an appropriate user-inputted cranking rating such as the battery's rated “cold cranking amperes” (CCA) .
- FCCC battery's rated “cold cranking amperes”
- the battery is assumed to have “failed” the SOH test if the calculated parameter value is less than a predetermined fraction, say 75%, of the rated parameter value.
- Either SOH method, or both methods may be employed — depending upon the type of service that the battery is expected to experience.
- FIG. 14 illustrates the "commonly accepted” equivalent circuit model of a cell/battery at the present time.
- the "commonly accepted” model also known as the “Randies equivalent circuit” places a "charge transfer resistance” and a “double layer capacitance” in parallel with one another. In my opinion, this model is fundamentally wrong and cannot possibly lead to correct evaluation of any of the • performance parameters or physical parameters evaluated herein.
- My invention is not limited to evaluating only these twelve parameters.
- FIG. 1 utilizes time-varying electrical excitation i(t) generated internally to apparatus 5 by internal measuring circuitry 10.
- the requisite time-varying electrical excitation could be developed by an external source 65 as disclosed in FIG. 16.
- Such an external source could simply comprise normal "noise” currents flowing through a cell/battery during service, such as ' taught in PCT Application WO 93/22666 to Robinson. It could also comprise "ripple" signals arising from an unfiltered battery charger during bench- charging of the cell/battery or charging by an alternator in a vehicle.
- time-varying current i(t) has been presented as an electrical excitation and time-varying voltage v(t) as an electrical response, the roles of i(t) and v(t) could be reversed.
- Time-varying voltage v(t) could be the electrical excitation and time-varying current i(t) the electrical response. All such modifications and variations are included in my invention.
- Measuring circuitry, electrical excitation circuitry, electrical response sensing circuitry, computational circuitry, etc. can be implemented in hardware, software, or combinations thereof. Such circuitry can share common elements or be implemented with common components such as a common microprocessor, microcontroller, or personal computer. Workers skilled in the art will recognize that these and other variations may be made in form and detail without departing from the true spirit and scope of my invention.
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Priority Applications (2)
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GB0417678A GB2401192B (en) | 2002-02-08 | 2003-02-07 | Method and apparatus using a circuit model to evaluate cell/battery parameters |
AU2003207861A AU2003207861A1 (en) | 2002-02-08 | 2003-02-07 | Method and apparatus using a circuit model to evaluate cell/battery parameters |
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US10/073,378 US6737831B2 (en) | 1999-09-01 | 2002-02-08 | Method and apparatus using a circuit model to evaluate cell/battery parameters |
US10/073,378 | 2002-02-08 |
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Also Published As
Publication number | Publication date |
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AU2003207861A1 (en) | 2003-09-02 |
GB0417678D0 (en) | 2004-09-08 |
US6737831B2 (en) | 2004-05-18 |
GB2401192B (en) | 2006-01-11 |
US20020109504A1 (en) | 2002-08-15 |
GB2401192A (en) | 2004-11-03 |
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