Cyclic Coulometry Method

Abstract

Systems, devices, and methods for diagnosing electrochemical cells using cyclic coulometry are discussed. An exemplary battery diagnostic system includes a current generator for generating symmetrical charge and discharge currents for exciting an electrochemical cell and a cyclic coulometer for evaluating the performance of the electrochemical cell. The cyclic coulometer can adjust at least one of a charge time for applying a charge current or a discharge time for applying a discharge current to maintain a monitored cell voltage toward a specific set value. Adjusting the charge or discharge time can be achieved by changing the current switch timing for reversing the current from a first current direction to a second current direction. The cyclic coulometer measures one or more electrical parameters during a charge or discharge cycle and generates a performance metric using the measured electrical parameters.

Description

[Technical field]

[0001] This document relates generally to electrochemical cells, and more specifically to systems, apparatus, and methods for cycling electrochemical cells using cyclic coulometry. [Background technology]

[0002] Coulometry is an electrochemical technique that measures the total coulombs of electricity consumed or produced during an electrochemical reaction. Today, there are two basic categories of coulometry techniques. Potentiostatic coulometry applies a constant potential to an electrochemical cell using a potentiostat. Galvanostatic coulometry applies a constant current to an electrochemical cell using a galvanostat. In both cases, the total charge Q passing through the electrochemical cell is calculated by integrating the current as a function of time. Coulometry has many applications in the field of electrochemistry. For example, coulometry can be used to characterize the performance of batteries, fuel cells, or other electrochemical reactions.

[0003] Lithium-ion (Li-ion) batteries are becoming the dominant battery chemistry. A Li-ion battery is a type of rechargeable battery in which lithium ions move from the negative electrode to the positive electrode during discharge and back during charging. Lithium-ion batteries have become the most common battery type in modern battery electric vehicles (BEVs) primarily due to their high energy density. Unlike starting, lighting, and ignition batteries, Li-ion batteries in BEVs provide power for sustained periods of time and are characterized by a relatively high power-to-weight ratio, specific energy, and energy density. They also have a low self-discharge rate.

[0004] Cycle life is a measure of the number of charge-discharge cycles a battery can undergo before its nominal capacity falls below a certain threshold (e.g., 80% of the initial rated capacity). Cycle life can vary widely depending on cycling conditions, chemistry, cell design, and manufacturing quality. For example, depending on how a lithium-ion battery is used in an application, it may show significant degradation and last only a few hundred cycles, or it may be designed to last thousands of cycles.

[0005] Technologies that improve the abuse resistance or cycle life of lithium-ion batteries would be of great commercial interest. However, given the existence of lithium-ion chemistries that can be cycled for many years, it is difficult to prove new technologies or even iterate existing formulations to improve cycle life.

[0006] Cycle testing is an important battery qualification test. A typical battery evaluation process involves cycling a test cell under a fixed current between a lower and upper voltage limit to investigate the battery's performance over the entire cycle life. The cell is subjected to repeated charge-discharge cycles to establish that the cell meets the manufacturer's cycle life claims. Various cell performance parameters such as temperature, capacity, impedance, power output, and discharge time can be monitored and recorded during the test. Cycle testing establishes that the battery's performance is in line with the reliability and life expectancy of the end product.

[0007] High-precision coulometers can measure the coulombic efficiency of lithium-ion batteries with an accuracy of 50 ppm. The coulombic efficiency metric compares the coulombs required to charge a battery with the coulombs obtained from discharging. Additional battery-specific tests can also be performed under rigorous and wide-ranging test conditions to evaluate the risk associated with the tested battery. Knowledge of the cell's performance in various operating environments and usage patterns can help optimize battery designs for various applications. Summary of the Invention [Problem to be solved by the invention]

[0008] This document discusses, among other things, systems, devices and methods for diagnosing electrochemical cells, such as battery cells, using the technique of cyclic coulometry. [Means for solving the problem]

[0009] An exemplary battery diagnostic system includes a current generator for generating symmetrical charge and discharge currents for exciting an electrochemical cell, and a cyclic coulometer for evaluating the performance of the electrochemical cell. The cyclic coulometer includes a controller circuit for adjusting at least one of a charge time for applying the charge current or a discharge time for applying the discharge current to maintain the cell voltage at a particular set value. Adjusting the charge or discharge time may be accomplished by changing a current switch timing for reversing the current from a first current direction to a second current direction. A measurement circuit measures one or more electrical parameters during the charge or discharge cycle and generates battery metrics using the measured electrical parameters.

[0010] Example 1 is a system for testing an electrochemical cell, comprising: a current generator configured to generate symmetrical charge and discharge currents during a cycling period to respectively charge and discharge the electrochemical cell; a cyclic coulometer including a controller circuit coupled to the current generator configured to adjust at least one of a charge time or a discharge time to control a monitored cell voltage of the electrochemical cell towards a particular set value and to control the current generator to electrically cycle the electrochemical cell using the charge and discharge currents according to at least one of the adjusted charge time or the adjusted discharge time; and a measurement circuit configured to measure one or more electrical parameters and generate a performance metric of the electrochemical cell using the measured one or more electrical parameters.

[0011] In Example 2, the subject matter of Example 1 optionally includes a current generator that can be configured to generate a square wave current using a unipolar DC source. In Example 3, the subject matter of any one or more of Examples 1-2 optionally includes a controller circuit that can be configured to adjust a charge time or a discharge time by varying a current switch timing to reverse from a charge current to a discharge current, where the charge current and the discharge current have opposite current directions.

[0012] In Example 4, the subject matter of Example 3 includes a current switch circuit including switches that can be configured to, optionally, in response to a control signal from a controller circuit, close only a first one or more of the switches to generate a charging current for charging the electrochemical cell, and close only a second one or more of the switches to generate a discharging current for discharging the electrochemical cell according to a current switch timing.

[0013] In Example 5, the subject matter of Example 4 optionally includes one or more of the switches, which may be FET transistors. In Example 6, the subject matter of any one or more of Examples 3-5 optionally includes one or more measured electrical parameters that may include a voltage or current response of the electrochemical cell, and the control circuitry is configured to determine or update the current switch timing using the monitored voltage or current response.

[0014] In Example 7, the subject matter of Example 6 optionally includes a controller circuit that may include a proportional-integral (PI) controller or a proportional-integral-derivative (PID) controller. In Example 8, the subject matter of any one or more of Examples 6-7 optionally includes a monitored voltage or current response that can include one or more of an average or peak cell voltage over all frames including the adjusted charge time and the adjusted discharge time, an average or peak cell voltage over the adjusted charge time, an average or peak cell voltage over the adjusted discharge time, an average or peak cell current over all frames, an average or peak cell current over the adjusted charge time, or an average or peak cell current over the adjusted discharge time.

[0015] In example 9, the subject matter of any one or more of examples 6-8 optionally includes a controller circuit that can be configured to use the monitored voltage or current response to determine current switch timing including determining an overcharge time or an overdischarge time, and to increase or decrease the charge time by the determined overcharge time, or to increase or decrease the base discharge time by the determined overdischarge time.

[0016] In example 10, the subject matter of example 9 optionally includes an overcharge time or an overdischarge time that can be represented by a count of ticks, each having a duration of a specified switching timer resolution.

[0017] In Example 11, the subject matter of any one or more of Examples 6-10 includes a controller circuit that can be configured to optionally further use one or more of ambient temperature information of the electrochemical cell testing environment, or a state of charge or state of health of the electrochemical cell to determine the current switch timing.

[0018] In Example 12, the subject matter of any one or more of Examples 1-11 optionally includes a measurement circuit that can include a performance metric generator configured to determine an amount of total charge applied during at least a portion of a cycling period, and to determine a self-discharge rate using the determined amount of total charge applied, the self-discharge rate representing an applied current required to maintain a cell voltage of the electrochemical cell at a particular set value.

[0019] In Example 13, the subject matter of Example 12 optionally includes a cyclic coulometer that can include a coulomb counter configured to measure an amount of total charge applied during a specified portion of a cycling period.

[0020] In example 14, the subject matter of any one or more of examples 12-13 optionally includes a cyclic coulometer that can be configured to determine an amount of total charge applied, including an amount of total charge applied per frame (QPF).

[0021] In Example 15, the subject matter of Example 14 optionally includes a cyclic coulometer that can be configured to determine the QPF by integrating the applied current over time in a frame.

[0022] In Example 16, the subject matter of any one or more of Examples 14-15 optionally includes a performance metric generator that can be configured to generate a trend of the QPF over time and determine the self-discharge rate using a slope of the generated QPF trend.

[0023] In example 17, the subject matter of any one or more of examples 14-16 optionally includes a cyclic coulometer that can be configured to determine a first amount of total charge applied only during a charge period and a second amount of total charge applied only during a discharge period following the charge period, and determine the QPF using a difference between the first amount of total charge applied and the second amount of total charge applied.

[0024] In Example 18, the subject matter of Example 17 includes a cyclic coulometer that can be optionally configured to determine a first amount of total charge applied using a first total tick count only during the charging period and to determine a second amount of total charge applied using a second total tick count only during the discharging period.

[0025] In Example 19, the subject matter of any one or more of Examples 12-18 optionally can include a cell voltage of the electrochemical cell, and wherein the performance metric generator is configured to determine an equivalent series resistance (ESR) of the electrochemical cell using at least one of: (1) a charge voltage during a charging period or a discharge voltage during a discharging period, and (2) an applied current.

[0026] In Example 20, the subject matter of Example 19 optionally includes a performance metric generator that can be configured to generate an ESR curve as a function of an amount of total charge applied and to use the slope of the ESR curve at a particular amount of total charge applied to determine the percentage ESR change per coulomb lost.

[0027] In Example 21, the subject matter of Example 20 optionally includes a performance metric generator that can be configured to determine a plurality of ESR rate changes under different test conditions, each of the different test conditions represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generate a representation of the plurality of ESR rate changes over the parameter set.

[0028] In Example 22, the subject matter of any one or more of Examples 19-21 optionally includes a performance metric generator that can be configured to determine the ESR of the electrochemical cell using at least one of a difference between a charge voltage and an average cell voltage, or a difference between a discharge voltage and an average cell voltage.

[0029] In Example 23, the subject matter of Example 22 optionally includes a performance metric generator that can be configured to determine the average cell voltage using an average or weighted average of the charge and discharge voltages.

[0030] In Example 24, the subject matter of any one or more of Examples 12-23 optionally includes a performance metric generator that can be configured to determine a plurality of self-discharge rates under different test conditions, each of the different test conditions represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generate a representation of the plurality of self-discharge rates across the parameter sets.

[0031] In Example 25, the subject matter of Example 24 optionally includes a representation of the multiple self-discharge rates, which may include a two- or multi-dimensional array, or a two- or multi-dimensional graph. In Example 26, the subject matter of any one or more of Examples 1-25 optionally includes an output device communicatively coupled to the cyclic coulometer, the output device configured to display the one or more measured electrical parameters or generated performance metrics of the electrochemical cell.

[0032] In Example 27, the subject matter of Example 26 optionally includes an output device that can be configured to display one or more of a plurality of self-discharge rates across the plurality of test conditions, or a plurality of rates of ESR change across the plurality of test conditions.

[0033] In Example 28, the subject matter of Example 27 optionally includes an output device that can be configured to display a three-dimensional (3D) loss rate map representing a plurality of self-discharge rates across a plurality of test conditions, each represented by two parameters selected from the parameter set.

[0034] In example 29, the subject matter of any one or more of examples 27-28 optionally includes an output device that can be configured to display a three-dimensional (3D) ESR rate map representing a plurality of ESR rate changes across a plurality of test conditions, each represented by two parameters selected from the parameter set.

[0035] Example 30 is a method for testing an electrochemical cell, comprising: electrically cycling an electrochemical cell by applying a charge current during a charging time and a discharge current during a discharging time via a current generator during a cycling period, the charge current and the discharge current being symmetrical and having opposite directions; measuring one or more electrical parameters during the electrical cycling of the electrochemical cell via a measurement circuit; adjusting the charge time or the discharge time to control a monitored cell voltage of the electrochemical cell toward a particular set value via a controller circuit; and generating a performance metric of the electrochemical cell using the one or more measured electrical parameters via the measurement circuit.

[0036] In Example 31, the subject matter of Example 30 optionally includes adjusting a charge time or a discharge time, which may include updating a current switch timing to reverse from a charge current to a discharge current.

[0037] In Example 32, the subject matter of Example 31 optionally includes measuring one or more electrical parameters, which may include a voltage or current response of the electrochemical cell, and updating the current switch timing using the monitored voltage or current response.

[0038] In example 33, the subject matter of any one or more of examples 31-32 optionally includes adjusting the charge time or discharge time, which can include increasing or decreasing the charge time by an overcharge time, the overcharge time being represented by a count of ticks, each having a duration of a specified switching timer resolution.

[0039] In example 34, the subject matter of any one or more of examples 31-33 optionally includes adjusting the charge time or discharge time, which can include increasing or decreasing the discharge time by an excess discharge time, the excess discharge time being represented by a count of ticks, each having a duration of a specified switching timer resolution.

[0040] In Example 35, the subject matter of any one or more of Examples 30-34 optionally includes generating a performance metric that can include determining an amount of total charge applied during a specified portion of a cycling period and determining a self-discharge rate using the determined amount of total charge applied, where the self-discharge rate represents an applied current required to maintain a cell voltage of the electrochemical cell at a particular set value.

[0041] In Example 36, the subject matter of Example 35 optionally includes an amount of total charge applied, which can include a total charge applied per frame (QPF) corresponding to a time of the frame, and determining the self-discharge rate includes using a slope of the trend of the QPF over time.

[0042] In Example 37, the subject matter of Example 36 optionally includes determining the QPF including integrating the applied current over time within the frame. In example 38, the subject matter of any one or more of examples 36-37 includes determining a QPF, which can optionally include determining a first amount of total charge applied only during a charging period and a second amount of total charge applied only during a discharging period following the charging period, and determining the QPF using a difference between the first amount of total charge applied and the second amount of total charge applied.

[0043] In Example 39, the subject matter of Example 38 optionally includes a first amount of total charge applied that can be determined by using a first total tick count only during the charging period, and a second amount of total charge applied that can be determined using a second total tick count only during the discharging period.

[0044] In example 40, the subject matter of any one or more of examples 35-39 optionally includes one or more measured electrical parameters that may include a cell voltage of the electrochemical cell, and generating the performance metric may include determining an equivalent series resistance (ESR) of the electrochemical cell using (1) at least one of a charge voltage during a charging period or a discharge voltage during a discharging period, and (2) an applied current.

[0045] In Example 41, the subject matter of Example 40 includes generating a performance metric which may optionally include generating an ESR curve as a function of the amount of total charge applied and determining the percentage ESR change per coulomb lost using the slope of the ESR curve at a particular amount of total charge applied.

[0046] In Example 42, the subject matter of Example 41 optionally includes determining a plurality of ESR rates of change under different test conditions, each of the different test conditions represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generating a representation of the plurality of ESR rates of change over the parameter set, the representation including a two-dimensional or multi-dimensional array, or a two-dimensional or multi-dimensional graph.

[0047] In Example 43, the subject matter of any one or more of Examples 35-42 optionally includes generating a performance metric that can include determining a plurality of self-discharge rates under different test conditions each represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generating a representation of the plurality of self-discharge rates across the parameter sets, where the representation can include a two-dimensional or multi-dimensional array, or a two-dimensional or multi-dimensional graph.

[0048] In Example 44, the subject matter of Example 43 optionally includes displaying one or more of the measured one or more electrical parameters or the measured performance metrics on a user interface.

[0049] Example 45 is at least one machine-readable medium containing instructions that, when executed by a machine, cause the machine to electrically cycle an electrochemical cell by applying a charge current during a charge time and a discharge current during a discharge time, during a cycling period, where the charge and discharge currents are symmetric and have opposite directions, measure one or more electrical parameters during the electrical cycling of the electrochemical cell, adjust the charge time or the discharge time to control a monitored cell voltage of the electrochemical cell toward a particular set value, and generate a performance metric for the electrochemical cell using the measured one or more electrical parameters.

[0050] In Example 46, the subject matter of Example 45 optionally includes instructions that, when executed by the machine, cause the machine to measure one or more electrical parameters including a voltage or current response of the electrochemical cell and update the current switch timing for reversing from a charging current to a discharging current using the monitored voltage or current response.

[0051] In example 47, the subject matter of any one or more of examples 45-46 optionally includes instructions that, when executed by the machine, cause the machine to determine an amount of total charge applied during a specified portion of a cycling period and determine a self-discharge rate using the determined amount of total charge applied, the self-discharge rate representing an applied current needed to maintain a cell voltage of the electrochemical cell at a particular set value.

[0052] In Example 48, the subject matter of Example 47 optionally includes an amount of total charge applied, which may include a total charge applied per frame (QPF) corresponding to a time of the frame, and instructions that, when executed by the machine, cause the machine to generate a trend of the QPF over time and use a slope of the generated QPF trend to determine the self-discharge rate.

[0053] In example 49, the subject matter of any one or more of examples 47-48 optionally includes one or more measured electrical parameters, which may include a cell voltage of the electrochemical cell, and instructions that, when executed by the machine, cause the machine to determine an equivalent series resistance (ESR) of the electrochemical cell using at least one of (1) the charge voltage during a charging period or the discharge voltage during a discharging period, and (2) the applied current, generate an ESR curve as a function of the amount of total charge applied, and use the slope of the ESR curve at a particular amount of total charge applied to determine the ESR rate of change per coulomb lost.

[0054] In Example 50, the subject matter of Example 49 optionally includes instructions that, when executed by a machine, cause the machine to determine a plurality of ESR rates of change under different test conditions, each of the different test conditions represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generate a representation of the plurality of ESR rates of change over the parameter sets, the representation including a two- or multi-dimensional array, or a two- or multi-dimensional graph.

[0055] In example 51, the subject matter of any one or more of examples 47-50 optionally includes instructions that, when executed by a machine, cause the machine to determine a plurality of self-discharge rates under different test conditions, each represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, and generate a representation of the plurality of self-discharge rates across the parameter sets, the representation including a two- or multi-dimensional array, or a two- or multi-dimensional graph.

[0056] Example 52 is at least one machine-readable medium comprising instructions that, when executed by a machine, cause the machine to perform a method as discussed in any one or more of Examples 30-44.

[0057] Example 53 is a system for testing an electrochemical cell. The system includes means for carrying out the method as discussed in any one or more of Examples 30-44. The cyclic coulometry techniques discussed in this document are useful for improving the determination of the relative performance effects of variables utilized to generate, manufacture, or store electrochemical cells and batteries in an accelerated manner. Cyclic coulometry can be useful for optimizing cell chemistries, manufacturing methods, material selection, or other variables of interest. According to some embodiments, the cyclic coulometry techniques discussed herein can be used to determine the quality of electrochemical cells available for purchase. Cyclic coulometry can also be used to non-destructively characterize the quality of cells prior to inclusion in a product for sale in an appropriate manner.

[0058] This summary is an overview of some of the teachings of the present application and is not intended to be an exclusive or exhaustive treatment of the present subject matter. Further details regarding the present subject matter are found in the detailed description and the appended claims. Other aspects of the present disclosure will be apparent to those skilled in the art upon reading and understanding the following detailed description and viewing the drawings that form a part thereof, each of which should not be taken in a limiting sense. The scope of the present disclosure is defined by the appended claims and their legal equivalents.

[0059] Various embodiments are illustrated by way of example in the accompanying drawing figures. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present subject matter. [Brief description of the drawings]

[0060] [Figure 1] FIG. 1 is a block diagram illustrating an example cyclic coulometer system and a portion of an environment in which the system may operate. [Figure 2A] FIG. 1 is a schematic diagram illustrating an example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes with specific current switch timing to generate charging and discharging currents. [Figure 2B] FIG. 1 is a schematic diagram illustrating an example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes with specific current switch timing to generate charging and discharging currents. [Figure 2C] FIG. 1 is a schematic diagram illustrating an example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes with specific current switch timing to generate charging and discharging currents. [Figure 3A] FIG. 13 is a schematic diagram illustrating another example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes at specific current switch timings to generate charging and discharging currents. [Figure 3B] FIG. 13 is a schematic diagram illustrating another example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes at specific current switch timings to generate charging and discharging currents. [Figure 3C] FIG. 13 is a schematic diagram illustrating another example of at least a portion of a current switching circuit configured to provide precisely timed polarity changes at specific current switch timings to generate charging and discharging currents. [Figure 4A] FIG. 11 is a timing diagram illustrating an example of using an overtime in a charge or discharge step to adjust the charge or discharge time. [Figure 4B] FIG. 11 is a timing diagram illustrating an example of using an overtime in a charge or discharge step to adjust the charge or discharge time. [Figure 4C] FIG. 11 is a timing diagram illustrating an example of using an overtime in a charge or discharge step to adjust the charge or discharge time. [Figure 4D] FIG. 11 is a timing diagram illustrating an example of using an overtime in a charge or discharge step to adjust the charge or discharge time. [Figure 4E] FIG. 11 is a timing diagram illustrating an example of using an overtime in a charge or discharge step to adjust the charge or discharge time. [Diagram 5] FIG. 2 is a block diagram illustrating an example of a battery testing system for diagnostic testing using the cycle coulometer system of FIG. 1. [Figure 6A] FIG. 2 illustrates an example of at least a portion of a current steering circuit configured to control current switch timing during charge and discharge cycles. [Figure 6B] 6B is a timing diagram illustrating, by way of example, the logical timing of forward (charging) and reverse (discharging) currents generated by the current steering circuit of FIG. 6A. [Figure 7]FIG. 1 illustrates at least a portion of a data acquisition system (DAS) for measuring electrical parameters during cyclic testing and the environment in which the DAS operates. [Figure 8] 6 is a graph illustrating, by way of example and not limitation, voltage and current responses during cyclic testing as obtained using the test system of FIG. 5 . [Figure 9] 1 is a graph illustrating, by way of example and not limitation, the equivalent series resistance (ESR) of a cell under test plotted against the amount of total charge applied. [Figure 10A] By way of example and not limitation, graphical representations of performance metrics calculated under different test conditions, such as self-discharge rate or ESR rate of change, are illustrated. [Figure 10B] By way of example and not limitation, graphical representations of performance metrics calculated under different test conditions, such as self-discharge rate or ESR rate of change, are illustrated. [Figure 10C] By way of example and not limitation, graphical representations of performance metrics calculated under different test conditions, such as self-discharge rate or ESR rate of change, are illustrated. [Figure 11] 2 is a flow chart illustrating an example of a method for performing diagnostic testing of a device under test (DUT) using cyclic coulometry as described with reference to FIG. 1. [Figure 12] 5A-5C are flow charts illustrating respective methods of generating various battery metrics using electrical measurements taken during cycle testing. [Figure 13] 5A-5C are flow charts illustrating respective methods of generating various battery metrics using electrical measurements taken during cycle testing. [Figure 14] 1 illustrates generally a block diagram of an example machine upon which any one or more of the techniques (eg, methodologies) discussed herein may be implemented. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0061] A battery cycler is an apparatus or tool for charging and discharging batteries under controlled conditions and evaluating battery performance based on various battery metrics such as slippage rate, coulombic efficiency, energy capacity, rate capability, or capacity retention, among others. Traditionally, battery cycling is performed between fixed voltage limits. During charging, current is passed until the battery reaches a preset charge voltage limit (charge setpoint). The battery is then discharged until it reaches a discharge voltage limit (discharge setpoint). The charge and discharge cycles then follow. The charge and discharge rates are typically determined by a fixed C-rate. For example, a fully charged battery rated at 1 ampere-hour (Ah) would deliver a discharge current of 1 A for 1 hour at a 1C rate, 500 mA for 2 hours at a 0.5C rate, or 2 A for 0.5 hours at a 2C rate. Cell inefficiencies accumulate during cell cycling, causing capacity loss (coulomb loss). As the cell ages, the internal resistance of the cell increases over time.

[0062] Coulometry is an electrochemical technique that measures the quantity of electricity, in coulombs, consumed or produced during an electrochemical reaction. Traditionally, two coulometry techniques are used. Potentiostatic coulometry (also known as constant-potential coulometry) applies a constant potential to the battery under test using a potentiostat, an electronic device for controlling three-electrode cells and performing electroanalytical experiments. Galvanostatic or amperostatic coulometry (also known as constant-current coulometry) applies a constant current to the battery using a galvanostat, a device that maintains the current through the electrolytic cell constant in a coulometric titration, ignoring any changes in the load itself. In both cases, the amount of applied total charge (Q) passing through the electrochemical cell may be calculated by integrating the current as a function of time.

[0063] Coulombic efficiency (CE) describes the efficiency of a battery system. CE is the total charge (Q 放電 ) the total amount of charge applied to the battery over the entire cycle (Q充電 ) CE is a strong function of the C-rate. At low C-rates, more time is available for parasitic losses to occur, resulting in a lower measured CE metric. A slower C-rate helps to spread the data and differentiate the cells, but a slower C-rate may not truly represent the usage conditions experienced in most applications.

[0064] High precision coulometry (HPC) is a technique for characterizing CE that can detect with improved precision differences in cell performance between cells of different chemistries made to last thousands of cycles. Compared to conventional precision cyclers, HPC systems use faster data processing, more accurate current sources, and more stable voltage measurements.

[0065] Although HPC has been considered an accepted standard for evaluating battery chemistries, it has some limitations. For example, HPC is often used to measure the CE of lithium-ion batteries under slow charge-discharge cycling. The design of an HPC system can be complex, at least due to the long time scales involved in the charge-discharge cycle. In particular, the current source must be very stable so that the applied current remains constant over the long time (e.g., 20 hours) required for a full cycle. Stable, high-precision current sources are expensive and contribute to the overall cost of the system. Newer systems may even maintain the electronics in a temperature-controlled environment to prevent drift in the power electronics. In some cases, HPC may measure coulombic efficiency to an accuracy of 50 parts per million (ppm).

[0066] The basic premise of HPC is that more efficient batteries last longer. However, data shows that using CE alone to predict cycle life can be insufficient. To overcome this limitation, it has been proposed to use post-cycling charge transfer resistance along with CE to predict cycle life. However, this presents challenges as traditional measurements of internal resistance (IR) generally cannot be implemented during HPC, which requires post-mortem characterization. The cumulative coulombs lost between different test cells from an HPC test protocol are not the same. Typically, the resistance after charge transfer is a single data point measured under poorly defined conditions. HPC does not adequately distinguish between the various loss mechanisms that may be present because it cannot measure the increase in resistance after charge transfer as a function of coulombs lost.

[0067] Energy storage solutions are defined by the requirements of the application. Grid level storage related to voltage stability or regulatory control requires short cycles operating at high frequency. Automotive applications as well as renewable energy integration require energy storage with large capacity and deeper depth of discharge. Optimizing pack designs for various applications requires both technical and economic models of cell performance and life. However, cycle life varies significantly depending on cycling conditions, so a design optimal for one condition may not be ideal for another. Using the tools that exist today, it is difficult to prove the effect of various operating conditions on electrochemical storage durability using simple battery cyclers. Furthermore, current approaches are slow and provide complex data on durability.

[0068] At least for the foregoing, the present inventors have recognized an unmet need for improved coulometry for battery evaluation. Disclosed herein are systems, devices, and methods of cyclic coulometry. According to some embodiments, the cyclic coulometer can introduce small DC pulses and automatically compensate for voltage drops over time due to cumulative coulomb losses, thereby maintaining the monitored cell potential at a set point. In some examples, the cyclic coulometer determines the applied coulomb rate required to maintain the test cell at a specified set point voltage under different cell conditions, thus effectively parameterizing the loss rate at a particular condition (e.g., temperature, set point voltage, or applied C-rate). Loss rate curves or loss rate maps can be generated and presented to a user using the parameterized loss rates.

[0069] The cyclic coulometry discussed herein may be implemented in a battery diagnostic system. According to some embodiments, the battery diagnostic system includes a current generator for generating symmetrical charge and discharge currents for exciting an electrochemical cell, and a cyclic coulometer for evaluating the performance of the electrochemical cell. The cyclic coulometer includes a controller circuit for adjusting at least one of a charge time for applying a charge current or a discharge time for applying a discharge current to maintain a monitored cell voltage toward a particular set value. Adjusting the charge or discharge time may be accomplished by changing a current switch timing for reversing the current from a first current direction to a second current direction. The measurement circuit measures one or more electrical parameters during a charge or discharge cycle and generates battery metrics using the measured electrical parameters.

[0070] Cyclic coulometry as discussed herein improves battery cycling and provides complete information on battery performance and diagnostics. For example, cyclic coulometry allows one to measure capacity loss at a given C-rate or temperature for any state of charge. In one example, researchers can independently examine fade rates at different pre-set cell voltages. High voltage stability can be studied while avoiding losses associated with full discharge depth cycling.

[0071] Cyclic coulometry provides simultaneous measurements of CE and internal resistance (IR). The average voltage for the full duty cycle is controlled to a set value, but the voltage response of each half cycle may be used to calculate an IR measurement. IR increases over time as coulomb inefficiencies accumulate. Traditional HPC cannot make IR measurements during HPC testing. Instead, the increase in IR must be measured after the completion of the HPC test (and thus the IR so measured is also known as the charge transfer resistance after cycling). However, the resistance after charge transfer is a single data point measured with poor definition. For example, the accumulated coulombs lost between different test cells after an HPC test are not the same. In contrast, the cyclic coulometry discussed in this document advantageously measures both the increase in CE and IR simultaneously. Thus, the increase in charge transfer resistance may be expressed as a function of coulombs lost. Because both IR and CE must be given to predict cycle life, the cyclic coulometry discussed herein provides a more complete picture of cycle life and represents a significant advance over the information available from using current HPC techniques.

[0072] Another advantage of cyclic coulometry as discussed in this document is that it directly measures and presents (e.g., graphically in a 3D plot) the battery's differential loss rate versus load condition. For example, by cycling the applied C-rate from low to high levels, cyclic coulometry can automatically provide insight into both battery storage (corresponding to zero C-rate) and cycling losses as a function of C-rate in the same test. Cyclic coulometer systems can be implemented and deployed to prove new lithium-ion formulations and characterize the durability of commercial cells in applications.

[0073] The battery metrology discussed in this document provides direct measurement of loss rates at various cell conditions (temperature, setpoint voltage, applied C-rate, etc.). This allows battery manufacturers, storage designers, and material suppliers to iterate faster while gaining greater insight. For example, cell manufacturers can quickly measure the impact of manufacturing processes and designs on cell fidelity. Similarly, material developers can measure the impact of electrolyte additives or electrode formulations on cell stability at various operating conditions. Finally, energy storage end users can use cyclic coulometry to identify different commercial products, targeting those that perform best for load requirements, and develop improved battery management algorithms. Compared to traditional HPC technologies, cyclic coulometry discussed herein can better characterize battery performance at various cell conditions (e.g., C-rates, state of charge, among others), enabling accurate techno-economic evaluation of batteries under development, improving battery design and development. The engineering data generated by cyclic coulometry and data formulation (e.g., in the form of loss rate curves or loss rate maps as discussed below) can be used to create improved battery management protocols and techno-economic models for deployment of energy storage requiring long life.

[0074] FIG. 1 is a block diagram illustrating an example of a cyclic coulometer system 100 and some of the environments in which the system 100 may operate. The system 100 may be used to measure the total coulombs applied during a charge / discharge cycle operation on a device under test (DUT) 150 to obtain information about the internal state of the DUT 150 and evaluate its performance. The system 100 includes a current source 110, a switching circuit 120, and a process controller 130. In contrast to conventional coulometry, which applies a set current or voltage, the cyclic coulometer system 100 may adjust the charge time for applying a charge current or the discharge time for applying a discharge current to the DUT 150 to achieve various battery test objectives. According to some embodiments, adjusting at least one of the charge time or the discharge time may be achieved by changing the current switch timing between the charge and discharge steps in a cycling period with high time resolution. In one example, the cyclic coulometer system 100 may measure the applied coulomb rate required to maintain a process variable in a desired state. In another example, the cyclic coulometer 100 may measure the loss rate of a battery received from a manufacturer to determine cell quality. In various examples, the cyclic coulometer system 100 can perform diagnostic tests under different cell conditions, such as temperature ranges, state of charge, or state of health, among other conditions of interest.

[0075] The DUT 150 can be any electrochemical cell, such as a battery, fuel cell, flow cell, or other electrochemical cell. Coulometric testing of the DUT 150 may be performed using conventional 2-wire, 3-wire, or 4-wire connections. To minimize noise to measure small applied currents, it is desirable to minimize disturbances to the DUT 150 that contribute noise in the measured variables. In one example, the DUT 150 may be placed in a tightly controlled thermal environment during cycle testing. Prior to testing, the DUT 150 may be stabilized at a set state of charge (representing the amount of energy remaining compared to the energy at full charge) or aged to achieve various states of health (representing the ability to provide a specified performance compared to a new battery).

[0076] The current source 110 can output a quiet current with little noise and can be a benchtop or precision power supply configured to provide a current for charging and discharging the DUT 150 during a full cycling period. The current source 110 can operate in a potentiostat mode or a galvanostat mode. The output current can have a predetermined waveform with specific parameter values ​​(e.g., amplitude, cycle period, frequency, duty cycle, etc.). In one example, the current source 110 can be a sine wave source. In another example, the current source 110 can be a square wave source.

[0077] In some examples, the current source 110 may be a direct current (DC) source configured to provide a unidirectional current at a specific amplitude. The current amplitude may be programmable. The cyclic coulometer system 100 may continuously measure the output current (e.g., charge current or discharge current). In one example, the current source 110 may output a stable current in a galvanostat mode and function substantially the same during the charge and discharge steps. In one example, the current source 110 may be a single unipolar current source including a reference, an amplifier, a sense resistor, and a feedback circuit, and may be configured to exhibit single digit PPM level stability for the duration of the test.

[0078] A switching circuit 120 coupled to the current source 110 may controllably (e.g., via a process controller 130) alternate the direction of a DC current output current to generate a square wave 122. A switching timer with a certain time resolution T may time the alternation of current direction. The switching timer may be part of the switching circuit 120 or may be otherwise coupled to the switching circuit 120. The resulting square wave has positive and negative phases, each with a duration that is a multiple of T. The resolution T of the switching timer may be a function of the frequency (f クロック ), where T=1 / f クロック seconds. For example, for a clock frequency of 5 MHz, the resolution of the switching timer is 200 nanoseconds (nsec). In one example, T is less than 500 nanoseconds. In another example, T is less than 1 microsecond (msec). In yet another example, T is about 5-10 milliseconds. A switched current may be applied to the DUT 150 during the cycling process.

[0079] If the current source 110 is a constant unipolar current source and the process controller 130 controls the switching circuit 120 to generate the square wave current 122, the process controller 130 may further control the switching circuit 120 to adjust at least one of the charge time or the discharge time to maintain an output variable, such as the average cell voltage, at a preset setting. 充電 and discharge time t 放電and t, both of which may be predetermined or programmable. The cycling period may be selected to be long enough for actual charge transfer to occur within the electrochemical cell under test so that the measured characteristics may be attributed to the desired cell state, yet short enough so that the cell voltage response to the charge and discharge steps does not deviate significantly from the cell set point. In one example, the cycling period is less than 10 minutes. In another example, the cycling period is about 5 minutes. In yet another example, the cycling period is about 60 seconds. Alternatively, the cycling period may be determined based on the desired applied current and the corresponding perturbation to the cell caused by the cycle. In one example, the charging time t 充電 is the discharge time t 放電 , resulting in symmetrical charge and discharge steps.

[0080] The process controller 130 controls the switching circuitry to adjust at least one of the charge time or the discharge time to control an output variable, such as the average cell voltage, toward a preset setting. In one example, adjusting the charge or discharge time may be accomplished by changing the timing of switching from the charge step to the discharge step during the charge / discharge cycle. Compared to a conventional cycler that controls the voltage (of a potentiostat) or the current (of a galvanostat), adjusting the charge or discharge time or current switch timing as discussed herein provides more precise yet stable control of the charge / discharge steps with a desired resolution. In various examples, the switching circuitry 120 can controllably switch the current direction using one or more voltage-controlled switches, such as transistors, examples of which are discussed below with reference to FIGS. 2A-2C. Alternatively, the current source 110 may be a bidirectional source that controllably outputs a current in either a first direction to charge the DUT 150 or a second direction opposite the first direction to discharge the DUT 150.

[0081] In various examples, the process controller 130 may monitor the voltage or current response of the DUT 150 during the cycling period and use the monitored voltage or current response to determine or update the current switch timing. The process controller 130 may include a proportional integral (PI) controller or a proportional integral derivative (PID) controller configured to determine or update the current switch timing to maintain a particular electrical parameter (e.g., average cell voltage) at a particular set point. Examples of voltage or current responses monitored and used to control the current switch timing may include average or peak cell voltage over the cycling period, average or peak charge voltage, average or peak discharge voltage, end of cycle voltage, average or peak current over the cycling period, average or peak charge current, or average or peak discharge current of the DUT 150. In one example, the process controller 130 may determine or update the current switch timing using information about the ambient temperature of the environment in which the cycling test is performed. Physically based or empirically derived models may be used for predictive control of the model. The control model may use many input variables for optimization of the current switch timing. In some examples, state of charge, state of health, faults, or other cell state information of interest may be used to determine or update current switch timing. State of charge is a measure of short-term battery capability and represents the amount of energy remaining compared to the energy at full charge. State of health is a measure of long-term capability and represents the ability to provide a specified performance compared to a new battery.

[0082] In some examples, the timing control of the charge / discharge steps may include an overtime Δt applied to the charge or discharge steps. The process controller 130 may use a PI or PID controller to maintain an output variable (e.g., current or voltage) at a desired set value by varying the overtime Δt used. The overtime Δt may be a positive or negative value. For example, a positive overtime charge time increases the charge time by t 充電+Δt, and the negative overcharge time is increased by t 充電 Similarly, the positive overdischarge time reduces the discharge time to t 放電 +Δt, and the negative excess discharge time is the discharge time t 放電 Alternatively, the process controller 130 may adjust both the charge time and the discharge time to keep the full cycling period constant (e.g., t 充電 + A longer charge time of Δt followed by a shorter discharge time of t 放電 -Δt).

[0083] The overcharge time Δt changes the ratio of charge time to discharge time. The total time of the cycling period plus the overcharge time Δt is called a frame. During the cycle test, the timed charge and discharge cycle is repeated for each frame. In one example, the process controller 130 may update the overcharge time Δt on a frame-by-frame basis, an example of which is discussed below with reference to FIGS. 4B-4E.

[0084] The overtime Δt may be provided by a switching timer. In one example, the overtime Δt may be a multiple of the switching timer resolution T, where Δt=k*T. The minimum overtime is equal to T. Such current switching techniques provided by the switching circuit 120 allow for stable, ultra-fine adjustment (in ticks, or increments of T) of the charge / discharge cycle. For example, for a 60 second cycling period consisting of a 30 second base charge time and a 30 second base discharge time, and a switching timer with a time resolution of T=200 nanoseconds, the minimum overcharge time is t 充電 = 30.0000002 seconds. The discharge time is t 放電If one stays at the base level of 0.5s = 30s, this results in a hyperfine change in duty cycle to 50.00000017%. The use of an overtime Δt also changes the ratio of charge to discharge time. The total coulombs applied per frame can be calculated based on the overtime Δt. The applied coulomb rate can be calculated by dividing the net applied total coulombs per frame by the duration of the frame.

[0085] The smallest possible time increment (i.e., T) is hereafter referred to as a tick. In the above example, a tick may be 200 nanoseconds. In some examples, the overtime Δt may be represented by an increment (k*T) of the switching timer resolution T, or a number of ticks "k". For example, the process controller 130 may extend the charging step by "k" ticks. The smallest amount that can be added or subtracted to the charging or discharging step is one tick, which corresponds to the resolution T of the switching timer. By adding or subtracting a certain number of ticks to the charging or discharging step, the process controller 130 may maintain an output variable (e.g., current or voltage) at a desired set value. Another way to implement such charge and discharge regulation is to allow the tick count to take positive or negative values. A positive tick count represents a period of a net charging condition (e.g., a charging time longer than a discharging time). A negative tick count represents a period of a net discharging condition (e.g., a charging time shorter than a discharging time).

[0086] Compared to conventional HPCs that typically require long cycling periods (e.g., 20 hours), the cyclic coulometer system 100 can be configured to cycle the charge / discharge process with substantially shorter cycling periods (e.g., about 1 minute). Due to the short charge / discharge times, the electrochemical cell under test (e.g., DUT 150) typically cannot reach the voltage limit set by conventional battery cycler techniques. Instead, the cell is expected to oscillate above and below the initial cell voltage. When cell coulombic inefficiency (self-discharge) occurs, the average cell voltage falls below the initial cell voltage. In one example, the process controller 130 can continuously or periodically monitor the voltage and current response of the DUT 150, optionally along with other output variables, and adjust the net overcharge time Δt (or tick count) to maintain the average cell voltage at a controlled set value. A high-speed microcontroller with appropriate timing can operate with a digital acquisition system to sample the measured battery current and voltage. The system may average both the measured input variables (e.g., charge and discharge currents) and the measured output variables (e.g., voltage and current responses of the DUT 150) to significantly reduce noise. In one example, the process controller 130 may measure the total applied coulombs using a coulomb counter or directly calculate the total applied coulombs based on the applied current and actual charge ticks. An example of measuring the total applied coulombs is discussed below, such as with reference to FIG. 5.

[0087] In various examples, the cyclic coulometer system 100 may parameterize the charge loss or charge loss rate (also called self-discharge rate) of an electrochemical cell (e.g., DUT 150) at specific test conditions, such as applied current (C-rate), temperature, and preset cell potential. In one example, the cyclic coulometer system 100 may measure the amount of total charge applied, or applied current (rate of applied coulombs), required to maintain the DUT 150 at a specific condition, such as substantially at a preset average cell voltage. If the average cell voltage remains controlled (i.e., the average cell voltage is held at a set value), the net applied current is the charge loss rate at the specific conditions of temperature, current, and cell potential. Conventional high-precision coulometry can only measure the CE of electrochemical cells that undergo very slow charge-discharge cycles. Coulomb inefficiency per hour (CIE / h) is a normalized metric that represents the average loss rate across many possible loss mechanisms across a range of cell potentials. Cyclic coulometry, as discussed in this document, advantageously evaluates charge loss rates over much shorter charge-discharge cycles and parameterizes the charge loss rates over a wide range of test conditions, including C-rate, temperature, and pre-set cell potential. According to some examples, the charge loss rates evaluated under different cell conditions can be represented graphically as loss rate curves or loss rate maps, examples of which are described below, such as with reference to Figures 10A-10B.

[0088] In some examples, the cyclic coulometer system 100 may be configured to measure the transient response of the DUT 150 to a step change in current or a step change in voltage, such as by using a spectrometer or acoustic spectrometer, among other transducers. The step response is indicative of the frequency response of the DUT 150. The step response information may be used to establish a cell model or cell algorithm, and may provide information similar to that obtained from impedance analysis, without the expense of additional equipment, or the need to interrupt cycle testing. The transient response also allows cyclic coulometry to continuously monitor the increase in charge transfer resistance while measuring the instantaneous loss rate at a given cell condition.

[0089] 2A-2C are schematic diagrams illustrating an example of a portion of a current switching circuit 200 configured to provide precisely timed polarity changes with specific current switch timings to generate charging and discharging currents, a process also referred to as current steering. The current switching circuit 200 may be an embodiment of the switching circuit 120. As shown in FIG. 2A, the current switching circuit includes switches S1, S2, S3, and S4, and a unidirectional DC current source 210, which is an embodiment of the current source 110. When all switches are open, no current flows to the DUT 150. FIG. 2B illustrates an equivalent circuit of the current switching circuit 200 when switches S2 and S3 are closed (as shown) and switches S1 and S4 are open, in which case the current source 210 provides a forward current 221 to charge the DUT 150. 2C illustrates an equivalent circuit of current switching circuit 200 when switches S1 and S4 are closed (as shown) and S2 and S3 are open, in which case current source 210 provides reverse current 222 to discharge DUT 150. The switch arrangement of FIG. 2A allows for dead time, which is a period when both forward and reverse timing are off. For example, if S4 and S2 were to be on at the same time, DUT 150 would be shorted.

[0090] The switches S1, S2, S3, and S4 may be transistors or other voltage controlled switching devices. In one example, the switches S1, S2, S3, and S4 are FET transistors, such as MOSFET transistors, and the open / closed state may be achieved by applying appropriate gate voltages relative to a threshold voltage. Because the forward current 221 (charging current) and the reverse current 222 (discharging current) are from the same single current source 210 that functions the same during charging and discharging operations, symmetry between the charging and discharging currents may be more easily and reliably achieved. The symmetry of the currents has the advantage that offset errors present in the charging cycle are cancelled with the same offset present in the discharging cycle. Using a single current source also helps improve the stability of the current output during the charging and discharging steps.

[0091] The current switching circuit 200 may change current direction (such as by opening and closing one or more switches in FIG. 2A) on a nanosecond time scale. The current switching circuit 200 has suitable voltage compliance so that the current does not exhibit a substantial change in value when the polarity is switched. In one example, the current switching circuit 200 includes a clocking circuit configured to control the operation of the switches S1, S2, S3, and S4 with a particular precision to achieve fine control of the current switch timing. For example, if the system clock frequency is 100 MHz, the current switch timing may have a resolution of 10 nS.

[0092] 3A-3C are schematic diagrams illustrating another example of a portion of a current switching circuit 300 configured to provide precisely timed polarity changes with specific current switch timings to generate charging and discharging currents. The current switching circuit 300 may be an embodiment of the switching circuit 120. As shown in FIG. 3A, the current switching circuit 300 includes two switches S4 and S5, two diodes D1 and D2, a power supply 310, and a unidirectional current regulator 320. The power supply 310 and the unidirectional current regulator 320 form a current source. If both the power supply 310 and the unidirectional current regulator 320 are used, the circuit 300 may source current to the DUT 150. If only the current regulator 320 is used, the circuit may sink current from the DUT 150. The states of the switches S4 and S5 determine which configuration occurs.

[0093] FIG. 3B illustrates an equivalent circuit of the current switching circuit 300 when switch S4 is closed and S5 is open. Diode D2 acts as a closed switch, passing forward current 321 from power supply 310 through regulator 320 to DUT 150 to charge DUT 150. FIG. 3C illustrates an equivalent circuit of the current switching circuit 300 when switch S4 is open and S5 is closed. Diode D1 acts as a closed switch in this configuration, passing reverse current 322 from DUT 150 back to DUT 150 through regulator 320 and S5. Reverse current 322 thus discharges DUT 150. The advantage of this operation is that current regulator 320 operates under identical current and polarity conditions when sinking or sourcing current to or from DUT 150, resulting in the symmetry of the circuit operation canceling out any small unavoidable anomalies in the current regulation circuit operation.

[0094] 4A-4E are illustrative timing diagrams showing the adjustment of the charge or discharge time in a cycling period using an overtime Δt. The adjustment may be performed by the switching circuit 120 in response to a control signal from the process controller 130 that schedules the overtime Δt. The cycling period (consisting of a basic charge time and a basic discharge time) and the overtime Δt form a frame. In one example, the basic charge time and the basic discharge time are each 30 seconds, giving a cycling period of 60 seconds. The 30 second charge step is long enough to allow the voltage profile to fully develop in the electrochemical cell. The overtime Δt may be represented by the number of overtime timer ticks. As discussed above, a tick in this document refers to the smallest increment (or decrement) of the charge or discharge time. In one example, the tick has a duration equal to the resolution T of the switching timer (e.g., 200 nanoseconds for a clock frequency of 5 MHz).

[0095] For comparison, FIG. 4A illustrates a frame with no overtime (Δt=0). The discharge operation starts immediately after the charge step. The charge and discharge steps are symmetric. FIG. 4B illustrates, by way of example, a frame with a positive overtime (i.e., Δt 充電 or exceeding timer ticks > 0), which reduces the charge time from 30 seconds to 30+Δt 充電 The discharge operation starts immediately after the overcharge time. The frame in FIG. 4B is 60+Δt 充電 sec. FIG. 4C shows, as an example, the negative overcharge time (i.e., Δt 充電 or exceeding timer ticks < 0), which reduces the charge time from 30 seconds to 30-Δt 充電 The discharge step starts immediately after the shortened charge step. The discharge time remains at 30 seconds. Therefore, the frame in FIG. 4C is 充電 seconds, less than 60 seconds.

[0096] Similarly, an excess time can be applied to the discharge step. FIG. 4D shows, as an example, a positive excess discharge time (i.e., Δt 放電 or exceeding timer ticks > 0), which reduces the discharge time from 30 seconds to 30+Δt 放電 The frame in Figure 4D is effectively increased to 60 + Δt 放電 FIG. 4E shows an example of the negative overdischarge time (i.e., Δt 放電 or exceeding timer ticks < 0), which reduces the discharge time from 30 seconds to 30-Δt 放電 The frame in Figure 4D effectively reduces the 60-Δt 放電 which is less than 60 seconds. The cyclic coulometer system 100 may continuously cycle through each frame, updating the overcharge time variable for each frame.

[0097] 5 is a block diagram illustrating an example of a battery testing system 500 configured to perform diagnostic testing of an electrochemical cell, such as the illustrated DUT 150, using cyclic coulometry as discussed above with reference to FIG. 1. The battery testing system 500 may include one or more current sources 510 for providing charge and discharge currents during testing, an interface board 520 for engaging the DUT 150, and a microcontroller 530 for providing control signals to operate the various components and circuits of the system 500, performing data processing, evaluating battery performance metrics, and generating battery diagnostics. In one example, to ensure temperature stability, some or all of the circuit components of the battery testing system 500 may be contained within a precision temperature controlled environment with the temperature stabilized to <±0.1° C.

[0098] Current source 510, an embodiment of current source 110 of FIG. 1, may provide charging and discharging currents to DUT 150 during cycle testing. In one example, current source 110 may be a single unipolar current source configured to provide a DC current. The amplitude of the current may be adjustable, such as via microcontroller 530. Examples of unipolar current sources are discussed above with reference to FIGS. 2A-2C and 3A-3C.

[0099] The interface board 520 may engage the DUT 150 to the test system 500 using a two-wire, three-wire, or four-wire connection, apply charge and discharge currents to the DUT 150, and measure currents and voltages from the DUT 150, among other variables. As illustrated in FIG. 5, the interface board 520 may include a data acquisition system (DAS) 521 configured to sample and digitize analog measurements under the control of the microcontroller 530. In various examples, the DAS 521 has a dynamic range large enough to digitize the charge and discharge currents, while at the same time having a resolution fine enough to detect the signal of interest. In one example, to improve the accuracy of batter diagnostics, the performance of the DAS 521 exceeds that of the current source 510, so that sources of errors that may result from the test can be accurately determined. An example of the DAS 521 is discussed below with reference to FIG. 7. In one example, the interface board 520 may be physically separate from the microcontroller 530 and the DAS 521 to allow flexible resistance sensing and current source options for various battery sizes.

[0100] In some examples, interface board 520 may include an embedded temperature sensor (not shown) for measuring the temperature of the environment of DAS 521. Based on the monitored temperature, microcontroller 530 may adjustably provide a thermally stable environment for the circuitry, such as by adjusting the temperature of DAS 521 using power resistors surrounding DAS 521 on interface board 520.

[0101] The microcontroller 530, an embodiment of the process controller 130, can be programmed to control the current source 510 to generate specific charge and discharge currents, drive data acquisition in the DAS 521, monitor the cycling process, and generate battery metrics. The microcontroller 530 can include communication peripherals to respond to commands and communicate with an external monitor 540 to report measurement results. In one example, the battery test system 500 runs on a 16 MHz temperature compensated crystal oscillator (TCXO) that directly drives the analog-to-digital converter (ADC) of the microcontroller 530 and the DAS 521. The microcontroller 530 can use a phase-locked loop to increase the 16 MHz to an internal frequency of a 40 MHz system clock, which is divided by 8 to 5 MHz. This 5 MHz is as accurate as the applied crystal clock and clocks a 32-bit timer used to generate charge and discharge periods with a time resolution of T=200 nanoseconds. For example, a 2 second periodic cycle would have 1 second or 5*10 Hz with a duration of 200 nanoseconds each (0.2 ppm resolution). 6 A high speed microcontroller 530 with appropriate timing can run the DAQ 521 to sample both the battery current and voltage.

[0102] The microcontroller 530 may be implemented as part of a microprocessor circuit, which may be a special purpose processor such as a digital signal processor, an application specific integrated circuit (ASIC), a microprocessor, or other type of processor for processing information, including physical activity information, or the microprocessor circuit may be a general purpose processor that may receive and execute a set of instructions to perform the functions, methods, or techniques described herein.

[0103] The microcontroller 530 may include a circuit set with one or more other circuits or subcircuits, including a timing controller 531, a battery metric generator 534, and a communication circuit 535. The circuits or subcircuits, alone or in combination, may perform the functions, methods, or techniques described herein. In one example, the hardware of the circuit set may be immutably designed (e.g., hardwired) to perform a particular operation. In one example, the hardware of the circuit set may include variably connected physical components (e.g., execution units, transistors, simple circuits, etc.) that include a computer-readable medium that is physically modified (e.g., magnetic, electrical, movable arrangement of immutable mass particles, etc.) to encode instructions for a particular operation. In connecting the physical components, the underlying electrical properties of the hardware constructs are modified, for example, from an insulator to a conductor or vice versa. The instructions allow the embedded hardware (e.g., execution units or loading mechanisms) to create members of the circuitry configured in the hardware through the variable connections to perform some of the particular operations when in operation. Thus, the computer-readable medium is communicatively coupled to other components of the circuit set members when the device is operating. In one example, any of the physical components may be used in more than one member of more than one circuit set. For example, during operation, an execution unit may be used in a first circuit of a first circuit set at one time and reused by a second circuit of the first circuit set or by a third circuit of the second circuit set at a different time.

[0104] The timing controller 531 may include a square wave generator 532 coupled to the current source 510 to generate a square wave current for application during the charge and discharge cycles. The square wave generator 532 may include a switch that operatively opens and closes at scheduled times, thereby changing the current direction, examples of which are discussed above with reference to FIGS. 2A-2C and 3A-3C. The timing controller 531 may include a current switching controller 533 configured to adjust at least one of the charge time or the discharge time to maintain an output variable (e.g., average cell voltage) at a preset setting, such as by changing the current switch timing between the charge and discharge steps in a cycling period. As discussed above with reference to FIG. 1, the timing control of the current switching may include an overtime Δt expressed by a duration or by a count of overtime timer ticks, added or subtracted to the charge time or discharge time (as illustrated in FIGS. 4B-4E).

[0105] In various examples, to accelerate the convergence of the electrochemical cell to a set point defined in the system controller, the current switching controller 533 may adjust at least one of the charge time or discharge time or update the current switch timing based on one or more input variables or cell conditions such as state of charge or state of health. In one example, the current switching controller 533 may use battery metrics and diagnostic information obtained from the battery metrics generator 534 to modify the initial current switch timing (which may be set to an empirical value as estimated from a process control algorithm) to achieve faster control. In one example, the current switching controller 533 may utilize information from many output variables (e.g., in-frame voltage and current response of the DUT 150) to predict an appropriate timing control strategy. For example, in response to a disturbance in the measured average cell voltage, the current switching controller 533 may use prior measurements of cell resistance and in-frame voltage response to bring the DUT 150 back to the set point more quickly. System controllers such as PI control, PID control, among other feedforward or feedback controllers, may be used to promote convergence of the measured output variables to the desired setpoints with little overshoot or oscillation. Battery metrics and diagnostic information, as well as the control strategies discussed above, may also be used to coordinate the operation of various elements of system 500, such as data acquisition with DAQ 521.

[0106] The microcontroller 530 and DAS 521 may require various voltages for proper operation. In some examples, a medical grade power converter, such as a cardiac floating "CF" type converter, may be used to isolate the AC power from the current source 510, the microcontroller 530, and the DAS 521, with little to no line frequency leakage current. A galvanic isolation barrier may be provided to isolate the microcontroller 530 (e.g., precision instrumentation therein, such as a coulomb counter) from the external monitor 540 and the current source circuit 510. Isolation from the current source circuit 510 may allow the current source 510 to be reversed from a charging to discharging configuration when the current source is reversed from a charging to discharging configuration.

[0107] The battery metric generator 534 may be configured to generate battery metrics and diagnostic information using measurements provided by the DAS 521. The battery metric generator 534 and the DAS 521 are collectively referred to as a measurement circuit that measures and processes signals. In one example, at least a portion of the battery metric generator 534 may be configured as a precision coulomb counter to count charges during charge and discharge cycles. In one example, the coulomb counter may use a high precision voltage reference. The system may average the measured input variables and the measured output variables to significantly reduce noise.

[0108] In one example, the battery metric generator 534 may determine the amount of total charge applied per frame (QPF, in coulombs). The sum of the frame coulombs represents the cumulative coulombs applied during the battery cycle test. In one example, the QPF may be calculated using the output of the DAS 521. In another example, the battery metric generator 534 may calculate the QPF by integrating the current applied over the entire frame. In one example, the QPF may be calculated using equation (1).

[0109]

number

[0110] In some examples, the battery metric generator 534 may instead measure the total charge applied during charging (Q 充電 ) and the total charge applied during discharge (Q 放電 In this case, the battery metric generator 534 may calculate the total charge applied during charging (Q 充電 Similarly, the battery metric generator 534 may calculate the total charge applied during discharge (Q 放電 ) can then be calculated using equation (2). QPF=Q 充電 -Q 放電 (2) In one example, Q 充電 is the average charging current I 充電 and the total tick count during charging (N_ticks 充電 ) can be calculated using the following formula: 放電 is the average discharge current I 放電 and the total tick count during discharge (N_ticks 放電 ) can be calculated using

[0111] Q 充電 =T*N_ticks 充電 *I 充電 (3) Q 放電 =T*N_ticks 放電 *I 放電 (4) The clock time per tick, T, is the resolution of the switching timer (T=1 / f クロック In one example, the time per tick is equal to the system clock frequency f クロック For a frequency of 5 MHz, T = 200 nanoseconds.

[0112] In another example, the square wave generator 532 can implement a symmetrical waveform from a single unipolar current source, so that the average charge and discharge currents are substantially identical over the timescale of a frame. 充電 or excess discharge tick Δ tick 放電 In this example, the QPF may be calculated by using the average source current (I) and the difference in excess tick counts between the charge and discharge periods, as given in equation (5).

[0113] QPF=T*(Δtick 充電 -Δ ticks 放電 )*I (5) In another example, the microcontroller 530 may adjust the overcharge Δtick as dictated by a PI or PID control algorithm. 充電 to maintain a desired average cell voltage. The integral term of the PI or PID controller is used to minimize the steady state error or offset from the average cell voltage set point. If the system is in control and the system control algorithm is properly tuned, the integral term will provide a constant overcharge Δtick added every frame. 充電 is a smoothed estimate of the integral term. That is, the integral term is both the control variable (timing) and the basis for the total charge per frame (QPF) and total applied coulomb rate. This is a beneficial feature of a cyclic coulometer because even in the presence of noisy current sources or measured output variables, the action of the integral term in the PI or PID control algorithm may result in smooth coulomb and total applied charge values. In one example, the QPF may be calculated by the average source current (I), clock time per tick (T), and integral value (INT) of the PI or PID algorithm used to generate the frame timing, as given in equation (6):

[0114] QPF=T*INT*I (6) In some examples, the battery metric generator 534 can trend the QPF over time to generate a total coulomb curve plotted versus time. The slope of the total coulomb curve at a particular time represents the effective applied current (also called applied coulomb rate, self-discharge rate, or loss rate) required to keep the system in control (e.g., the output average cell voltage is held at a controlled level). Examples of applied total charge and self-discharge rates are discussed below, such as with reference to FIG. 8.

[0115] In one example, the battery metric generator 534 may determine the equivalent series resistance (ESR) of the DUT 150 as a function of the total charge applied. The ESR may be calculated using the change in cell voltage (ΔV) (such as obtained from the cell voltage response of the charge or discharge step compared to the average cell voltage 810) and the magnitude of the applied current (ΔI). The cell voltage used to calculate the ESR may be represented by the average voltage over the cycling period, or the average or terminal voltage of only the charge or discharge cycle. In one example, the ESR may be calculated based on half the difference between the charge and discharge voltages, divided by the applied current used during the charge and discharge steps, and calculated symmetrically around the current switching. The battery metric generator 534 may further parameterize the ESR as a function of the total charge applied (such as by generating ESR curves over different values ​​of total charge applied) and determine the percentage ESR change per coulomb lost, which represents the rate of ESR change relative to the change in total charge applied (dESR / dQ), an example of which is discussed below with reference to FIG. 9.

[0116] In addition to or instead of the QPF, total charge applied, self-discharge rate, ESR, and ESR rate of change as discussed above, the battery metric generator 534 may generate other battery metrics or diagnostic information, such as the frequency response of the DUT 150. The battery metric generator 534 may generate battery metrics according to the electrochemical tests being performed and / or the monitor devices being used. In some examples, the battery testing system 500 may include spectrometers, ultrasonic sources and sensors, fiber optic cables, or pressure transducers, among others.

[0117] The communication circuitry 535 is configured to establish data communication with a monitor device 540, such as a personal computer (PC) or mobile device, which may process, store, and present battery metric and diagnostic information to system users (e.g., material developers, cell designers, cell manufacturers, algorithmic battery engineers, quality control and reliability engineers, among others). The battery metric and diagnostic information may be presented in the form of tables, charts, trends, diagrams, or any other type of textual, tabular, or graphic display. For example, the graphs of FIG. 8 and FIG. 9, or variations thereof, may be presented on the display of the monitor device 540. In one example, the monitor device 540 may present the total charge applied and / or self-discharge rate under individually addressable and specified test conditions, such as different C-rates, different temperatures, different setpoint voltages, or any combination of these variables, among others. For example, a loss rate curve or loss rate map, such as those shown in FIG. 10A-10B, may be presented on the display of the monitor device 540. The monitor device 540 may generate an alert notification of the status of the DUT 150. The monitor device 540 also includes a user interface that allows a system user to monitor the cycling process (either online or offline monitoring) and program the cyclic coulometry with input commands to the microcontroller 530, such as programming one or more test condition variables (e.g., C-rate, cell voltage set point, or temperature set point). In some examples, at least a portion of the battery metric generator 534 may be implemented within the monitor 540, which may perform online measurements of battery metrics.

[0118] FIG. 6A illustrates an example of at least a portion of a current steering circuit 600 configured to control current switch timing between charge and discharge steps during cycle testing. The current steering circuit 600, an embodiment of the switching circuit 120 of FIG. 1, includes a microcontroller (MCU) 610, an embodiment of the current switching controller 533. The microcontroller 610 is coupled to a current source 630, an embodiment of the current source 110, which may generate a square wave to excite the DUT 150 during cycle testing. The microcontroller 610 may generate timing control signals for the current steering circuit 620, which may include a switch (e.g., a FET transistor or other type of voltage controlled switch, as illustrated in FIGS. 2A-2C and 3A-3C) to perform current switching according to the timing control signals provided by the microcontroller 610. A forward (charging) current and a reverse (discharging) current may be applied to the DUT 150. FIG. 6B is a timing diagram illustrating, by way of example, the logical timing of the forward and reverse currents from the current steering circuit 620. The forward and reverse currents alternate at scheduled times according to the current switch timing.

[0119] Electrical parameters such as the voltage of the DUT 150, the voltage across the current sense resistor 650, and the applied current through the DUT 150 may be measured using a data acquisition system (DAS) 640. The DAS 640 may include an analog-to-digital converter (ADC) for converting the analog measurements to digital data at a specified level of accuracy and stored in a data storage device. In one example, the DAS has a dynamic range large enough to digitize the charge / discharge current and at the same time has a resolution fine enough to detect the signal of interest. In one example, the performance of the DAS 640 may exceed that of the current source 630, so that the cyclic coulometry process may more reliably determine sources of errors that may occur during cycle testing.

[0120] The digital data may be pre-processed using techniques such as oversampling, filtering, or noise shaping, among others, to increase data accuracy and improve data quality. The digital data may be used, such as by the battery metric generator 534, to generate new data forms and performance specifications, and / or to generate battery metrics and diagnostics that characterize the state of charge or state of health of the DUT 150, among other conditions of interest. In some examples, the microcontroller 610 may update the current switch timing using one or more information regarding the status of the current source 630, measurements from the DAS 640, and battery metrics and diagnostics from the battery metric generator 534.

[0121] FIG. 7 is a diagram illustrating a data acquisition system (DAS) 740 for measuring electrical parameters in a cycle test and at least a portion of the environment in which the DAS 740 operates. The DAS 740 may be an example of the DAS 521 as illustrated in FIG. 5 or the DAS 640 of FIG. 6. A constant current source 730, which is an embodiment of the current source 630, provides an excitation current to the DUT 150. The cell specific interface 720 is a physical interface with the DUT 150 and may be implemented in the interface board 520. The DAS 740 includes a multiplexer (MUX) 741 for selecting among analog measurements, such as a cell voltage of the DUT 150 and a cell current based on a voltage across a current sense resistor 650 having a known resistance, as discussed above with reference to FIG. 6. The DAS 740 includes an analog-to-digital converter (ADC) 742 for digitizing the analog measurements (e.g., voltage or current). In one example, the ADC 742 is connected to a precision voltage reference (V 基準 ) and a 16 MHz timing source 750. In one example, the ADC 742 is configured to continuously provide digitized voltage and current samples at a particular sampling rate, such as 1250 samples per second (SPS).

[0122] In one example, the ADC742 is configured for 32-bit conversion, of which 28 bits are used by the coulomb counter. At this data rate and 2.5V reference, the ADC742 is quiet down to about 20 bits, so samples taken at 1250 SPS can be quiet down to about 2 ppm. Subsequent averaging can reduce the noise significantly. For example, even if the frame is very short (2 seconds in duration), there are about 1250 samples in each half. This decimation is roughly equivalent to an additional 4 bits of resolution.

[0123] The DAS 740 may output digitized measurements to the MCU 610. Various metrics and diagnostic information may be generated (e.g., by the battery metric generator 534) based on the measurements, including actual coulombs applied per step, average voltage of the charge step, average voltage of the discharge step, average cell potential, equivalent series resistance calculated from the charge step, equivalent series resistance calculated symmetrically around the current switching, equivalent series resistance calculated from the discharge step, integral and proportional terms of the system controller (i.e., the "P" and "I" terms of a PI or PID controller), and the like. Examples of battery metrics are discussed below, such as with reference to FIGS. 8, 9, and 10A-10B. If the average cell potential is substantially the same as the setpoint, the system may be determined to be in control. When in control, the average proportional term (P) will be zero.

[0124] FIG. 8 is a graph illustrating the voltage and current response during cycling tests performed on the tested battery, as obtained using system 500, by way of example and not limitation. By way of example and not limitation, the tested battery can be assembled using the following method. The cathode ink was made using a Thinky ARE-500 planetary mixer. Then, 9.42 grams of NMC532 cathode, 0.340 grams of Timcal C65 carbon black, and 0.240 grams of PVDF were added to a Thinky mixing cup. Then, 6.85 grams of NMP were added and the mixture was spun at 1000 RPM for a total of 10 minutes, with two short pauses added to prevent excessive heating of the ink. The cathode ink was then cast onto aluminum foil, dried, and cut into electrodes.

[0125] The cathed and dried cathodes were used to construct homemade pouch lithium-ion test cells using graphite anodes. After degassing, the assembled battery was filled with electrolyte. The electrolyte used in this example was 1M LiPF6 in a mixture of ethylene carbonate, ethyl methyl carbonate, and diethyl carbonate (EC / EMC / DEC 3 / 5 / 2 v / v) with 1% vinylene carbonate.

[0126] Cycle testing was performed on the battery cell thus prepared. The cell was charged to 4.3V and tested using cyclic coulometry as described above with reference to Figures 1 and 5. Cyclic coulometry was performed with a cycling period of 60 seconds (base charge time of 30 seconds and base discharge time of 30 seconds) and a C-rate of 0.5C (i.e., 2 hour charge rate). The PI controller can be commanded to maintain the average cell voltage at 4.3V (setpoint). The cell was placed in a 45°C oven and allowed to equilibrate.

[0127] The average cell voltage, charge voltage, and discharge voltage may be continuously monitored, and the data obtained, such as using the system 500. As illustrated in FIG. 8, the microcontroller 520 (e.g., a PI controller) adjusts timing variables to maintain the output average cell voltage at a desired set voltage. The average cell voltage response 810 maintains at approximately the set value of 4.3V. The average charge voltage response 820 measured during the first half of the cycling period increases over time. Similarly, the average discharge voltage response 830 obtained during the second half of the cycling period decreases over time. That is, both the average charge voltage and the average discharge voltage grow over time during the cycling test.

[0128] Also shown in FIG. 8 is a total coulomb curve 840 representing the cumulative charge applied (scaled on the second Y-axis) at different times during the cycle test. The total charge applied increases with time. The total charge applied is the sum of the total charge applied per frame (QPF). As discussed above with reference to FIG. 5, the QPF can be determined using a coulomb counter or calculated by integrating the current corresponding to the number of ticks required per frame to maintain the average cell voltage at a set level (e.g., 4.3V in this example) as given in equation (1). In some examples, the total applied charge can be calculated for only the charge step or only the discharge step as given in equations (3) and (4). Alternatively, the QPF can be calculated using one of equations (2), (5), or (6).

[0129] The applied coulombic rate, which is the effective charge or discharge current used for each cycling period of the cyclic coulometry, can be determined using the total coulombic curve 840. The applied coulombic rate changes for each cycle of the cyclic coulometry. The effective coulombic rate can be averaged over the cycling period. When the battery under test is stable at a set cell condition (e.g., the average cell voltage of the battery is substantially maintained at a voltage set point of 4.3V in this example), the applied coulombic rate from the cyclic coulometry required to maintain the stable cell condition on average is called the self-discharge rate at that condition. In one example, the self-discharge rate (or loss rate) can be determined using the slope (dQ / dt) of the total coulombic curve 840 at a particular time. In this example, a steeper slope of the total coulombic curve 840, and therefore a higher self-discharge rate, is observed earlier in the test (e.g., before 100,000 seconds) than later in the test (e.g., after 100,000 seconds). This could be because the cell slowly becomes more efficient over time as the solid electrolyte interphase (SEI) develops further, or because the reactivity of the cathode decreases.

[0130] Voltage and current responses, such as average cell voltage 810, charge voltage 820, discharge voltage 830, and total coulomb curve 840, can be obtained under individually addressable and specified test conditions. Each test condition can be represented by one or more control variables (e.g., C-rate, temperature, cell voltage set points during the cycling process), each of which can take multiple values. For example, the voltage and current responses shown in FIG. 8 were obtained under a particular test condition defined by a set of parameters (C-rate=0.5C, temperature=45°C, average voltage set point=4.3V). Different sets of voltage or current responses can be generated under different test conditions, such as by changing one or more of the C-rate, temperature, or cell voltage set points.

[0131] FIG. 9 is a graph illustrating, by way of example and not limitation, the equivalent series resistance (ESR, in ohms) of a tested cell plotted against the total charge applied (cumulative coulombs represented by total coulomb curve 840 of FIG. 8), both determined using measurements from cycle testing as described above with reference to FIG. 7. The ESR may be determined using the change in cell voltage and the change in current (ΔI) during a charge or discharge period. In one example, the ESR is calculated as a function of the charge current (I 充電 ) vs. Average Charging Voltage (V 充電 )820 and average cell voltage (V 平均 ) 810. Alternatively, the ESR can be calculated using the ratio of the difference between the discharge current (I 充電 ) vs. Average Discharge Voltage (V 放電 )830 and average cell voltage (V 平均 ) 810.

[0132] ESR = (V 充電 -V 平均 ) / (I 充電 ) (7) ESR = (V 放電 -V 平均 ) / (I 放電 ) (8) Average cell voltage, V 平均 , represents the average voltage over the cycling period. In one example, V 平均 may be determined using the average of the charge and discharge voltages. Alternatively, V 平均 V 充電 and V 放電 It can be determined using a weighted average of V 充電 and V 放電 The weighting coefficients of are given by the number of ticks during charging (N_tick), respectively, as given by equation (9). 充電 ) and the number of ticks being discharged (N_ticks 放電 ) respectively.

[0133]

number

[0134] Alternatively, the cell voltage used to calculate the ESR may be calculated using the average or terminal voltage of the charge cycle (maximum voltage) and the average or terminal voltage of the discharge cycle. In another example, the cell voltage for calculating the ESR may be obtained by calculating the average charge and discharge voltages symmetrical around the current switch with respect to time. In these examples, V 充電 and V 放電 The difference between is divided by 2 and the applied current (I).

[0135] ESR = (V 充電 -V 放電 ) / (2*I) (10) As illustrated in FIG. 9, the ESR increases as self-discharge reactions accumulate in the cell. The slope of the ESR curve 910 represents the rate of ESR change per lost coulomb (dESR / dQ), which is an indication of how damaging each lost coulomb is to the cell resistance. In this cycle test, the cycling period was set to 60 seconds. Because of the time scale, the calculation of ESR provides a direct measurement of the low frequency resistance of the battery cell during the actual charge transfer. Given that an empirical correlation of cycle life requires data on both the loss rate and the increase in charge transfer resistance, the cyclic coulometry discussed herein represents a significant improvement over the state of the art of battery metrology. In particular, the cyclic coulometry discussed herein allows the experimenter to measure the change in ESR of the test cell as a function of lost coulombs, and the coulometry advantageously quantifies in a continuous manner how damaging each lost coulomb is to the cell resistance.

[0136] As discussed above with reference to FIG. 8, the total coulombic curve 840 and the self-discharge rate derived from the curve 840 may be obtained under individually addressable and specified test conditions. In some examples, multiple loss rates may be determined at different test conditions. Each test condition may be represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point, among other variables. Each parameter may take on multiple values, such as multiple C-rates, multiple temperatures, or multiple set point voltages. The resulting loss rate may be represented as a parameterized representation over one or more of the variables. In one example, the parameterized representation includes a multi-dimensional array. In another example, the parameterized representation includes a multi-dimensional graph, such as a loss rate curve or a loss rate map or surface, examples of which are discussed below with reference to FIGS. 10A-10B.

[0137] In some examples, the loss rate may be expressed by the amount of charge lost per day (Ah / day) required to maintain the test cell at the setpoint potential. Traditionally, the loss rate of energy storage is expressed by voltage fade. Voltage fade generally requires interpretation and thus does not provide a quick and easy representation. Instead, the loss rate maps discussed herein allow for a simpler interpretation of the total charge lost per day (Ah / day) required to maintain the test cell at the setpoint potential under different test conditions.

[0138] In some examples, multiple ESR change rates may be determined at different test conditions. Each test condition may be represented by a parameter set that includes one or more of a C-rate value, a temperature measurement, or a cell voltage set point, among other variables. Each parameter may take multiple values, such as multiple C-rates, multiple temperatures, or multiple set point voltages. The resulting ESR change rate may be represented as a parameterized representation over one or more of the variables. Examples of parameterized representations include multi-dimensional arrays or graphs, such as the ESR change rate map discussed below with reference to FIG. 10C.

[0139] 10A-10C illustrate, by way of example and not limitation, graphical representations of performance metrics calculated under different test conditions, such as self-discharge rate or ESR rate of change. In particular, FIG. 10A is a graph illustrating loss rate curves 1010 under different applied C-rates obtained during cycle testing of a battery. In this example, the set point of the cell voltage was 4.4V and the cycle testing was performed at a controlled temperature of 45° C. The loss rate curves 1010 are represented by the amount of charge loss per day (Ah / day) and can be measured under different applied C-rates. FIG. 10A shows that a higher C-rate results in more charge loss (Ah / day) to maintain the test cell at the set point potential.

[0140] FIG. 10B illustrates a loss rate map 1020 of self-discharge rates (in mA) under various test conditions represented by different C-rates and different cell voltage set points. The single battery cell is of the same type as described above with reference to FIG. 8. By way of example and not limitation, the self-discharge rates may be measured at various combinations of (1) one of four different C-rates (0.25C, 0.5C, 0.75C, and 1C) and (2) one of four different cell potentials (4.1V, 4.2V, 4.3V, and 4.4V). The resulting loss rate map 1020 shows that the discharge rate of the battery is a major function of cell potential and a minor function of C-rate at the conditions studied. The discrete C-rates and discrete cell potentials are by way of example and not limitation. For example, loss rate maps with finer resolution, a wider range of C-rates, or different average cell voltage set points may be generated. The dissipation rate map may be rendered as a 3D contour plot, surface plot, mesh plot, etc., or as a 2D color or grayscale map in which the self-discharge rates may be represented by different colors or grayscales.

[0141] Similar to the multiple self-discharge rates that can be calculated under various test conditions as shown in the loss rate map 1020, multiple ESR change rates can be calculated under different test conditions. FIG. 10C illustrates an ESR change rate map 1030 showing the ESR change rate (in ohms / coulombs) under various test conditions represented by different C-rates and different cell voltage set points. The single battery cell is of the same type as described above with reference to FIG. 8. In this non-limiting example, the ESR change rate can be calculated from the slope of the ESR per total applied coulomb graph of FIG. 9 at various combinations of (1) one of four different C-rates (0.25C, 0.5C, 0.75C, and 1C) and (2) one of four different cell potentials (4.1V, 4.2V, 4.3V, and 4.4V). The resulting ESR change rate map 1030 shows that the change in ESR per coulomb lost is a major function of cell potential and C-rate at the conditions studied. Discrete C-rates and discrete cell potentials are by way of example and not limitation. For example, ESR rate change maps with finer resolution, a wider range of C-rates, or different average cell voltage setpoints may be generated. ESR rate change maps may be rendered as 3D contour plots, surface plots, mesh plots, etc., or as 2D color or grayscale maps in which self-discharge rates may be represented by different colors or grayscales.

[0142] The loss rate map 1020 or the ESR rate of change map 1030 may be generated in such a way that each data point (e.g., the self-discharge rate corresponding to a particular C-rate and a particular cell potential, or the ESR rate of change corresponding to a particular C-rate and a particular cell potential) is calculated from different battery cells of similar structure to check for hysteresis effects. For example, when the loss rate map 1020 and the ESR rate of change map 1030 each have 16 data points corresponding to 16 test conditions (C-rate and cell potential pairs), 16 batteries can be mapped to the 16 test conditions and tested simultaneously under each test condition. The resulting 16 data points are then obtained from different batteries. This may avoid or substantially reduce hysteresis. Hysteresis may occur during repeated testing of one battery under different test conditions. For example, if a cell is damaged in one test condition at high voltage, subsequent data points may be systematically switched off from that point on.

[0143] The loss rate map 1020 or ESR rate of change map 1030 may be generated for the cell at different times, such as after aging of the battery. In one example, an initial map (initial loss rate map or initial ESR rate of change map) may be generated from a fresh cell. The battery may then be stored in an oven for a specified period of time (e.g., 3-5 days) and new tests may be performed to generate a new loss rate map or a new ESR rate of change map. A comparison of the newly generated map to the initial map may be used to characterize changes in battery characteristics over time.

[0144] 11 is a flow chart illustrating an example of a method 1100 for performing diagnostic testing of a device under test (DUT) using cyclic coulometry, as discussed above with reference to FIG. 1. Examples of DUTs may include any electrochemical cell, such as a battery, a fuel cell, a flow cell, or other electrochemical cell. Method 1100 may be implemented and performed in a battery testing system, such as battery testing system 500. In one example, at least a portion of method 1100 may be implemented in an apparatus, such as a cyclic coulometer, as discussed above with reference to FIG. 1.

[0145] The method 1100 begins at 1110, where a DUT may be loaded into a test environment and test condition variables may be programmed into the test system. The test environment may be a precision temperature controlled environment with temperature stabilized to <±0.1° C. In one example, the DUT is loaded into a temperature controlled oven. The DUT may be engaged with a test system or device (e.g., battery test system 500 or cyclic coulometer system 100), such as through an interface board 520 of the system 500. Examples of DUT connections may include 2-wire, 3-wire, or 4-wire connections, among other state-of-the-art connection configurations. The test system or device may be programmed with test condition variables, such as through a user interface of the monitor device 540. For example, the test condition variables include a set cell potential, also known as a voltage set point, of the DUT. In another example, the test condition variables include a C-rate. In yet another example, the test condition variables include a set temperature of the test environment. Other examples of test condition variables may include a cycling period, a base charge time, and a base discharge time, among others.

[0146] At 1120, the electrical cycling process begins by applying a charging current during a charging step of a cycling period, followed by applying a discharging current during a discharging step of the cycling period. The charging and discharging steps may last for a specified base charge time and a specified base discharge time. The base charge time and base discharge time may be programmable. In one example, the base charge time and base discharge time are each 30 seconds, giving a cycling period of 60 seconds. The 30 second charging step is long enough to allow the voltage profile to fully develop within the electrochemical cell.

[0147] The charging and discharging currents may be provided by a current source, such as current source 110. In one example, the current source may be a single DC current source configured to provide a unidirectional current. To provide symmetrical charging and discharging currents in opposite directions, the direction of current flow may be reversed at a specific current switch timing from forward flow (charging current) to reverse flow (discharging current). Reversing the current direction may be accomplished, for example, by using switching circuit 120 or a variant thereof (e.g., current switching circuit 200 or 300), as discussed above. The symmetry of the current has the advantage that offset errors present in the charging cycle are cancelled with the same offset present in the discharging cycle. Using a single current source also helps improve the stability of the current output during the charging and discharging steps.

[0148] At 1130, one or more electrical parameters may be measured during the cycling process (e.g., during charging or discharging the DUT). Examples of electrical parameters may include voltage or current response of the DUT, such as average or peak cell voltage over the cycling period, average or peak charge voltage, average or peak discharge voltage, end of cycle voltage, average or peak current over the cycling period, average or peak charge current, average or peak discharge current, among others. In one example, the one or more electrical parameters may be measured using DAS 521 or a variant thereof (e.g., DAS 640 or 740). The measured parameters may be pre-processed and digitized.

[0149] At 1140, one or more of the charge time or discharge time may be adjusted to maintain a measured output variable, such as an average voltage of the DUT, at a preset cell voltage setpoint. Such adjustment of the charge time or discharge time may be automatically controlled, for example, by the process controller 130 or the current switching controller 533. In one example, the charge time or discharge time adjustment may include a change in current switch timing between the charge and discharge steps in a cycling period. In one example, the current switching may include an overtime Δt that is added or subtracted from the charge time or discharge time. As an example, as illustrated in FIGS. 4A-4E, the charge time or discharge time may be independently increased or decreased by the overtime Δt. The overtime Δt may be represented by a duration (e.g., in milliseconds or microseconds) or by a count of overtime timer ticks. A tick has a duration of the switching timer resolution T. In one example, T is approximately 200 nanoseconds. Thus, stable ultra-fine adjustment (of ticks, or increments of T) of the charge / discharge cycle may be achieved.

[0150] In various examples, the one or more electrical parameters measured at 1130 may include a voltage or current response of the DUT during the cycling period. The monitored voltage or current response may be used to determine or update the current switch timing at 1140 (e.g., overcharge time Δt or overtimer tick count) to maintain a particular electrical parameter (e.g., average cell voltage) at a particular set value. In one example, the overcharge time Δt or overtimer tick count may be initialized to zero at the start of the test. A system controller such as PI control, PID control, among other feedforward or feedback control, may be used to facilitate convergence of the measured output variable to a desired set value with little overshoot or oscillation. The current switch timing (e.g., overcharge time Δt or overtimer tick count) may be updated continuously or periodically. In one example, the current switch timing (e.g., overcharge time Δt or overtimer tick count) may be updated on a frame-by-frame basis. In some examples, one or more input variables may be additionally used to control adjustments to the charge or discharge time. In one example, the temperature of the electrochemical cell may be monitored. In another example, a cell state, such as the state of charge or state of health of the DUT, may be measured or estimated. One or more of these monitored variables may be further used to update the overcharge time Δt or overtimer tick count, which may accelerate the convergence to a set point average potential of the electrochemical cell. In one example, the initial current switch timing may be modified using electrical measurements, or battery metrics and diagnostic information, to achieve faster control.

[0151] At 1150, battery metrics may be generated using one or more measured electrical parameters, such as using the battery metric generator 534. The battery metrics may indicate a performance specification of the DUT or characterize the state of charge or state of health of the DUT. In one example, the battery metrics include an amount of total charge applied during a specified portion of a cycling period. In one example, the battery metrics may include a self-discharge rate (also known as a loss rate), which may be determined based on a rate of change of the total charge applied over time. In some examples, the battery metrics may include an equivalent series resistance (ESR) of the DUT. Other examples of battery metrics may include actual coulombs applied per step, average voltage of a charge step, average voltage of a discharge step, average cell potential, or proportional and integral terms of a system controller (i.e., the "P" and "I" terms of a PI or PID controller), among others. Examples of generating battery metrics are discussed below, such as with reference to FIG. 12 and FIG. 13.

[0152] At 1160, the generated battery metrics may be provided to a user or process. In one example, the battery metrics may be output to a system user and displayed on a monitor such as a personal computer (PC) or mobile device. The battery metrics and diagnostic information may be presented in text, tables, or graphs, optionally with other measurements. As an example, a loss rate curve or loss rate map representing the applied total charge and self-discharge rate as illustrated in FIG. 8, an ESR curve as illustrated in FIG. 9, and a parameterized self-discharge rate as illustrated in FIG. 10A-B may be displayed on an output device. The system user may take further actions based on the battery metrics (e.g., generate battery diagnostics or perform further tests).

[0153] 12 and 13 are flow charts illustrating respective methods 1200 and 1300 of generating various battery metrics using electrical measurements made during cycle testing, such as according to method 1100. Method 1200 shown in FIG. 12 begins at 1210 for determining an amount of total charge applied per frame (QPF, in coulombs). The QPF may be determined using a coulomb counter or calculated by integrating the applied current over time within an entire frame, as given by equation (1). In one example, the QPF may be determined from the difference between the total charge applied during charging and the total charge applied during discharging, as given by equation (2). In one example, the battery metrics may include the amount of total charge applied during charging or the amount of total charge applied during discharging, which may be determined according to equations (3) and (4), respectively. In one example, the QPF may be calculated by using the difference in excess tick counts between the charge and discharge periods, as given in equation (5), or by using the integral (INT) of the PI or PID algorithm used to generate the frame timing, as given in equation (6). At 1220, the QPF is trended over time to generate a total coulomb curve plotted versus time, an example of which is shown in FIG. 8. At 1230, the applied coulomb rate (also known as the self-discharge rate) may be determined, such as by using the slope (dQ / dt) of the total coulomb curve at a particular time. The applied coulomb rate represents the effective applied current required to keep the system in control (e.g., the output average cell voltage is maintained at a control level).

[0154] The self-discharge rate represents the applied current required to maintain the cell voltage of an electrochemical cell at a particular set point. In some examples, the applied total charge and the self-discharge rate may be determined under individually addressable and specified test conditions. Each test condition may be represented by a set of parameters including, for example, one or more of a C-rate value, a temperature measurement, or a cell voltage set point, among other variables. Each parameter may take multiple values. The resulting loss rate may be represented as a parameterized representation over one or more of the variables. In one example, the parameterized representation includes a multi-dimensional array. In another example, the parameterized representation includes a multi-dimensional graph, such as a loss rate curve or a loss rate map or surface.

[0155] The method 1300 shown in FIG. 13 starts at 1310 for determining the amount of total charge (QPF) applied per frame. At 1320, the equivalent series resistance (ESR) of the DUT during charging and discharging per frame may be determined. The ESR may be calculated using the change in cell voltage (ΔV) (as obtained from the difference between the average charging voltage 820 and the average cell voltage response 810 or the average discharging voltage 830 and the average cell voltage 810) and the applied current, such as according to Equation (7) and Equation (8). In one example, the average cell voltage used to calculate the ESR may be represented by the average voltage over the cycling period. The average cell voltage may be determined using a simple average of the average charging voltage and the average discharging voltage. Alternatively, the average cell voltage may be determined using a weighted average of the cell voltage during charging and the cell voltage during discharging, such as according to Equation (9). In another example, the average or terminal voltage of only the charging or discharging cycles may be used to determine the cell voltage used to calculate the ESR. In another example, the cell voltages used to calculate the ESR may be obtained by calculating the average charge and discharge voltages symmetric around the current switch with respect to time, as given by equation (10).

[0156] At 1330, an ESR curve may be generated. The ESR curve may be plotted versus the total charge applied, an example of which is shown in FIG. 9. At 1340, the percentage change in ESR per coulomb lost may be determined, which represents the percentage change in ESR over the change in total charge applied (dESR / dQ). The percentage change in ESR per coulomb lost indicates how damaging each lost coulomb is to the cell resistance. The coulometry techniques discussed herein advantageously quantify in a continuous manner how damaging each lost coulomb is to the cell resistance.

[0157] In various examples, the 1200 and 1300 methods can be complementary. The information on the rate of ESR change per lost coulomb at 1340 is a measure of how damaging each lost coulomb is to cell performance. The information on the applied coulomb rate (self-discharge rate) at 1230 is a measure of the rate of generation of lost coulombs. Together, the battery metrics generated by the 1200 and 1300 methods present new battery metrics for understanding cell degradation at individual addressable load conditions such as temperature, C-rate, and cell potential.

[0158] 14 generally illustrates a block diagram of an example machine 1400 upon which any one or more of the techniques (e.g., methodologies) discussed herein may be implemented. Portions of this description may apply to the computing framework of various portions of the cyclic coulometer system 100 or the battery testing system 500.

[0159] In alternative embodiments, machine 1400 may operate as a standalone device or may be connected (e.g., networked) to other machines. In a network deployment, machine 1400 may operate in a server-client network environment in the processing capacity of a server machine, a client machine, or both. In one example, machine 1400 may operate as a peer machine in a peer-to-peer (P2P) (or other distributed) network environment. Machine 1400 may be a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web appliance, network router, switch or bridge, or any machine capable of executing instructions (sequential or otherwise) that specify actions to be taken by the machine. Furthermore, although only a single machine is illustrated, the term "machine" should also be construed to include any collection of machines individually or jointly executing a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein, such as cloud computing, software as a service (SaaS), other computer cluster configurations, etc.

[0160] An embodiment as described herein may include or be operated by logic or some components or mechanisms. A circuit set is a collection of circuits implemented in a tangible entity that includes hardware (simple circuits, gates, logic, etc.). The membership of a circuit set may be flexible over time and to the variability of the underlying hardware. A circuit set includes members that, alone or in combination, may perform a specified operation when operated. In one example, the hardware of a circuit set may be immutably designed (e.g., hardwired) to perform a specific operation. In one example, the hardware of a circuit set may include variably connected physical components (e.g., execution units, transistors, simple circuits, etc.) that include a computer-readable medium that has been physically modified (e.g., magnetic, electrical, movable arrangement of immutable mass particles, etc.) to encode instructions for a specific operation. In connecting the physical components, the underlying electrical properties of the hardware constructs are modified, for example, from an insulator to a conductor or vice versa. The instructions enable the embedded hardware (e.g., an execution unit or loading mechanism) to create members of the configured circuits within the hardware via variable connections to perform some of the specific operations during operation. Thus, the computer-readable medium is communicatively coupled to other components of the circuit set members when the device is operating. In one example, any of the physical components may be used in more than one member of more than one circuit set. For example, during operation, an execution unit may be used in a first circuit of a first circuit set at one time and reused by a second circuit of the first circuit set or by a third circuit of the second circuit set at a different time.

[0161] The machine (e.g., computer system) 1400 may include a hardware processor 1402 (e.g., a central processing unit (CPU), a graphics processing unit (GPU), a hardware processor core, or any combination thereof), a storage device such as a machine-readable medium 1422 that may include one or more of a main memory 1404, a static memory 1406, or a mass storage 1408, some or all of which may communicate with each other via an interlink (e.g., a bus) 1430. The machine 1400 may further include a display unit 1410 (e.g., a raster display, a vector display, a holographic display, etc.), an alphanumeric input device 1412 (e.g., a keyboard), and a user interface (UI) navigation device 1414 (e.g., a mouse). In one example, the display unit 1410, the input device 1412, and the UI navigation device 1414 may be touch screen displays. The machine 1400 may additionally include one or more sensors 1416 (such as a Global Positioning System (GPS) sensor, a compass, an accelerometer, or other sensor), a signal generating device 1418 (e.g., a speaker), and a network interface device 1420. The machine 1400 may include an output controller 1428, such as a serial (e.g., Universal Serial Bus (USB), parallel, or other wired or wireless (e.g., infrared (IR), near field communication (NFC), etc.) connection, for communicating with or controlling one or more peripheral devices (e.g., a printer, a card reader, etc.).

[0162] A storage device, such as machine-readable medium 1422, stores one or more sets of data structures or instructions 1424 (e.g., software) embodied or utilized by any one or more of the techniques or functions described herein. The instructions 1424 may reside, completely or at least partially, within main memory 1404, within static memory 1406, within mass storage 1408, or within the hardware processor 1402 during its execution by the machine 1400. In one example, one or any combination of the hardware processor 1402, main memory 1404, static memory 1406, or mass storage 1408 may constitute a machine-readable medium.

[0163] Although the machine-readable medium 1422 is illustrated as a single medium, the term “machine-readable medium” may include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) configured to store one or more instructions 1424.

[0164] The term "machine-readable medium" may include any medium capable of storing, encoding, or carrying instructions for execution by the machine 1400 and causing the machine 1400 to perform any one or more of the techniques of this disclosure, or capable of storing, encoding, or carrying data structures used by such instructions or associated with such instructions. Non-limiting examples of machine-readable media may include solid-state memory, and optical and magnetic media. In one example, a mass machine-readable medium includes a machine-readable medium having a plurality of particles having an unchanging (e.g., stationary) mass. Thus, a mass machine-readable medium is not a transitory propagating signal. Specific examples of mass machine-readable media may include non-volatile memory such as semiconductor memory devices (e.g., electrically programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM)) and flash memory devices, magnetic disks such as internal hard disks and removable disks, magneto-optical disks, and CD-ROM and DVD-ROM disks.

[0165] The instructions 1424 may further be transmitted or received over a communications network 1426 using a transmission medium via a network interface device 1420 utilizing any one of a number of transport protocols (e.g., Frame Relay, Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Hypertext Transfer Protocol (HTTP), etc.). Examples of communications networks include local area networks (LANs), wide area networks (WANs), packet data networks (e.g., the Internet), mobile phone networks (e.g., cellular networks), Plain Old Telephone (POTS) networks, and wireless data networks (e.g., the Institute of Electrical and Electronics Engineers (IEEE) 802.11 family of standards known as WiFi®, the IEEE 802.16 family of standards known as WiMax®), the IEEE 802.15.4 family of standards, peer-to-peer (P2P) networks, among others. In one example, the network interface device 1420 may include one or more physical jacks (e.g., Ethernet, coaxial, or telephone jacks) or one or more antennas for connecting to the communications network 1426. In one example, the network interface device 1420 may include multiple antennas for wireless communication using at least one of single-input multiple-output (SIMO), multiple-input multiple-output (MIMO), or multiple-input single-output (MISO) technologies. The term "transmission medium" should be interpreted to include any intangible medium capable of storing, encoding, or carrying instructions for execution by the machine 1400, including digital or analog communications signals or other intangible media for facilitating communication of such software.

[0166] Various embodiments are illustrated in the figures above. One or more features from one or more of these embodiments may be combined to form other embodiments. Examples of the methods described herein may be at least partially implemented on a machine or computer. Some examples may include a computer-readable medium or machine-readable medium encoded with instructions operable to configure an electronic device or system to perform the methods described in the above examples. Implementations of such methods may include code such as microcode, assembly language code, high-level language code, and the like. Such code may include computer-readable instructions for performing various methods. The code may form part of a computer program product. Additionally, the code may be tangibly stored on one or more volatile or non-volatile computer-readable media during execution or at other times.

[0167] The above detailed description is intended to be illustrative and not restrictive, and therefore the scope of the disclosure should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims

1. 1. A method for testing an electrochemical cell, comprising: electrically cycling the electrochemical cell by applying a charge current during a cycling period and a discharge current during a discharge period, the charge current and the discharge current being symmetrical and having opposite directions; measuring one or more electrical parameters of the electrochemical cell during the cycling of the electrochemical cell, including a cell voltage of the electrochemical cell; electrically cycling the electrochemical cell includes adjusting the charge time or the discharge time to maintain the cell voltage of the electrochemical cell at a particular set value; maintaining the cell voltage of the electrochemical cell at the particular set value through electrically cycling the electrochemical cell and generating a performance metric of the electrochemical cell using the measured one or more electrical parameters, the performance metric being indicative of a total amount of coulombs applied to or output from the electrochemical cell during the cycling period.

2. The method of claim 1 , wherein adjusting the charge time or the discharge time comprises updating a current switch timing for reversing from the charge current to the discharge current.

3. The method of claim 2 , wherein updating the current switch timing is by using the cell voltage or current response of the electrochemical cell contained in the measured one or more electrical parameters.

4. 4. The method of claim 2 or 3, wherein adjusting the charge time or the discharge time includes increasing or decreasing the charge time by an overcharge time, the overcharge time being represented by a count of ticks, each having a duration of a specified switching timer resolution.

5. 5. The method of claim 2, wherein adjusting the charge time or the discharge time comprises increasing or decreasing the discharge time by an excess discharge time, the excess discharge time being represented by a count of ticks, each having a duration of a specified switching timer resolution.

6. generating the performance metric, determining a total amount of charge applied during a specified portion of the cycling period; and determining a self-discharge rate using the determined amount of total charge applied, the self-discharge rate representing an applied current required to maintain the cell voltage of the electrochemical cell at the particular set value.

7. 7. The method of claim 6, wherein the amount of total charge applied comprises a total charge applied per frame (QPF) corresponding to a frame time formed from (i) a duration of the cycling period consisting of a base charge time and a base discharge time, and (ii) an overcharge time, and determining the self-discharge rate comprises using a slope of the trend of QPF over time.

8. The method of claim 7 , wherein determining the QPF comprises integrating the applied current over time within the frame.

9. determining the QPF determining a first amount of total charge applied only during a charging period and a second amount of total charge applied only during a discharging period following the charging period; and determining the QPF using a difference between the first amount of total charge applied and the second amount of total charge applied.

10. 10. The method of claim 9, wherein the first amount of total charge applied is determined by using a first total tick count only during the charging period, and the second amount of total charge applied is determined by using a second total tick count only during the discharging period, the first total tick count representing a first number of ticks each having a duration of a switching timer resolution, and the second total tick count representing a second number of ticks each having a duration of a switching timer resolution.

11. 11. The method of any one of claims 6 to 10, wherein generating the performance metric comprises determining an equivalent series resistance (ESR) of the electrochemical cell using (1) at least one of a charge voltage during a charging period or a discharge voltage during a discharging period, and (2) the applied current.

12. generating the performance metric, generating an ESR curve as a function of the amount of total charge applied; and using the slope of the ESR curve at a particular amount of total charge applied to determine the percentage ESR change per coulomb lost.

13. determining a plurality of ESR change rates under different test conditions, each of the different test conditions represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point; 13. The method of claim 12, comprising: generating a representation of the plurality of ESR rates of change over the parameter sets, the representation comprising a two-dimensional or multi-dimensional array or a two-dimensional or multi-dimensional graph.

14. generating the performance metric, determining a plurality of self-discharge rates under different test conditions, each represented by a parameter set including one or more of a C-rate value, a temperature measurement, or a cell voltage set point; and generating a representation of the plurality of self-discharge rates across the parameter sets, the representation comprising a two-dimensional or multi-dimensional array or a two-dimensional or multi-dimensional graph.

15. The method of claim 14 , comprising displaying one or more of the measured one or more electrical parameters or the measured performance metrics on a user interface.

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