Method and apparatus for monitoring a DC power source

Evaluation of a DC power source can include communication with a voltmeter that is arranged to monitor electrical potential across positive and negative electrodes. The method includes determining a full-cell open-circuit voltage (“OCV”), an associated positive half-cell OCV, and an associated negative half-cell OCV at a start-of-life point of the DC power source. A lithium balance model is executed to determine a plurality of beginning states associated with an electrode alignment of the DC power source. An in-use state for the full-cell OCV is determined. An optimization routine is executed employing the lithium balance model to determine in-use states associated with the electrode alignment of the DC power source based upon the in-use state for the full-cell OCV and the beginning states associated with electrode alignment. A negative-to-positive (“N/P”) ratio is determined based upon the in-use states, and battery life is evaluated based upon the N/P ratio.

INTRODUCTION

Some DC power sources may have a tendency to undergo changes in performance in-use.

SUMMARY

A DC power source including a positive electrode and a negative electrode is described. A method for evaluating the DC power source is embodied in a controller in communication with a voltmeter that is arranged to monitor electrical potential across the positive and negative electrodes. The method includes determining a full-cell open-circuit voltage (“OCV”), an associated positive half-cell OCV, and an associated negative half-cell OCV at a start-of-life point of the DC power source. A lithium balance model is executed to determine a plurality of beginning states associated with an electrode alignment of the DC power source based upon the full-cell OCV, the positive half-cell OCV and the negative half-cell OCV at the start-of-life point of the DC power source. An in-use state for the full-cell OCV is determined. An optimization routine is executed employing the lithium balance model to determine in-use states associated with the electrode alignment of the DC power source based upon the in-use state for the full-cell OCV and the beginning states associated with electrode alignment. A negative-to-positive (“N/P”) ratio is determined based upon the in-use states associated with the electrode alignment of the DC power source, and battery life is evaluated based upon the N/P ratio.

An aspect of the disclosure includes determining the plurality of beginning states associated with electrode alignment, which includes determining an initial positive stoichiometric coefficient, a final positive stoichiometric coefficient, an initial negative stoichiometric coefficient and a final negative stoichiometric coefficient associated with a fractional lithium occupancy at the start-of-life point of the DC power source.

Another aspect of the disclosure includes determining the in-use states associated with the in-use electrode alignment, which includes determining in-use values for the initial positive stoichiometric coefficient, the final positive stoichiometric coefficient, the initial negative stoichiometric coefficient and the final negative stoichiometric coefficient associated with the fractional lithium occupancy of the DC power source in-use.

Another aspect of the disclosure includes determining the N/P ratio based upon the in-use values for the initial positive stoichiometric coefficient, the final positive stoichiometric coefficient, the initial negative stoichiometric coefficient and the final negative stoichiometric coefficient.

Another aspect of the disclosure includes determining data for the full-cell OCV and the half-cell OCV for each of the positive and negative electrodes employing a low charge-rate charge/discharge profile.

Another aspect of the disclosure includes the lithium balance model having a form associated with the equation:
Ucell(SOC)=Upos(yf−SOC(yf−yi))−Uneg(xf+SOC(xi−xf))

wherein:SOC is the present state of charge,Ucell(SOC) is the full-cell OCV at the SOC,Upos is the positive half-cell OCV at the SOC,Uneg is the negative half-cell OCV at the SOC,yi is the initial positive stoichiometric coefficient,yf is the final positive stoichiometric coefficient,xi is the initial negative stoichiometric coefficient, andxf is the final negative stoichiometric coefficient.

Another aspect of the disclosure includes executing the optimization routine employing the lithium balance model to determine in-use states associated with the electrode alignment of the DC power source, which includes executing a least-squares minimization method to determine values for yi, yf, xi, xf based upon the full-cell OCV, the positive half-cell OCV, and the negative half-cell OCV for the DC power source.

Another aspect of the disclosure includes evaluating battery life based upon the N/P ratio, which includes evaluating a remaining service life of the DC power source based upon the N/P ratio.

Another aspect of the disclosure includes determining a positive SOC capacity based upon the in-use values for the initial positive stoichiometric coefficient and the final positive stoichiometric coefficient, and determining a negative SOC capacity based upon the in-use values for the initial negative stoichiometric coefficient and the final negative stoichiometric coefficient.

Another aspect of the disclosure includes evaluating a battery state estimator based upon the positive and negative SOC capacities.

Another aspect of the disclosure includes evaluating a battery state estimator based upon a ratio of the negative and positive SOC capacities.

Another aspect of the disclosure includes evaluating the battery state estimator based upon a ratio of the negative and positive SOC capacities, which includes indicating an end-of-service life of the DC power source when the ratio of the negative and positive SOC capacities is less than one.

Another aspect of the disclosure includes determining the full-cell OCV, the associated positive half-cell OCV, and the associated negative half-cell OCV for each of a plurality of SOC states between a minimum SOC and a maximum SOC at a start-of-life point of the DC power source.

Another aspect of the disclosure includes the DC power source being a lithium-ion battery.

DETAILED DESCRIPTION

The components of the disclosed embodiments, as described and illustrated herein, may be arranged and designed in a variety of different configurations. Thus, the following detailed description is not intended to limit the scope of the disclosure, as claimed, but is merely representative of possible embodiments thereof. In addition, while numerous specific details are set forth in the following description in order to provide a thorough understanding of the embodiments disclosed herein, some embodiments can be practiced without some or all of these details. Moreover, for the purpose of clarity, certain technical material that is understood in the related art has not been described in detail in order to avoid unnecessarily obscuring the disclosure. Furthermore, the disclosure, as illustrated and described herein, may be practiced in the absence of an element that is not specifically disclosed herein.

Referring to the drawings, wherein like reference numerals correspond to like or similar components throughout the several Figures,FIG. 1, consistent with embodiments disclosed herein, illustrates a rechargeable DC power source10having a positive terminal12and a negative terminal14. In one embodiment, the DC power source10is configured as a lithium-ion battery. A voltmeter20is disposed to monitor electrical potential between the positive terminal12and the negative terminal14. The voltmeter20is in communication with a controller30, which includes executable code32.

The term “controller” and related terms such as control module, module, control, control unit, processor and similar terms refer to one or various combinations of Application Specific Integrated Circuit(s) (ASIC), electronic circuit(s), central processing unit(s), e.g., microprocessor(s) and associated non-transitory memory component(s) in the form of memory and storage devices (read only, programmable read only, random access, hard drive, etc.). The non-transitory memory component is capable of storing machine readable instructions in the form of one or more software or firmware programs or routines, combinational logic circuit(s), input/output circuit(s) and devices, signal conditioning and buffer circuitry and other components that can be accessed by one or more processors to provide a described functionality. Input/output circuit(s) and devices include analog/digital converters and related devices that monitor inputs from sensors, with such inputs monitored at a preset sampling frequency or in response to a triggering event. Software, firmware, programs, instructions, control routines, code, algorithms and similar terms mean controller-executable instruction sets including calibrations and look-up tables. Each controller executes control routine(s) to provide desired functions. Routines may be executed at regular intervals, for example each 100 microseconds during ongoing operation. Alternatively, routines may be executed in response to occurrence of a triggering event. Communication between controllers, and communication between controllers, actuators and/or sensors may be accomplished using a direct wired point-to-point link, a networked communication bus link, a wireless link or another suitable communication link, and is indicated by line25. Communication includes exchanging data signals in suitable form, including, for example, electrical signals via a conductive medium, electromagnetic signals via air, optical signals via optical waveguides, and the like. The data signals may include discrete, analog or digitized analog signals representing inputs from sensors, actuator commands, and communication between controllers. The term “signal” refers to a physically discernible indicator that conveys information, and may be a suitable waveform (e.g., electrical, optical, magnetic, mechanical or electromagnetic), such as DC, AC, sinusoidal-wave, triangular-wave, square-wave, vibration, and the like, that is capable of traveling through a medium.

The term ‘model’ refers to a processor-based or processor-executable code and associated calibration that simulates a physical existence of a device or a physical process. As used herein, the terms ‘dynamic’ and ‘dynamically’ describe steps or processes that are executed in real-time and are characterized by monitoring or otherwise determining states of parameters and regularly or periodically updating the states of the parameters during execution of a routine or between iterations of execution of the routine. The terms “calibration”, “calibrate”, and related terms refer to a result or a process that compares an actual or standard measurement associated with a device with a perceived or observed measurement or a commanded position. A calibration as described herein can be reduced to a storable parametric table, a plurality of executable equations or another suitable form. The term “parameter” refers to a measurable quantity that represents a physical property of a device or other element that is discernible using one or more sensors and/or a physical model. A parameter can have a discrete value, e.g., either “1” or “0”, or can be infinitely variable in value.

A process for monitoring and evaluating an embodiment of the DC power source10is described, and includes determining and employing a full-cell open-circuit voltage (OCV) and half-cell OCVs from charge-discharge profiles. The full-cell OCV and half-cell OCVs are advantageously employed in estimating cell stoichiometry for the DC power source10. This includes monitoring of individual electrode capacities and an N/P ratio at the beginning of life and in-use, including characterizing an OCV shift in-use in an onboard battery state estimation (BSE). A cell balance of the DC power source10can be determined, which can be employed to predict cell performance. Such results can support root-cause analysis efforts to identify cell fault mechanisms, such as occurrence of lithium plating or a loss of electrode capacity. The process can provide baseline data for cell porous electrode models that can be used for predicting cell performance and early detection of occurrence of a cell fault in the DC power source10.

The process for monitoring and evaluating an embodiment of the DC power source10provides a cell diagnostic tool that determines the alignment of positive and negative electrodes12,14in the DC power source10. This includes determining start of life half-cell OCVs for the positive and negative electrodes12,14, which are preferably derived from low-rate charge-discharge profiles. Examples of low-rate charge-discharge profiles for determining the start of life half-cell OCVs for the positive and negative electrodes are shown graphically with reference toFIGS. 3 and 4, respectively. The process also includes execution and analysis employing parameters associated with a lithium balance model, which can be employed to determine electrode alignment (stoichiometry) from the full-cell OCV data and to estimate individual electrode capacities and a negative-to-positive (“N/P”) ratio. The electrode alignment is described in context of stoichiometry, which indicates a quantitative relationship between products and reactants in a chemical reaction. As employed herein, the stoichiometric term is an accounting of how much lithium is transferred from the anode or positive electrode12to the cathode or negative electrode14during discharge, and is preferably expressed relative to the total lithium storage capacity of each electrode. An example of parameters related to the lithium balance model is described with reference toFIG. 2and EQ. 1.

FIG. 2graphically shows data100that is associated with an embodiment of the DC power source10that is described with reference toFIG. 1, including parameters that can be employed in a lithium balance model to determine electrode alignment (stoichiometry) from the full-cell OCV data and to estimate individual electrode capacities and a negative-to-positive (“N/P”) ratio. The lithium balance model can be expressed as follows:
Ucell(SOC)=Upos(yf−SOC*(yf−yi))−Uneg(xf+SOC*(xi−xf))   [1]

wherein:SOC is the state of charge of the DC power source10,Ucell(SOC) is the full-cell OCV at the SOC,Upos is the positive half-cell OCV at the SOC,Uneg is the negative half-cell OCV at the SOC,yi is the initial positive stoichiometric coefficient,yf is the final positive stoichiometric coefficient,xi is the initial negative stoichiometric coefficient, andxf is the final negative stoichiometric coefficient

The term “initial” refers to the state when the cell is fully charged, and “final” refers to the state when the cell is fully discharged.

The horizontal axis ofFIG. 2shows a cell power capacity (Ah)102and SOC (%)104, wherein the SOC ranges between a maximum value (100%) and a minimum value (0%). Plotted results include the full-cell OCV130, a positive half-cell OCV110and a negative half-cell OCV120. The left vertical axis106shows magnitude of the full-cell OCV and the positive half-cell OCV, and the right vertical axis108shows magnitude of the negative half-cell OCV, wherein the zero-point scale and order of magnitude of the left vertical axis differs from the zero-point scale and order of magnitude of the right vertical axis for purposes of illustrating the concepts described herein.

The positive half-cell OCV110, i.e., Upos, represents the potential difference between the positive electrode, e.g., positive electrode12, and a reference electrode13, and Uneg is the difference between the negative and the same reference electrode13. The reference electrode in this case is lithium metal, which has a fixed and unchanging potential that is arbitrarily described as 0.0V in this system. A reference electrode13may be fabricated from materials other than lithium metal, albeit with different but fixed and unchanging potentials and may be substituted to the same effect. Methods and devices for measuring the positive and negative half-cell OCVs are understood. The full-cell OCV, i.e., Ucell, represents an arithmetic difference between the positive half-cell OCV and the negative half-cell OCV, which can be determined at a given magnitude of SOC.

The positive half-cell OCV is indicated by line110inFIG. 2. Parameters associated with the positive half-cell OCV110include the initial positive stoichiometric coefficient yi, which is indicated by point112, and the final positive stoichiometric coefficient yf, which is indicated by point114. The initial positive stoichiometric coefficient yi represents an initial fractional lithium occupancy of the positive electrode at a cell SOC=100%, and the final positive stoichiometric coefficient yf represents a final fractional lithium occupancy of the positive electrode at a cell SOC=0%. The negative half-cell OCV is indicated by line120inFIG. 2. The initial negative stoichiometric coefficient xi122represents an initial fractional lithium occupancy of the negative electrode at SOC=100%, and the final negative stoichiometric coefficient xf124represents a final fractional lithium occupancy of the negative electrode at SOC=0%. The initial positive stoichiometric coefficient yi112, the final positive stoichiometric coefficient yf114, the initial negative stoichiometric coefficient xi122and the final negative stoichiometric coefficient xf124relate to electrode alignment of the DC power source10. A range for a positive capacity QposT140and a range for a negative capacity QnegT150are also indicated.

The positive capacity QposT140is determined based upon the cell power capacity (capacity) in relation to the initial positive stoichiometric coefficient yi and the final positive stoichiometric coefficient yf, and can be calculated as follows:

The negative capacity QnegT150is determined based upon the cell power capacity (capacity) in relation to the initial negative stoichiometric coefficient xi and the final negative stoichiometric coefficient xf, and can be calculated as follows:

Parametric states for the positive half-cell OCV at the SOC, i.e., Upos, and the negative half-cell OCV at the SOC, i.e., Uneg, can be determined at a start-of-life point of the DC power source10.

The OCV of the DC power source10has a tendency to shift in-use. In-use states of the initial positive stoichiometric coefficient yi, the final positive stoichiometric coefficient yf, the initial negative stoichiometric coefficient xi and the final negative stoichiometric coefficient xf can be employed to monitor the OCV shift, all relate to electrode alignment of the DC power source10. The positive capacity QposT140and the negative capacity QnegT150can be employed to characterize the OCV shift.

FIG. 5graphically shows data that is associated with an embodiment of the DC power source10that is described with reference toFIG. 1at a start-of-life point. The horizontal axis shows a cell power capacity (Ah)502. Plotted results include the full-cell OCV504, a positive half-cell OCV506and a negative half-cell OCV508. The left vertical axis shows magnitude of the full-cell OCV and the positive half-cell OCV, and the right vertical axis shows magnitude of the negative half-cell OCV, wherein the zero-point scale and order of magnitude of the left vertical axis differs from the zero-point scale and order of magnitude of the right vertical axis for purposes of illustrating the concepts described herein. A positive capacity QposT540can be determined by determining the relevant states and employing EQ. 2, and a negative capacity QnegT550can be determined by determining the relevant states and employing EQ. 3. Overlap of the positive capacity QposT540and the negative capacity QnegT550can be employed to define a cell window, with unused portions of the full-cell OCV504, the positive half-cell OCV506and the negative half-cell OCV508being indicated by dashed lines.

FIG. 6graphically shows data that is associated with an embodiment of the DC power source10that is described with reference toFIG. 1when it is in-use, including repetitive cycles of charging and discharging. The horizontal axis shows a cell capacity (Ah)602. Plotted results include the full-cell OCV604, a positive half-cell OCV606and a negative half-cell OCV608. The left vertical axis shows magnitude of the full-cell OCV and the positive half-cell OCV, and the right vertical axis shows magnitude of the negative half-cell OCV, wherein the zero-point scale and order of magnitude of the left vertical axis differs from the zero-point scale and order of magnitude of the right vertical axis for purposes of illustrating the concepts described herein. A positive capacity QpTas640can be determined by determining the relevant states and employing EQ. 2, and a negative capacity QnegT650can be determined by determining the relevant states and employing EQ. 3. Overlap of the positive capacity QposT640and the negative capacity QnegT650can be employed to define a cell window, with unused portions of the full-cell OCV604, the positive half-cell OCV606and the negative half-cell OCV608being indicated by dashed lines.

A comparison between the cell window525associated with start-of-life of the DC power source10ofFIG. 5and the cell window625associated with in-use performance of the DC power source10ofFIG. 6can be employed to characterize the OCV shift and improve predictability of parameters related to battery state. The indicated overlap of the positive capacity QposT540and the negative capacity QnegT550can be employed to determine electrode alignment from the full-cell OCV data, which may be an indication of a stoichiometric point.

A ratio, referred to herein as negative/positive or “N/P” can be determined as follows, based upon the initial positive stoichiometric coefficient yi, the final positive stoichiometric coefficient yf, the initial negative stoichiometric coefficient xi and the final negative stoichiometric coefficient xf.

The N/P ratio is an indicator of the cell capacity (Ah) of the DC power source10. This relationship is shown with reference toFIG. 9.

The lithium balance model described with reference to EQ. 1 andFIG. 2can be advantageously employed to provide an in-use evaluation of an embodiment of the DC power source10described with reference toFIG. 1. This evaluation can include characterizing the DC power source10by monitoring states to determine a positive half-cell OCV, a negative half-cell OCV, and a full-cell OCV for each of a plurality of SOC states between a minimum SOC and a maximum SOC at a start-of-life point of the DC power source10.FIG. 3graphically shows an example of a characteristic curve310for the positive half-cell OCV, wherein the positive half-cell OCV310is shown in relation to SOC305. The characteristic curve310is preferably determined employing low charge/discharge rates, wherein the characteristic curve during charging is indicated by line313and the characteristic curve during discharging is indicated by line311.FIG. 4graphically shows an example of a characteristic curve410for the negative half-cell OCV, wherein the negative half-cell OCV is shown in relation to SOC405, which is plotted on the horizontal axis. The characteristic curve410is preferably determined employing low charge/discharge rates, wherein the characteristic curve during charging is indicated by line411and the characteristic curve during discharging is indicated by line413.

The lithium balance model, including EQ. 2, can be transformed to executable code including an algorithm and calibrated coefficients, which are stored in the memory storage device of the controller30. The lithium balance model can be executed to determine a plurality of states, including the initial positive stoichiometric coefficient yi, the final positive stoichiometric coefficient yf, the initial negative stoichiometric coefficient xi, and the final negative stoichiometric coefficient xf, all of which associated with a fractional lithium occupancy at the start-of-life point of the DC power source. These values can be stored in the memory device34of the controller30.

During in-use operation of a system that employs the DC power source10, an in-use state for the full-cell OCV can be determined by direct monitoring or another suitable measurement system.

The controller30can execute an optimization routine employing the lithium balance model of EQ. 2 and the in-use state for the full-cell OCV to determine in-use states for the initial positive stoichiometric coefficient yi, the final positive stoichiometric coefficient yf, the initial negative stoichiometric coefficient xi, and the final negative stoichiometric coefficient xf. The optimization routine can be a suitable routine, e.g., a least-squares minimization method that employs the in-use state for the full-cell OCV, i.e., Ucell(SOC). The optimization routine employs the in-use state for the full-cell OCV and the values for the positive half-cell OCV in relation to the SOC and the negative half-cell OCV in relation to the SOC to determine the in-use states.

The optimization routine can be simplified so that it finds in-use values for the final positive stoichiometric coefficient yf and the initial negative stoichiometric coefficient xi.FIG. 7graphically shows states for the final positive stoichiometric coefficient yf710and the initial negative stoichiometric coefficient xi720in relation to the cell capacity (Ah), which is indicated on the x-axis705and decreases from left to right. The cell capacity (Ah) indicates a maximum amount of electrical energy that can be stored on the DC power source10. As indicated, the final positive stoichiometric coefficient yf710and the initial negative stoichiometric coefficient xi720both decrease with a decrease in the cell capacity (Ah).FIG. 8graphically shows states for the initial positive stoichiometric coefficient yi810and the final negative stoichiometric coefficient xf820in relation to the cell power capacity (Ah), which is indicated on the x-axis805and decreases from left to right. As indicated, the initial positive stoichiometric coefficient yi810and the final negative stoichiometric coefficient xf820remain unchanged with a decrease in the cell capacity (Ah). As such, the initial positive stoichiometric coefficient yi810and the final negative stoichiometric coefficient xf820can be pre-calibrated and stored in the memory device34, and do not have to be determined in-use.

The in-use states for the initial positive stoichiometric coefficient yi, the final positive stoichiometric coefficient yf, the initial negative stoichiometric coefficient xi, and the final negative stoichiometric coefficient xf are associated with the electrode alignment of the DC power source10, and can be employed to calculate the negative-to-positive (“N/P”) ratio, e.g., as is described with reference to EQ. 4. The N/P ratio can be employed to evaluate the DC power source10, including evaluating its service life.

FIG. 9graphically shows data associated with in-use service of an embodiment of the DC power source10described with reference toFIG. 1, and include an N/P ratio910and cell capacity (Ah)920that is plotted in relation to service life905(e.g., in units of days). The scale for the N/P ratio is indicated on the left vertical axis and the scale for the cell capacity (Ah) is indicated on the right vertical axis. The N/P ratio of 1.0 is indicated by a horizontal line. The cell capacity920is shown to decrease with an increase in the service life. The N/P ratio is greater than 1.0 for a long period of time, and then begins to decrease with a decrease in the cell capacity920. Critically, when the cell capacity920is about 50% of its original capacity, the N/P ratio910decreases to a level that is less than 1.0. This relationship between the cell capacity920and the N/P ratio910has been shown to be a repeatable characteristic of embodiments of the DC power source10, and thus can be employed in an on-board routine to monitor the DC power source10non-intrusively.

The concepts described herein illustrate an example method of a computing system that either stores instructions thereon or receives instructions from a remote controller that is in communication with the system. The concepts may be implemented through a computer algorithm, machine executable code, non-transitory computer-readable medium, or software instructions programmed into a suitable programmable logic device(s), such as the one or more modules, a server in communication therewith, a mobile device communicating with the computing system and/or server, or a combination thereof.

Any combination of one or more computer-usable or computer-readable media may be utilized. For example, a computer-readable medium may include one or more of a portable computer diskette, a hard disk, a random access memory (RAM) device, a read-only memory (ROM) device, an erasable programmable read-only memory (EPROM or Flash memory) device, a portable compact disc read-only memory (CDROM), an optical storage device, and a magnetic storage device. Computer program code for carrying out operations of the present disclosure may be written in a combination of one or more programming languages.