Electrochemical cell systems and associated power systems, components, and methods

Abstract

An electrochemical cell system includes one or more electrochemical cells. The electrochemical cell system further includes one or more pulse width modulation controllers configured to pulse power associated with the electrochemical cells. The electrochemical cell system also includes one or more testing apparatus coupled to the electrochemical cells in parallel with the pulse width modulation controllers, the testing apparatus configured to measure voltage changes across the electrochemical cells between pulses of the power caused by the pulse width modulation controllers.

Description

[0001] ELECTROCHEMICAL CELL SYSTEMS AND ASSOCIATED POWER SYSTEMS, COMPONENTS, AND METHODS

[0002] PRIORITY CLAIM

[0003] This application claims the benefit of the filing date of United States Provisional Patent Application Serial No. 63 / 624,227, filed January 23, 2024, for “ELECTROCHEMICAL CELL SYSTEMS AND ASSOCIATED POWER SYSTEMS, COMPONENTS, AND METHODS,” the disclosure of which is hereby incorporated herein in its entirety by this reference.

[0004] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0005] This invention was made with government support under Contract Number DE- AC07-05-ID14517 awarded by the United States Department of Energy. The government has certain rights in the invention.

[0006] TECHNICAL FIELD

[0007] This disclosure relates generally to electrochemical cell systems. More specifically, electrochemical cell systems and associated power systems, components, and methods are disclosed.

[0008] BACKGROUND

[0009] Electrochemical cells, such as batteries, fuel cells, and electrolysis systems may be used to convert power. For example, electrochemical cells may generate and / or store power and power electrical loads, such as electric motors, electronic devices, resistance heaters, lights, etc. Other electrochemical cells may generate or extract elements, such as hydrogen, through electrolysis upon receiving power. Electrochemical cells may be tested to determine the efficiency of the electrochemical cell through several conventional methods. One exemplary method of testing an electrochemical cell is a resistance test performed by interrupting the current from the electrochemical cell in a process known in the art as current interrupt testing. Because the current is interrupted, current interrupt testing is conventionally used only for scheduled testing of the electrochemical cell and often occurs in a lab environment. DISCLOSURE

[0010] Embodiments of the disclosure include an electrochemical cell system. The system includes one or more electrochemical cells, one or more pulse width modulation controllers configured to pulse power associated with the electrochemical cells, and one or more testing apparatus coupled to the electrochemical cells in parallel with the pulse width modulation controllers. The testing apparatus is configured to measure voltage changes across the electrochemical cells between pulses of the power caused by the pulse width modulation controllers.

[0011] Another embodiment of the disclosure includes a power system. The power system includes two or more electrochemical cell systems, each of the two or more electrochemical cell systems comprising one or more electrochemical cells and a testing apparatus coupled to the one or more electrochemical cells. The power system further includes a system controller, the system controller including a pulse width modulation controller configured to pulse power to a load, where the power is received from the two or more electrochemical cell systems. The system controller is configured to receive data from the testing apparatus of each of the two or more electrochemical cell systems. The system controller is also configured to distribute power provided to the load between the two or more electrochemical cell systems based on the data received from the testing apparatus of each of the two or more electrochemical cell systems.

[0012] Another embodiment of the disclosure includes a method of operating an electrochemical cell system. The method includes providing power to a load with an electrochemical cell. The method further includes controlling a perceived power received by the load from the electrochemical cell by interrupting the power to the load for short periods of time with a pulse width modulation controller. The method also includes calculating a cell resistance of the electrochemical cell by using voltage change measurements obtained when the pulse width modulation controller interrupts the power to the load.

[0013] BRIEF DESCRIPTION OF THE DRAWINGS

[0014] While the specification concludes with claims particularly pointing out and distinctly claiming embodiments of the present disclosure, the advantages of embodiments of the disclosure may be more readily ascertained from the following description of embodiments of the disclosure when read in conjunction with the accompanying drawings in which:

[0015] FIGS. 1 A and IB illustrate schematic views of electrochemical cell systems, in accordance with embodiments of the disclosure;

[0016] FIG. 2A illustrates a plot of a pulse width modulation (PWM) control signal, in accordance with embodiments of the disclosure;

[0017] FIG. 2B illustrates a plot of a voltage measurement across an electrochemical cell associated with the PWM control signal of FIG. 2 A, in accordance with embodiments of the disclosure;

[0018] FIG. 2C illustrates a plot of a voltage measurement across an electrochemical cell associated with a single cycle period, in accordance with embodiments of the disclosure;

[0019] FIG. 3 illustrates an equivalent circuit, in accordance with embodiments of the disclosure;

[0020] FIG. 4 illustrates a power system, in accordance with embodiments of the disclosure;

[0021] FIG. 5 illustrates a flow diagram of a method of monitoring an electrochemical cell, in accordance with embodiments of the disclosure;

[0022] FIG. 6A illustrates a flow diagram of a method of obtaining cell resistance, in accordance with embodiments of the disclosure;

[0023] FIG. 6B illustrates a flow diagram of a method of obtaining the cell resistance associated with the flow diagram of FIG. 6 A, in accordance with embodiments of the disclosure;

[0024] FIG. 7 illustrates a plot of the electrochemical impedance spectroscopy (EIS) spectrum at open circuit voltage (OCV), in accordance with embodiments of the disclosure; and

[0025] FIG. 8 illustrates a plot of experimental voltage measurements across an electrochemical cell during a current interrupt, in accordance with embodiments of the disclosure.

[0026] MODE(S) FOR CARRYING OUT THE INVENTION

[0027] The following description provides specific details, such as material compositions, shapes, and sizes, in order to provide a thorough description of embodiments of the disclosure. However, a person of ordinary skill in the art would understand that the embodiments of the disclosure may be practiced without employing these specific details. Indeed, the embodiments of the disclosure may be practiced in conjunction with conventional techniques employed in the industry.

[0028] Drawings presented herein are for illustrative purposes only and are not meant to be actual views of any particular material, component, structure, device, or system. Variations from the shapes depicted in the drawings as a result, for example, of manufacturing techniques and / or tolerances, are to be expected. Thus, embodiments described herein are not to be construed as being limited to the particular shapes or regions as illustrated, but include deviations in shapes that result, for example, from manufacturing. For example, a region illustrated or described as box-shaped may have rough and / or nonlinear features, and a region illustrated or described as round may include some rough and / or linear features. Moreover, sharp angles that are illustrated may be rounded, and vice versa. Thus, the regions illustrated in the figures are schematic in nature, and their shapes are not intended to illustrate the precise shape of a region and do not limit the scope of the present claims. The drawings are not necessarily to scale. Additionally, elements common between figures may retain the same numerical designation.

[0029] As used herein, the terms “configured” and “configuration” refers to a size, a shape, a material composition, a material distribution, orientation, and arrangement of at least one feature (e.g., one or more of at least one structure, at least one material, at least one region, at least one device) facilitating use of the at least one feature in a pre-determined way.

[0030] As used herein, the term “substantially” in reference to a given parameter means and includes to a degree that one skilled in the art would understand that the given parameter, property, or condition is met with a small degree of variance, such as within acceptable manufacturing tolerances. By way of example, depending on the particular parameter, property, or condition that is substantially met, the parameter, property, or condition may be at least 90.0 percent met, at least 95.0 percent met, at least 99.0 percent met, at least 99.9 percent met, or even 100.0 percent met.

[0031] As used herein, “about” in reference to a numerical value for a particular parameter is inclusive of the numerical value and a degree of variance from the numerical value that one of ordinary skill in the art would understand is within acceptable tolerances for the particular parameter. For example, “about” in reference to a numerical value may include additional numerical values within a range of from 90.0 percent to 110.0 percent of the numerical value, such as within a range of from 95.0 percent to 105.0 percent of the numerical value, within a range of from 97.5 percent to 102.5 percent of the numerical value, within a range of from 99.0 percent to 101.0 percent of the numerical value, within a range of from 99.5 percent to 100.5 percent of the numerical value, or within a range of from 99.9 percent to 100.1 percent of the numerical value.

[0032] As used herein, relational terms, such as “below,” “lower,” “bottom,” “above,” “upper,” “top,” and the like, may be used for ease of description to describe one element’s or feature’s relationship to another element(s) or feature(s) as illustrated in the drawings. Unless otherwise specified, the spatially relative terms are intended to encompass different orientations of the materials in addition to the orientation depicted in the figures. For example, if materials in the figures are inverted, elements described as “below” or “under” or “on bottom of’ other elements or features would then be oriented “above” or “on top of’ the other elements or features. Thus, the term “below” can encompass both an orientation of above and below, depending on the context in which the term is used, which will be evident to one of ordinary skill in the art. The materials may be otherwise oriented (e.g., rotated 90 degrees, inverted, flipped) and the spatially relative descriptors used herein interpreted accordingly.

[0033] As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0034] As used herein, the term “and / or” means and includes any and all combinations of one or more of the associated listed items.

[0035] As used herein, the terms “vertical,” “longitudinal,” “horizontal,” and “lateral” are in reference to a major plane of a structure and are not necessarily defined by earth’s gravitational field. A “horizontal” or “lateral” direction is a direction that is substantially parallel to the major plane of the structure, while a “vertical” or “longitudinal” direction is a direction that is substantially perpendicular to the major plane of the structure. The major plane of the structure is defined by a surface of the structure having a relatively large area compared to other surfaces of the structure.

[0036] Electrochemical cells, such as batteries, fuel cells, solid oxide electrolysis cells, and other electrolysis systems, may be used to convert energy, such as by generating chemical compounds through electrolysis, generating and / or storing power and powering electrical loads, such as electric motors, electronic devices, resistance heaters, lights, etc. In some embodiments, the multiple electrical loads may be collectively powered by one or more electrochemical cells. Controllers may be used to modulate the power provided to or from the electrochemical cells, such as to match power needs of the system. For example, a speed of the electric motor may be controlled by modulating the power provided to the electric motor. In another example, heat provided by a resistant heater may be controlled by modulating the power provided to the resistance heater. In another example, the chemical output from an electrolysis process may be controlled by modulating the power provided to the electrolysis cell.

[0037] The health (e.g., performance) of the electrochemical cells may be determined by measuring cell resistance. Conventionally, cell resistance is measured through current interrupt tests, which are conducted by measuring a voltage change across the electrochemical cell when the current supplied by the electrochemical cell is interrupted. While the measurement may be taken in a relatively short period of time, such as in a range from about 1 millisecond to about 10 milliseconds, interrupting the current from the electrochemical cell may be difficult to achieve in a conventional electrochemical cell system on a regular basis.

[0038] FIGS. 1 A and IB illustrate schematic views of electrochemical cell systems 100A and 100B. The electrochemical cell system 100 A includes an electrochemical cell 102 A connected to a load 104 A through a controller 106 A. The electrochemical cell system 100B includes an electrochemical cell 102B configured to be the load, such as for using electrolysis for generating chemical compounds, and the power is provided to the electrochemical cell 102B by a power source 104B connected to the electrochemical cell 102B through a controller 106B. The controller 106 A, 106B may be configured to control the power supplied to or from the respective electrochemical cell 102 A, 102B through pulse width modulation (PWM) (e.g., pulse-duration modulation (PDM) or pulselength modulation (PLM)). PWM is a control strategy that changes a perceived power at the load 104 A or the electrochemical cell 102B acting as a load by switching a power supply on and off during specified intervals, such that the ratio between the time the power supply is on and the time the power supply is off defines the perceived power or average power at the load 104 A or at the electrochemical cell 102B acting as a load. For example, if the power supply is always on, the perceived power is 100% of the power being provided by the power supply. If the power supply is on 50% of the time, the perceived power is 50% of the power being provided by the power supply. Thus, using a PWM controller results in the power supply being operated at full power with the controller 106 A, 106B changing the perceived power at the load rather than changing the operating power of the power supply.

[0039] Conventionally, PWM control is used to control loads in line voltage systems (e.g., alternating current systems, systems powered directly from power wiring in a building or facility, etc.), systems receiving power from an inverter (e.g., direct current systems receiving power through an inverter), or systems receiving power from a transformer (e.g., low voltage systems) where it is conventionally more difficult to vary the power supply, because the power is being supplied at a constant rate from a distinct system (e.g., a generator, a power plant, a transformer, etc.). It is surprising and unexpected that using a PWM controller 106 A, 106B to control power output from an electrochemical cell 102 A or to an electrochemical cell 102B would not result in accelerated stress of the associated electrochemical cell 102A or 102B. It is noted that cycling the power from the electrochemical cell 102A or to the electrochemical cell 102B with a PWM controller 106 A, 106B reduces the heat generation of the electrochemical cell 102 A, 102B due at least in part to the rest periods between on-cycles.

[0040] In embodiments where the controller 106A, 106B is a PWM controller 106A, 106B, the control of the perceived voltage may result in multiple current interruptions in a short period of time. For example, a PWM controller 106 A, 106B may interrupt the power multiple times per second, such as in a range from about 2 times per second to about 100 times per second. The electrochemical cell systems 100 A, 100B may include an analytic tool 108 A, 108B coupled to the electrochemical cell 102 A, 102B in parallel with the load 104 A or power source 104B. The analytic tool 108 A, 108B may include a high-speed power monitor (e.g., testing apparatus), such as a potentiostat or oscilloscope. The analytic tool 108 A may be configured to measure a voltage across the electrochemical cell 102 A when the current from the electrochemical cell 102A is interrupted by the PWM controller 106 A. Similarly, the analytic tool 108B may be configured to measure a voltage across the electrochemical cell 102B when the current from the power source 104B is interrupted by the PWM controller 106B. The analytic tool 108 A, 108B may be configured to measure the voltage change when the current is interrupted and calculate cell resistances of the associated electrochemical cell 102 A, 102B. Calculating the cell resistances of the electrochemical cell 102A, 102B based on voltage measurements taken when the current is interrupted by the PWM controller 106 A, 106B may facilitate monitoring the status of the electrochemical cell 102A, 102B in real-time. The status of the electrochemical cell 102 A, 102B may be monitored during operation of the associated electrochemical cell system 100A, 100B, facilitating in situ monitoring of the electrochemical cells 102A, 102B.

[0041] As an electrochemical cell 102A, 102B degrades, the resistance of the electrochemical cell 102A, 102B may increase. Monitoring the resistance of the electrochemical cell 102A, 102B may facilitate determining when to replace an electrochemical cell 102A, 102B before the electrochemical cell 102A, 102B fails. Monitoring resistance of an electrochemical cell 102A, 102B in real-time may also facilitate capturing data about the electrochemical cell 102A, 102B, such as types of loads and / or conditions that lead to accelerated degradation of the electrochemical cell 102 A, 102B.

[0042] FIG. 2 A illustrates a PWM control signal 200. The PWM control signal 200 illustrates variations of a current 202 over time 204. As illustrated in the plot in FIG. 2A, the current 202 is pulsed, such that the plot defines a pulse region 206 where current is supplied to or from an electrochemical cell (e.g., electrochemical cell 102A (FIG. 1 A), electrochemical cell 102B (FIG. IB)) and a gap region 208 between pulse regions 206. The gap region 208 defines a time period where the current 202 is interrupted, such that the current 202 is substantially zero in the gap region 208. Each pulse region 206 may have a substantially constant current 202 between a start 210 and a stop 212.

[0043] The pulse region 206 has a pulse period 216 and the gap region 208 has a gap period 218. The combined pulse period 216 and gap period 218 define a cycle period 214. The percentage of the cycle period 214 defined by the pulse period 216 may be referred to as the duty cycle and is proportional to the ratio between the instantaneous current, such as the instantaneous current being provided during a pulse period 216 and the average current, such as an average of the current being provided over several cycles including an equal number of pulse periods 216 and gap periods 218.

[0044] An analytic tool, such as the analytic tools 108A, 108B of FIGS. 1 A and IB, may be configured to measure voltage changes across the electrochemical cell while the current is interrupted during the gap region 208. The voltage changes across the electrochemical cell during the gap region 208 may be used to calculate cell resistances. The measurements may be taken during each gap region 208, such that the cell resistances may be calculated between each pulse region 206. As discussed above, the current 202 may be pulsed multiple times each second, such that the cell resistances may also be calculated multiple times per second.

[0045] FIG. 2B illustrates a plot 219 of cell voltage measurements 224 of the electrochemical cell associated with the PWM control signal 200. The plot 219 illustrates the voltage 220 over time 222, where the time 222 is substantially the same as the time 204 in the plot of the PWM control signal 200 illustrated in FIG. 2A. The cell voltage measurements 224 illustrate a load voltage 226, which is representative of the voltage 220 measured across the electrochemical cell during a pulse period 216, where power is being supplied to the load. The cell voltage measurements 224 also illustrate an initial no load voltage 228, which is representative of the voltage 220 measured across the electrochemical cell immediately after the current from the electrochemical cell is interrupted. For example, the initial no load voltage 228 may be measured at substantially the stop 212 point of the pulse. The cell voltage measurements 224 also illustrate a final no load voltage 230 immediately before a subsequent pulse period 216.

[0046] As illustrated in FIG. 2B, the voltage 220 measured across the electrochemical cell experiences a sudden drop off between the load voltage 226 and the initial no load voltage 228 when the current is interrupted. The voltage 220 then gradually decreases through the rest of the gap period 218. The sudden drop off between the load voltage 226 and the initial no load voltage 228 is representative of the ohmic resistance of the electrochemical cell. The gradual reduction in the voltage 220 through the gap period 218 is representative of the polarization resistance, such as due to capacitance throughout the system. The cell resistance of the electrochemical cell may be calculated by using the following formula:

[0047] Where Vi is the load voltage 226, V2 is the initial no load voltage 228, 1 is the current 202 during the pulse period 216 associated with the load voltage 226, and iR is the cell resistance. The cell resistance may be calculated immediately after each pulse period 216 of the PWM control signal 200. The PWM control signal 200 may have multiple cycle periods 214 each second, such that the cell resistance may be calculated multiple times per second through the cell voltage measurements 224.

[0048] FIG. 2C illustrates a plot 232 of cell voltage measurements 224 of the electrochemical cell associated with a single cycle period 214. The plot 232 illustrates the voltage 234 over time 236, where the time 236 illustrated in the plot 232 is constrained to a single cycle period 214 of the plot 219 of the cell voltage measurements 224 illustrated in FIG. 2B.

[0049] As illustrated in FIG. 2C, the voltage 234 measured across the electrochemical cell experiences an initial voltage drop 238, where there is a sudden drop off in voltage 234 from the load voltage 226 to the initial no load voltage 228 immediately after the current from the electrochemical cell is interrupted. After the initial voltage drop 238, the voltage 234 then experiences a gradual voltage drop 240, where the voltage 234 gradually decreases through the rest of the gap period 218 until it reaches the final no load voltage 230. The initial voltage drop 238 is representative of the ohmic resistance of the electrochemical cell. The gradual voltage drop 240 is representative of the polarization resistance, such as due to capacitance throughout the system. Together the ohmic resistance and the polarization resistance account for the total cell resistance.

[0050] The resistances of the electrochemical cell that lead to both the initial voltage drop 238 and the gradual voltage drop 240, may be modeled using an equivalent circuit 300. FIG. 3 illustrates an embodiment of the equivalent circuit 300. The equivalent circuit 300 may include an initial resistor 302 used to account for the initial voltage drop 238. The equivalent circuit 300 may further include multiple subcircuits 304 in series after the initial resistor 302. The multiple subcircuits 304 may be used to account for different electrochemical processes occurring within the electrochemical cell that contribute to the polarization resistance that leads to the gradual voltage drop 240.

[0051] The multiple subcircuits 304 may include subcircuits 306-1 - 306-M in series. Each of the individual subcircuits 306-1 - 306-M may account for individual electrochemical processes occurring within the electrochemical cell. The number M of subcircuits 306-1 - 306-M may be defined by the number of electrochemical processes being accounted for in the model. In some embodiments, the multiple subcircuits 304 may comprise up to 3 subcircuits 306-1 - 306-M, up to 6 subcircuits 306-1 - 306-M, or an even greater number of subcircuits 306-1 - 306-M. In some embodiments, each subcircuit 306-1 - 306-M may comprise a resistor 308-1 - 308-M and a capacitor 310-1 - 310-M in parallel. However, the components that make up each subcircuit 306-1 - 306-M may vary depending on the model being used to account for the gradual voltage drop 240. For example, instead of including a resistor 308-1 - 308-M and capacitor 310-1 - 310-M in parallel, a subcircuit may include a constant phase element used to model the behavior of an imperfect capacitor. Referring to FIGS. 2A through 3, the ohmic resistance of the electrochemical cell that leads to the initial voltage drop 238 may be calculated by using formula 1 :

[0052] M = / ?(1)

[0053] Where Vi is the load voltage 226, V2 is the initial no load voltage 228, 1 is the current 202 during the pulse period 216 associated with the load voltage 226, and iR is the ohmic resistance. The ohmic resistance may be calculated immediately after each pulse period 216 of the PWM control signal 200. The PWM control signal 200 may have multiple cycle periods 214 each second, such that the ohmic resistance may be calculated multiple times per second through the cell voltage measurements 224.

[0054] The polarization resistance that leads to the gradual voltage drop 240 may be calculated using curve fitting or machine learning technology. For example, the gradual voltage drop 240 across the equivalent circuit 300 may correspond to an expected voltage response curve following formula 2:

[0055] Where Vi is the load voltage 226, e is Euler’s number, t is a variable that can be changed to calculate the voltage at a given time, to is the time at the beginning of the gap period 218, Ai, . . ., Am are constants for each subcircuit 306-1 - 306-M, TI, ... , Tm are the resistor-capacitor time constant for each subcircuit 306-1 - 306-M, and V is the voltage 234.

[0056] The resistance of each subcircuit 306-1 - 306-M may be calculated using formula 3:

[0057] Where I is the current 202 during the pulse period 216 associated with the load voltage 226, e is Euler’s number, to is the time at the beginning of the gap period 218, Am is a constant for each subcircuit 306-1 - 306-M, rmis the resistor-capacitor time constant for each subcircuit 306-1 - 306-M, and Rm is the resistance for each subcircuit 306-1 - 306-M.

[0058] The capacitance of each subcircuit 306-1 - 306-M (e.g., Cm) may be calculated using formula 4: c —TmmRm(4)

[0059] Where Rm is the resistance of each subcircuit 306-1 - 306-M obtained from formula 3, rmis the resistor-capacitor time constant for each subcircuit 306-1 - 306-M, and Cm is the capacitance of each subcircuit 306-1 - 306-M. Thus, an analytic tool (e.g., analytic tool 108A / 108B) may use a curve fitting technique to define a curve fit to the cell voltage measurements 224 from the gradual voltage drop 240. Curve fitting techniques may include, but are not limited to, linear regression, non-linear regression (e.g., polynomial regression, etc.), or the use of machine learning. The analytic tool may then use the curve fit, based on the expected voltage response curve (e.g., formula 2), to obtain the missing constants (e.g., Ai, . . ., Am and TI, . . . , Tm) to calculate the resistance and capacitance of each subcircuit 306-1 - 306-M using formulas 3 and 4, respectively. The analytic tool may then output a value for the polarization resistance by adding the resulting resistances of all subcircuits 306-1 - 306-M, as shown by formula 5:

[0060] The ohmic resistance and the polarization resistance may be combined or added together to find the total cell resistance. The ohmic resistance, polarization resistance, and total cell resistance can be used to determine the performance and health of the electrochemical cell.

[0061] The expected voltage response curve may be different depending on the equivalent circuit 300 being used to model the cell resistance. Therefore, formulas 1 - 5 may change depending on the expected voltage response curve being used for the model.

[0062] FIG. 4 illustrates a power system 400 including multiple electrochemical cell systems 402a, 402b, 402c, 402d. The electrochemical cell systems 402a, 402b, 402c, 402d may be similar to the electrochemical cell systems 100 A or 100B described above, with respect to FIGS. 1 A and IB and include similar components (e.g., one or more electrochemical cells 102A, 102B) in substantially the same arrangement as described in FIGS. 1 A and IB. Each of the electrochemical cell systems 402a, 402b, 402c, 402d may include an analytic tool (e.g., testing apparatus) 408a, 408b, 408c, 408d configured to measure voltage across the associated electrochemical cell system 402a, 402b, 402c, 402d. In some embodiments, each of the electrochemical cell systems 402a, 402b, 402c, 402d include a PWM controller similar to the PWM controllers 106 A, 106B illustrated in FIGS. 1 A and IB. The PWM controller may control power provided by each of the electrochemical cell systems 402a, 402b, 402c, 402d to a system controller 404. The system controller 404 may then be configured to distribute the power provided by the electrochemical cell systems 402a, 402b, 402c, 402d to one or more system loads 406. In other embodiments, the system controller 404 may be a PWM controller that is configured to pulse the power received from the electrochemical cell systems 402a, 402b, 402c, 402d when supplying the power to the system loads 406. For example, the system controller 404 may include separate PWM control modules coupled to each of the electrochemical cell systems 402a, 402b, 402c, 402d such that the system controller 404 may control the power output of each of the electrochemical cell system 402a, 402b, 402c, 402d individually through PWM controls. In other embodiments, the system controller 404 may be configured to pulse the output to the system loads 406, such that all of the electrochemical cell systems 402a, 402b, 402c, 402d are pulsed substantially simultaneously by the system controller 404. In yet other embodiments, the system controller 404 may be configured to receive data from the analytic tool (e.g., testing apparatus) 408a, 408b, 408c, 408d and distribute the power provided by the electrochemical cell systems 402a, 402b, 402c, 402d to one or more system loads 406 based on the data received from the analytic tool (e.g., testing apparatus) 408a, 408b, 408c, 408d.

[0063] The system controller 404 may also be configured to distribute the system loads 406 across the electrochemical cell systems electrochemical cell system 402a, 402b, 402c, 402d. For example, in an ideal power system 400, the system controller 404 may distribute the system loads 406 equally across the electrochemical cell systems 402a, 402b, 402c, 402d. The system controller 404 may be configured to monitor a status of the electrochemical cell systems 402a, 402b, 402c, 402d, such as the cell resistance measured and / or calculated by the analytic tools 408a, 408b, 408c, 408d in each of the electrochemical cell systems 402a, 402b, 402c, 402d. In some embodiments, the system controller 404 is configured to distribute the system loads 406 between the electrochemical cell systems 402a, 402b, 402c, 402d based on the status of the individual electrochemical cell systems 402a, 402b, 402c, 402d. For example, if a first electrochemical cell system 402a is exhibiting a high cell resistance based on the measurements taken by the associated analytic tool 408a and a second electrochemical cell system 402b is exhibiting a low cell resistance based on the measurements taken by the associated analytic tool 408b, the system controller 404 may distribute the system load 406 in such a way that a greater amount of the system load 406 is applied to the second electrochemical cell system 402b than is applied to the first electrochemical cell system 402a. Distributing the system load 406 between the electrochemical cell systems 402a, 402b, 402c, 402d based on the cell resistance of the electrochemical cell systems 402a, 402b, 402c, 402d may facilitate a greater efficiency by distributing a greater amount of the system load 406 to the more efficient electrochemical cell systems 402a, 402b, 402c, 402d.

[0064] In some embodiments, the system controller 404 distributes the system loads 406 by routing individual loads of the system loads 406 to a specific electrochemical cell system 402a, 402b, 402c, 402d of the electrochemical cell systems 402a, 402b, 402c, 402d. In other embodiments, the system controller 404 distributes the system loads 406 by modulating a perceived load of the system controller 404 to each of the electrochemical cell systems 402a, 402b, 402c, 402d, such as through individual PWM modules, before combining the received power into a common power and supplying the common power to the system loads 406.

[0065] FIG. 5 illustrates a method 500 of monitoring an electrochemical cell system, such as the electrochemical cell systems 100 A and 100B or the electrochemical cell systems 402a, 402b, 402c, 402d. The power output from the associated electrochemical cell (e.g., electrochemical cell 102) may be controlled through pulse width modulation (PWM) in act 502. As discussed above, PWM may be used to alter a perceived power provided by the electrochemical cell through regularly interrupting the power provided to define pulses and gaps between pulses. When the pulsed power is received by a load, the load will perceive the power to have been reduced to a percentage of the total power, where the perceived percentage is proportional to the ratio of the pulse length to a cycle length, where the cycle includes both the pulse length and the gap length, as discussed in more detail with respect to FIG. 2A.

[0066] Current interrupt testing may be performed between pulses in act 504. As discussed above, current interrupt testing is a process where the voltage across an electrochemical cell is measured when the current is interrupted. The cell resistance may then be calculated by comparing the voltage before and after the current was interrupted, as explained below by method 600 and extended method 600a. When controlling the power output from the electrochemical cell through PWM, the current is interrupted at regular intervals to create the pulse gap pattern and reduce the perceived power output. The current interrupt testing of act 504 may be performed each time the power is interrupted by the PWM controller to perform substantially real-time current interrupt testing of the electrochemical cell and obtain cell resistance data in substantially real-time.

[0067] The cell resistance data may then be supplied to an operator or operating system in act 506. For example, the cell resistance data may be displayed on a user interface, such as a computer screen, a mobile device, a touch screen control interface, etc., where the operator may interact with the system. In some cases, the cell resistance data may be used to create an alert if the cell resistance of an electrochemical cell is above a threshold value. For example, the system may alert a user that the electrochemical cell is due to be replaced or have maintenance performed when the cell resistance is above a threshold value. In some embodiments, the cell resistance data is provided to a system controller that may be configured to distribute loads between multiple electrochemical cells. The cell resistance data may be used to determine where to distribute loads to create an efficient distribution.

[0068] FIG. 6A illustrates a method 600 of obtaining the cell resistance based on voltage measurements from current interrupt testing. In act 602, voltage measurements are obtained from current interrupt testing, where voltage measurements are obtained during the interruptions caused by PWM. The voltage measurements may be measured by an analytical tool (e.g., testing apparatus) that may include a high-speed analog device, such as a potentiostat or an oscilloscope. The voltage measurements may also be stored and processed in a memory device and a processor that are part of the analytical tool or that are separate components from the analytical tool.

[0069] The analytic tool 108 A, 108B may include a high-speed power monitor, such as a potentiostat or oscilloscope. The analytic tool 108 A may be configured to measure a voltage across the electrochemical cell 102 A when the current from the electrochemical cell 102A is interrupted by the PWM controller 106A. Similarly, the analytic tool 108B may be configured to measure a voltage across the electrochemical cell 102B when the current from the power source 104B is interrupted by the PWM controller 106B. The analytic tool 108 A, 108B may be configured to measure the voltage change when the current is interrupted and calculate a cell resistance of the associated electrochemical cell 102 A, 102B. For example, the analytic tool 108 A, 108B may include a processor and a memory. The memory may be configured to store measurements and / or instructions that cause the processor to calculate cell resistances based on the stored measurements.

[0070] As discussed above, cell resistance may be calculated by adding the ohmic resistance and the polarization resistance. Thus, in act 604, the ohmic resistance of the electrochemical cell is calculated using the voltage measurements obtained from current interrupt testing (e.g., formula 1 above). Once ohmic resistance is obtained, the subcomponent values (e.g., polarization resistance) may also be calculated. In act 606, the polarization resistance is calculated by choosing an expected voltage response curve, such as by applying formula 2, to model the voltage measurements. The form of the expected voltage response curve may differ depending on how the voltage measurements are being modeled. Furthermore, each term, 1 to m, of the expected voltage response curve may correspond to a different subcircuit in an equivalent circuit. After the expected voltage response curve is chosen, the expected voltage response curve is then fitted to the voltage measurements in act 608. The expected voltage response curve may be fitted using curve fitting techniques that may include, but are not limited to, linear regression, non-linear regression (e.g., polynomial regression, etc.), or the use of machine learning. The resulting expected voltage response curve fit from act 608 is then used to calculate the resistances and / or capacitances associated with the polarization resistance in act 610. Once the ohmic resistance and the polarization resistance are calculated, both of these values may be added together to obtain the total cell resistance in act 612.

[0071] FIG. 6B illustrates an extended method 600a. Extended method 600a includes acts 602 to 608 and act 612 from method 600. However, extended method 600a shows one embodiment of method 600 where act 610 from method 600 is expanded into acts 610a, 610b, and 610c. Extended method 600a may be used when the expected voltage response curve follows a form similar to that in formula 2, where acts 610a, 610b, and 610c may be used to calculate the polarization resistance in an electrochemical cell. In extended method 600a, act 610 further comprises using the resulting curve fit from act 608 to calculate a value for the missing constants (e.g., Ai, . . . , Am and TI, . . . , Tm) in the expected voltage response curve, as seen in act 610a. In act 610b, the values obtained for the missing constants in act 610a are then used to calculate a corresponding resistance and / or capacitance of each subcircuit (e.g., formula 3) in the equivalent circuit model. In act 610c, the resulting resistances and / or capacitances for each subcircuit obtained from act 610b are added up (e.g., formula 5) to obtain a value for the polarization resistance. Once the polarization resistance has been calculated using acts 610a, 610b, and 610c, extended method 600a may proceed to act 612, where the ohmic resistance from act 604 and the polarization resistance from act 610c are added to obtain the total cell resistance. The resulting ohmic resistance from act 604, polarization resistance from act 610 / 610c, and the total resistance from act 612 in both methods, method 600 and extended method 600a, may be used to determine the health (e.g., performance) of an electrochemical cell.

[0072] One or more of the acts that make up method 600 and extended method 600a may be accomplished through the use of an analytic tool. For example, the curve fitting in act 608, the calculation of a value for the missing constants in act 610a, the calculation of the resistances for each subcircuit in act 610b, or other acts, may be accomplished through instructions directing a processor of an analytic tool.

[0073] The following example serves to explain embodiments of the disclosure in more detail. These examples are not to be construed as being exhaustive or exclusive as to the scope of this disclosure.

[0074] Example

[0075] Current Interrupt Analysis During PWM Control of Solid Oxide Electrochemical Cell (SOEC)

[0076] Current leads were connected to a power supply set at 0.92 A (-613 mA cm’2) through a mechanical relay. A potentiostat measured the voltage of the electrochemical cell at 10,000 pt / s and produced a potential square wave to drive the relay at 1 Hz with a duty cycle of 50%. The tested electrochemical cell was an LSCF-GDC|GDC|YSZ|Ni-YSZ button cell with a 2.413 cm diameter and an active area of 1.5 cm2. The electrochemical cell was tested at 750 °C with 50% H2O balance H2 in the fuel electrode and ambient air in the air electrode. For ease of comparison between techniques, the resistances were not normalized by area.

[0077] FIG. 7 illustrates a plot 700 (e.g., a Nyquist plot) of the electrochemical impedance spectroscopy (EIS) spectrum 702 at open circuit voltage (OCV). The plot illustrates a real part 704 of a function plotted on the X-axis, while an imaginary part 706 is plotted on the Y-axis. An EIS spectrum 702 was taken as a means of comparison between an accepted EIS methodology and the PWM current interrupt methodology according to embodiments of the disclosure. In the Nyquist plot, the cell resistance obtained using the EIS methodology (RoEIS) was calculated from the high-frequency intercept with the real axis (e.g., X-axis). As shown in FIG. 7, the intercept occurred at RoEIS = 0.119 Q.

[0078] For the calculation of cell resistance from the PWM current interrupt methodology using voltage change data, the voltage change data was fit using a two-phase exponential decay function, with a similar formula to that of formula 2 discussed above.

[0079] FIG. 8 illustrates a plot 800 of experimental voltage measurements of the electrochemical cell during a current interrupt, similar to FIG. 2C, along with a voltage decay function curve fit 802. The plot 800 illustrates the voltage 804 in the Y-axis over time 806 in the X-axis. The end of the initial voltage drop 808 was selected to be 344.5 ms, where the measured values significantly deviated from the fitted voltage decay function. A voltage VI was calculated from the voltage decay curve fit 802, a voltage Vo is the load voltage, a time to is the instant the current is removed, AV is the difference between Vo and VI, Ro is the cell resistance calculated from the voltage change over the current, and p is the percent error or the percent difference between the calculated Ro and the measured RoEIS. Thus, using the voltage decay curve fit 802, VI = 1.202 V, Vo = 1.302 V, to = 344.4 ms, AV = 0.100 V, Ro = 0.109 Q, and p = -8.66%.

[0080] Table 1 below summarizes the results for VI, Vo, to, AV, Ro, and p for the voltage decay curve fit 802 in FIG. 8 as well as the results from identical curve fitting analysis applied in nine other interrupts. Table 1 also shows the average Ro over the ten measurements was 0.116 , which is -2.61% off from the RoEIS.

[0081] Table 1

[0082] Embodiments of the disclosure may facilitate real-time monitoring of cell resistances for an electrochemical cell. Monitoring the cell resistances in real-time may facilitate improved control of electrochemical cells and improved load distribution. Monitoring the cell resistances in real-time may also facilitate improved maintenance for the electrochemical cell, such as by alerting an operator to problems in the electrochemical cell before the electrochemical cell fails. This may facilitate changing a electrochemical cell before the electrochemical cell fails, which may reduce downtime for the associated system and may reduce unexpected power failures.

[0083] Additional non-limiting embodiments include: Embodiment 1 : An electrochemical cell system comprising: one or more electrochemical cells; one or more pulse width modulation controllers configured to pulse power associated with the electrochemical cells; and one or more testing apparatus coupled to the electrochemical cells in parallel with the pulse width modulation controllers, the testing apparatus configured to measure voltage changes across the electrochemical cells between pulses of the power caused by the pulse width modulation controllers.

[0084] Embodiment 2: The electrochemical cell system according to embodiment 1, wherein the one or more testing apparatus comprises a high-speed analog device.

[0085] Embodiment 3 : The electrochemical cell system according to embodiment 2, wherein the high-speed analog device comprises a potentiostat.

[0086] Embodiment 4: The electrochemical cell system according to any of embodiments 2 or 3, wherein the high-speed analog device comprises an oscilloscope.

[0087] Embodiment 5: The electrochemical cell system according to any of embodiments 1 through 4, wherein the one or more pulse width modulation controllers are configured to interrupt power in a range from about 2 times per second to about 100 times per second.

[0088] Embodiment 6: The electrochemical cell system according to any of embodiments 1 through 5, wherein the voltage changes measured by the one or more testing apparatus are entered into an analytic tool, and the analytic tool uses curve fitting techniques to output a total cell resistance.

[0089] Embodiment 7: The electrochemical cell system according to embodiment 6, wherein the curve fitting techniques used to output the total cell resistance comprise the use of machine learning.

[0090] Embodiment 8: A power system comprising: two or more electrochemical cell systems, each of the two or more electrochemical cell systems comprising: one or more electrochemical cells; and a testing apparatus coupled to the one or more electrochemical cells; and a system controller comprising: a pulse width modulation controller configured to pulse power to a load, wherein the power is received from the two or more electrochemical cell systems; the system controller configured to receive data from the testing apparatus of each of the two or more electrochemical cell systems, the system controller configured to distribute power provided to the load between the two or more electrochemical cell systems based on the data received from the testing apparatus of each of the two or more electrochemical cell systems. Embodiment 9: The power system according to embodiment 8, wherein the testing apparatus in each of the two or more electrochemical cell systems comprises a high-speed analog device, a potentiostat, or an oscilloscope.

[0091] Embodiment 10: The power system according to any of embodiments 8 or 9, wherein each of the two or more electrochemical cell systems further comprises a pulse width modulation system configured to pulse power from each of the two or more electrochemical cell systems to the control system.

[0092] Embodiment 11 : The power system according to any of embodiments 8 through 10, wherein the testing apparatus is configured to measure voltage changes, and the testing apparatus further comprises an analytic tool configured to receive the voltage change measurements and apply curve fitting techniques to output electrochemical cell performance data.

[0093] Embodiment 12: The power system according to embodiment 11, wherein the electrochemical cell performance data comprises cell resistance data.

[0094] Embodiment 13: The power system according to any of embodiments 11 or 12, wherein the curve fitting techniques comprise machine learning.

[0095] Embodiment 14: The power system according to any of embodiments 11 through 13, wherein the curve fitting techniques comprise an expected voltage response curve associated with an equivalent circuit.

[0096] Embodiment 15: The power system according to embodiment 14, wherein the equivalent circuit comprises an initial resistor and subcircuits.

[0097] Embodiment 16: A method of operating an electrochemical cell system comprising: providing power from an electrochemical cell to a load; controlling a perceived power received by the load from the electrochemical cell by interrupting the power to the load for short periods of time with a pulse width modulation controller; and calculating a cell resistance of the electrochemical cell by using voltage change measurements obtained when the pulse width modulation controller interrupts the power to the load.

[0098] Embodiment 17: The method according to embodiment 16, wherein interrupting the power to the load for short periods of time comprises interrupting the power in a range from about 2 times per second to about 100 times per second.

[0099] Embodiment 18: The method according to any of embodiments 16 or 17, wherein calculating the cell resistance of the electrochemical cell comprises: receiving the voltage change measurements; calculating an ohmic resistance of the electrochemical cell based on the voltage change measurements; choosing an expected voltage response curve to model the voltage change measurements; generating an expected voltage response curve using fitting techniques to fit the expected voltage response curve to the voltage change measurements; and calculating the cell resistances based on the expected voltage response curve fit.

[0100] Embodiment 19: The method according to embodiment 18, wherein calculating the cell resistance further comprises: calculating values for missing constants in the expected voltage response curve based on the expected voltage response curve fit; calculating the cell resistance and / or capacitance, based on the values obtained for the missing constants, of each subcircuit in an equivalent circuit associated with the expected voltage response curve; adding the cell resistance and / or capacitance of all the subcircuits to obtain a value for a polarization resistance; and adding the ohmic resistance and the polarization resistance to obtain the total cell resistance.

[0101] Embodiment 20: The method according to any of embodiments 16 through 19, wherein generating an expected voltage response curve using fitting techniques comprises generating an expected voltage response curve using machine learning.

[0102] The embodiments of the disclosure described above and illustrated in the accompanying drawing figures do not limit the scope of the invention, since these embodiments are merely examples of embodiments of the invention, which is defined by the appended claims and their legal equivalents. Any equivalent embodiments are intended to be within the scope of this disclosure. Indeed, various modifications of the present disclosure, in addition to those shown and described herein, such as alternative useful combinations of the elements described, may become apparent to those skilled in the art from the description. Such modifications and embodiments are also intended to fall within the scope of the appended claims and their legal equivalents.

Claims

CLAIMSWhat is claimed is:

1. An electrochemical cell system comprising: one or more electrochemical cells; one or more pulse width modulation controllers configured to pulse power associated with the electrochemical cells; and one or more testing apparatus coupled to the electrochemical cells in parallel with the pulse width modulation controllers, the testing apparatus configured to measure voltage changes across the electrochemical cells between pulses of the power caused by the pulse width modulation controllers.

2. The electrochemical cell system of claim 1, wherein the one or more testing apparatus comprises a high-speed analog device.

3. The electrochemical cell system of claim 2, wherein the high-speed analog device comprises a potentiostat.

4. The electrochemical cell system of claim 2, wherein the high-speed analog device comprises an oscilloscope.

5. The electrochemical cell system of claim 1, wherein the one or more pulse width modulation controllers are configured to interrupt power in a range from about 2 times per second to about 100 times per second.

6. The electrochemical cell system according to any one of claims 1-5, wherein the voltage changes measured by the one or more testing apparatus are entered into an analytic tool, and the analytic tool uses curve fitting techniques to output a total cell resistance.

7. The electrochemical cell system of claim 6, wherein the curve fitting techniques used to output the total cell resistance comprise the use of machine learning.

8. A power system comprising: two or more electrochemical cell systems, each of the two or more electrochemical cell systems comprising: one or more electrochemical cells; and a testing apparatus coupled to the one or more electrochemical cells; and a system controller comprising: a pulse width modulation controller configured to pulse power to a load, wherein the power is received from the two or more electrochemical cell systems; the system controller configured to receive data from the testing apparatus of each of the two or more electrochemical cell systems; and the system controller configured to distribute power provided to the load between the two or more electrochemical cell systems based on the data received from the testing apparatus of each of the two or more electrochemical cell systems.

9. The power system of claim 8, wherein the testing apparatus in each of the two or more electrochemical cell systems comprises a high-speed analog device, a potentiostat, or an oscilloscope.

10. The power system of claim 8, wherein each of the two or more electrochemical cell systems further comprises a pulse width modulation system configured to pulse power from each of the two or more electrochemical cell systems to the system controller.

11. The power system according to any one of claims 8-10, wherein the testing apparatus is configured to measure voltage changes, and the testing apparatus further comprises an analytic tool configured to receive the voltage change measurements and apply curve fitting techniques to output electrochemical cell performance data.

12. The power system of claim 11, wherein the electrochemical cell performance data comprises cell resistance data.13 The power system of claim 11, wherein the curve fitting techniques comprise machine learning.

14. The power system of claim 11, wherein the curve fitting techniques comprise an expected voltage response curve associated with an equivalent circuit.

15. The power system of claim 14, wherein the equivalent circuit comprises an initial resistor and one or more subcircuits.

16. A method of operating an electrochemical cell system comprising: providing power from an electrochemical cell to a load; controlling a perceived power received by the load from the electrochemical cell by interrupting the power to the load for short periods of time with a pulse width modulation controller; and calculating a cell resistance of the electrochemical cell by using voltage change measurements obtained when the pulse width modulation controller interrupts the power to the load.

17. The method of claim 16, wherein interrupting the power to the load for short periods of time comprises interrupting the power in a range from about 2 times per second to about 100 times per second.

18. The method of claim 16, wherein calculating the cell resistance of the electrochemical cell comprises: receiving the voltage change measurements; calculating an ohmic resistance of the electrochemical cell based on the voltage change measurements; choosing an expected voltage response curve to model the voltage change measurements; generating an expected voltage response curve using fitting techniques to fit the expected voltage response curve to the voltage change measurements; and calculating the cell resistance based on the expected voltage response curve fit.

19. The method of claim 18, wherein calculating the cell resistance further comprises: calculating values for missing constants in the expected voltage response curve based on the expected voltage response curve fit; calculating the cell resistance and / or capacitance, based on the values obtained for the missing constants, of each subcircuit in an equivalent circuit associated with the expected voltage response curve; adding the cell resistance and / or capacitance of all the subcircuits to obtain a value for a polarization resistance; and adding the ohmic resistance and the polarization resistance to obtain the total cell resistance.

20. The method according to any one of claims 16-19, wherein generating an expected voltage response curve using fitting techniques comprises generating an expected voltage response curve using machine learning.

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