Phenomenon-in-the-loop simulation system and method

Abstract

An exemplary system and method are disclosed for a hybrid computational-experimental simulator that allows for increased investigation and understanding of temperature field evolution in solid oxide fuel cells and electrolyzer cells. The hybrid computational-experimental simulator can be employed as a phenomenon-in-the-loop simulation (PiLS) for combined modeling and experimentation of complex computational electrochemical models.

Description

PHENOMENON-IN-THE-LOOP SIMULATION SYSTEM AND METHODRelated Application

[0001] The PCT international application claims priority to, and the benefit of, U.S. Provisional Patent Application No. 63 / 659,735, filed June 13, 2024, entitled “METHODS AND SYSTEMS FOR OPTIMIZING SOLID OXIDE CELLS,” which is incorporated by reference herein in its entirety.Background

[0002] Solid oxide cells can efficiently produce electricity by electrochemically oxidizing a fuel (typically hydrogen) as a solid oxide “fuel” cell (SOFC) or can electrochemically reduce inlet water (electrolysis) to high-purity hydrogen via an external power source as a solid oxide “electrolysis” cell (SOEC). Stable and efficient operation of high-temperature SOEC systems over long life cycles has been a challenge due to component / material stability at elevated temperatures, problematically high temperature gradients forming across / along the cells, and increased associated balance-of-plant parasitic losses for active thermal management purposes.

[0003] The current practice of managing the temperature of SOECs is to operate them at the thermal neutral voltage where the cell current density is set to a level where the heat generated by the cell matches the heat required by the reaction to maintain a constant, set temperature. The approach can limit the storage of variable and dynamic clean energy via electrolysis because such operational practice does not allow for variations in the coupled renewable energy-sourced energy / electrolysis (e.g., resulting curtailment renewable energy power supply to avoid rising above the thermal neutral voltage). Another approach to thermal management is to allow the SOECs to operate off thermal neutral voltage settings, e.g., using larger reactant flows which provide higher heat capacitance rates, to flatten the SOEC temperature profiles. The approach can introduce greater parasitic balance-of-plant costs and rigors - thus increasing the balance of the system costs and complexity of the controls.

[0004] The control and design of solid oxide cells can be complex. There is a benefit to improving the development of solid oxide cells.Summary

[0005] An exemplary system and method are disclosed for a hybrid computational- experimental simulator that allows for increased investigation and understanding oftemperature field evolution in solid oxide fuel cells and electrolyzer cells. The hybrid computational-experimental simulator can be employed as a phenomenon-in-the-loop simulation (PiLS) for combined modeling and experimentation of complex computational electrochemical models.

[0006] The phenomenon-in-the-loop simulation with a composite computational- experimental approach may be employed to evaluate and prototype solid oxide cells and its associated plant. The exemplary system and method employ reduced-order electrochemical models coupled in a real-time, closed control loop simulation platform with a thermal replica of a physical electrochemical cell (stack). The exemplary' system and method may be embedded resistance heaters to replicate by-product heat from use-case operation. The exemplary system and method allow for the coupling of complex, computational electrochemical simulation and experimental thermal system performance to reliably inform high-fidelity design and controls development. This approach also allows for more flexible, rapid design iterations to unfold without the financial risks of testing high capital cost components as well as the extensive efforts to proceed with full cell / stack tests.

[0007] In an example, the validation and / or calibration of known computational electrochemical models, over temperatures ranges are first obtained. Then, the authenticated model, in the form of validated code, are applied to a real-time simulation platform, which comprises a thermal replica solid oxide cell (SOC), containing embedded resistor heaters that emulate distributed heat generation throughout the SOC during variable operating conditions. As distributed heat generation evolves, so do the resulting temperature fields, and the evolved temperature fields are measured and recorded. The updated temperature fields are also fed back into the real-time simulation platform, forming a feedback loop that depends on (1) evolving distributed heat generation and (2) the resulting temperature field. The feedback loop results in measurable temperature field evaluation in the replica, a task previously unobtainable because the placement of measuring instruments inside SOC devices are found to impede device performance. By obtaining the validated temperature fields that evolve over time, the simulator allows for improved thermal characterization and management protocols.

[0008] Phenomenon-in-the-Loop Simulation methodology / claim can be employed for any vessel that entails coupled heat generation / absorption and temperature fields evolution (e.g., Phenomenon-in-the-Loop Simulation for chemical reactors with temperature-dependent reaction rates). Also, Phenomenon-in-the-Loop Simulation may be employed for simulation vessels that do or don’t also employ general environmental control features (e.g., insulativeenclosures without any environmental thermal regulation: furnaces with temperature set points).

[0009] In an aspect a method is disclosed to determine physical phenomenon (e.g., temperature field evolution) in solid oxide fuel cells and electrolyzer cells using a computational-experimental simulator, the method comprising: obtaining validation and / or calibration of known computational electrochemical models for components of a plant over a temperature range for a phenomenon-in-the-loop simulation; applying an authenticated model in the form of validated code in a closed-control-loop computation simulation platform in combination with a real-time physical simulation platform, the real-time physical simulation platform comprising a thermal replica solid oxide cell (SOC), the real-time phy sical simulation platform having embedded resistor heaters that emulate distributed heat generation throughout the SOC during variable operating conditions (e.g., to replicate by-product heat), wherein the real-time physical simulation platform is synchronized with the closed-control- loop computation simulation platform; in a closed loop operation in the closed control loop computation simulation platform: generating distributed heat generation throughout the SOC during variable operating conditions measuring and recording the generation of distributed heat and resulting temperature fields; adjusting the distributed heat generation using updated temperature fields in the real-time simulation platform in a feedback loop, wherein the recorded generation of distributed heat and resulting temperature fields are employ for measurable temperature field evaluation in the replica, to be used for the design or evaluation of a solid oxide fuel cell and / or solid oxide electrolyzer cell.

[0010] In some embodiments, temperature profile are measured and employed in the closed-control-loop computation simulation platform through a data acquisition board that couples to the closed-control-loop computation simulation platform through an Object Linking and Embedding for Process Control (OPC) data transmission.

[0011] In some embodiments, the embedded resistor heaters comprises SOEC thermal replica with MOSFET-driven embedded heater power control.

[0012] In some embodiments, the real-time physical simulation platform interfaces to the closed-control-loop computation simulation platform through a data-acquisition board having DAC channels and ADC channels, wherein the DAC channels are connected to a power supply to energize each of the embedded resistor heaters, and wherein the ADC channels are connected to temperature sensors placed in the embedded resistor heaters.

[0013] In some embodiments, the real-time physical simulation platform comprises repeating unit cells of embedded resistor heaters within a co-flow SOFC.

[0014] In another aspect, a system is disclosed comprising a closed-control-loop computation simulation platform; and a real-time physical simulation platform, the real-time physical simulation platform comprising a thermal replica solid oxide cell (SOC), the realtime physical simulation platform having embedded resistor heaters that emulate distributed heat generation throughout the SOC during variable operating conditions (e.g., to replicate by-product heat), wherein the real-time physical simulation platform is synchronized with the closed-control-loop computation simulation platform; wherein, in a closed loop operation in the closed control loop computation simulation platform, the real-time physical simulation platform is configured to (i) generate distributed heat generation throughout the SOC during variable operating conditions, (ii) measure and record the generation of distributed heat and resulting temperature fields, and (iii) adjust the distributed heat generation using updated temperature fields in the real-time simulation platform in a feedback loop, wherein the recorded generation of distributed heat and resulting temperature fields are employ for measurable temperature field evaluation in the replica, to be used for the design or evaluation of a solid oxide fuel cell and / or solid oxide electrolyzer cell.

[0015] In some embodiments, temperature profile are measured and employed in the closed-control-loop computation simulation platform through a data acquisition board that couples to the closed-control -loop computation simulation platform through an Object Linking and Embedding for Process Control (OPC) data transmission.

[0016] In some embodiments, the embedded resistor heaters comprise SOEC thermal replica wi th MOSFET-driven embedded heater power control.

[0017] In some embodiments, the real-time physical simulation platform interfaces to the closed-control-loop computation simulation platform through a data-acquisition board having DAC channels and ADC channels, wherein the DAC channels are connected to a power supply to energize each of the embedded resistor heaters, and wherein the ADC channels are connected to temperature sensors placed in the embedded resistor heaters.

[0018] In some embodiments, the real-time physical simulation platform comprises repeating unit cells of embedded resistor heaters within a co-flow SOFC.Brief Description of the Drawings

[0019] Fig. 1 shows an example phenomenon-in-the-loop simulation (PiLS) and composite computational-experiment for solid state oxide development in accordance with an illustrative embodiment.

[0020] Figs. 2A and 2B each show an example setup for a solid oxide cell phenomenon- in-the-loop simulation. Fig. 2A shows an example PiLS simulation for a solid oxide fuel cell. Fig. 2B shows an example PiL simulation for a solid-oxide electrolyzer cell.

[0021] Fig. 3 shows an example method to setup a phenomenon-in-the-loop hardware.

[0022] Fig. 4 shows a solid oxide cell with hollow interconnect structure that is evaluated in a phenomenon-in-the-loop simulation.

[0023] Fig. 5 shows a phenomenon-in-the-loop simulation solid oxide cell replica used in a phenomenon-in-the-loop simulation.

[0024] Fig. 6 shows experimental setup for the phenomenon-in-the-loop simulation solid oxide cell replica of Fig 5.

[0025] Fig. 7 shows a heating circuit for the experimental setup of Fig. 6.

[0026] Fig. 8 A and 8B show a measurement sensor circuit for the experimental setup ofFig. 6.

[0027] Fig. 9 shows an example analysis of SOC replica locational temperatures with variable heater array heat generation dtermined from the experiment using the phenomenon- in-the-loop simulation solid oxide cell replica of Fig 5.Detailed Description

[0028] Some references, which may include various patents, patent applications, and publications, are cited in a reference list and discussed in the disclosure provided herein. The citation and / or discussion of such references is provided merely to clarify the description of the disclosed technology and is not an admission that any such reference is “prior art” to any aspects of the disclosed technology' described herein. In terms of notation, “[n]” corresponds to the nth reference in the list. For example, [1] refers to the first reference in the list. All references cited and discussed in this specification are incorporated herein by reference in their entirety and to the same extent as if each reference were individually incorporated by reference.

[0029] Example System

[0030] Fig. 1 shows an example phenomenon-in-the-loop simulation (PiLS) 100 for use in a composite computational-experiment for solid state oxide development in accordance with an illustrative embodiment. A phenomenon-in-the-loop simulation employs a hybrid computational-experimental simulator that allows for increased investigation and understanding of temperature field evolution in solid oxide fuel cells and electrolyzer cells. In the example shown in Fig. 1, the phenomenon-in-the-loop simulation 100 includes asoftware-based real-time SOFC system simulation model 102 that is configured to operate in real-time operation with a hardware simulator 104 comprising a real-time phenomenon-in- the-loop simulator hardware. The real-time SOFC system simulation model 102 is configured to execute a model of the plant of the solid oxide cell system (e.g., electrolyzer or fuel cell) and a control model to control actuatable elements of the solid oxide cell system. The phenomenon-in-the-loop hardware simulator 104 includes a physical tangible device that mimics the operation of the solid oxide cell for a particular phenomenon, e.g., temperature gradients. Certain physical interactions, e g., of new electrochemical processes or processes, are too complex to accurately model in software. The phenomenon-in-the-loop simulator allows for a physical phenomenon to be replicated in a controlled setting.

[0031] Real-time SOFC system simulation software 102. The real-time SOFC system simulation software 102 includes a physics-based model 106 of the plant of a solid oxide cell system, e.g., electrolyzer, fuel cell, or both. The plant model may include pumps, actuators, separators, and balance-of-plant elements to operate a set of solid oxide fuel cells or electrolyzer cells. Notably, the solid oxide fuel cells or electrolyzer cells are not included in the model 106 but are rather reproduced in the phenomenon-in-the-loop hardware simulator 104 . The real-time SOFC system simulation software 102 includes a control module 108 having control code that is configured to control a fuel cell or electrolyzer plant system. The control module 108 is connected to both the model 106 and the phenomenon-in-the-loop hardware simulator 104. The control module 108 is configured to actuate and control the pumps, actuators, separators, and balance-of-plant elements in the model 104. Outputs of the different model elements are provided to other model elements to mirror the operation of a solid oxide fuel cell plant or solid-oxide electrolyzer plant.

[0032] Phenomenon-in-the-loop hardware 104. The phenomenon-in-the-loop hardware 104 includes control boards and data acquisition instrument to implement a simulation of fuel cell phenomenon, e.g., heat generation and distribution. In Fig. 1, the phenomenon-in-the- loop hardware 104 includes a set of resistor heaters 110 as a physical replica configured to replicate the thermal output of solid oxide cells in which the resistor heaters 110 (shown as resistor heaters 110a. 110b, .. . , 11 On) that are physically placed in proximity to one another in an environment chamber 112. Phenomenon-in-the-Loop Simulation may be employed for simulation vessels that do or don’t also employ general environmental control features (e.g., insulating enclosures without any environmental thermal regulation; furnaces with temperature set points).

[0033] Phenomenon-in-the-Loop Simulation methodology / claim can be employed for any vessel that entails coupled heat generation / absorption and temperature fields evolution (e.g., Phenomenon-in-the-Loop Simulation for chemical reactors with temperature-dependent reaction rates).

[0034] In the example shown in Fig. 1, each resistor 110 is connected to a physical power supply 114 configured to output, e.g., kilowatt power, to the resistors 110. The power supply 114 may be connected to the resistors through a set of switches 116 configured to control the actuation of the solid oxide cells. The physical contacts are connected to a controller board 118 that is coupled to the control software 108 executing on the real-time SOFC system simulation software 102.

[0035] The phenomenon-in-the-loop hardware 104 is instrumented with sensors 120, e.g., temperature sensors, at each of the set of resistors 110 and the environment chamber 112. The sensors are operatively coupled to a multi-channel data acquisition board 122. The data acquisition board 122 converts the temperature measurement (e.g., from RTD) to a current or voltage that is converted to a temperature value to be provided to the control software 108 and the physics-based model 106. Indeed, the resistors 110 in the environment chamber 112 of the phenomenon-in-the-loop hardware 104 serve as a physical mimic of the solid oxide cells that would otherwise be implemented in software. The real-world sensor measurements are presented to the digital world simulation model, to which the solid-oxide cell control can control the overall plant. The phenomenon-in-the-loop hardware 104 provides higher fidelity solid oxide cell dynamic simulation as compared to a conventional model of the solid oxide cell purely in software.

[0036] The phenomenon-in-the-loop simulation 100 may be used to simulate and evaluate solid oxide cell components or used as a system-in-the-loop simulation where the phenomenon-in-the-loop simulation 100, as a fuel cell or electrolyzer system, is employed as a component to a larger system (see, e.g., Fig. 7).

[0037] Solid Oxide Cell Phenomenon-in-the-Loop Simulation. Figs. 2A and 2B each show an example setup for a solid oxide cell phenomenon-in-the-loop simulation. Fig. 2A shows an example PiLS simulation for a solid oxide fuel cell. Fig. 2B shows an example PiL simulation for a solid-oxide electrolyzer cell.

[0038] In the example shown in Fig. 2A, the PiLS simulation 200a includes a system plant 202 comprising a fuel cell 204 and gas lines to provide hydrogen and oxygen to the fuel cell 204 to generate electricity and water (as a byproduct). The output of the fuel cell 204 is provided to a load 206. The plant 208 for the fuel cell 204 includes a hydrogen source 210aand oxygen source 210b. pumps 212a, 212b, and control valves 214a, 214b. The plant 208 are connected to a controller 216 (shown as “Control” 216).

[0039] The controller 216 is operatively connected, shown via lines 218a, 218b, to the pump 212a, 212b, control valve 214a, 214b to control the gas inlet to the fuel cell 204. The plant 208 includes sensors (referred to as 220, not shown) installed on the pumps 212a, 212b, control valves 214a, 214b, and load 206 to measure the operation of the plant components, e.g., pump speed, valve positions, pressure, current and voltage applied to the load, and temperatures at the various components. The controller 216 is operatively connected, via lines 222a, 222b, 222c, 222d, and 222e, to the sensors 220.

[0040] In this system 200a, the pump 212a, 212b, control valve 214a, 214b, hydrogen source 210a and oxygen source 210b, and load 206 are implemented purely in software, e.g., in the model 106, and the fuel cell 204 is implemented as the phenomenon-in-the-loop hardware 104 comprising of resistors 110a, 110b, ... HOn in environment chamber 112.

[0041] Fig. 2B shows an example PiLS simulation for a solid-oxide electrolyzer cell. In the example shown in Fig. 2B. the PiLS simulation 200b includes a system plant comprising an electrolyzer 230 connected to a water line and power supply 232. The water line is shown being directed from a water source 234 through a pump 236 and control valve 238. The outputs of the electrolyzer 230 include hydrogen and oxygen in a water stream that is then separated by gas separators 242a, 242b. The electrolyzer plant is connected to a controller 244 (shown as “Control” 244).

[0042] The controller 21 is operatively connected, shown via lines 246a, 246b, 246c, to the pump 236 and control valve 238 to control the water flow7and pressure to the electrolyzer cells 230. The plant includes sensors (referred to as 248, not shown) installed on the pump 236, valve 238 gas separator 242a, 242b, to measure the operation of the plant components, e.g., pump speed, valve positions, pressure, current and voltage applied to the electrolyzer cells, and temperatures at the various components. The controller 244 is operatively connected, via lines 250a, 250b, 250c, 250d, and 250e, to the sensors 248.

[0043] In this system 200b, the pump 236, control valve 240, water source 234, and gas separator 242a. 242b, are implemented purely in software, e.g.. in the model 106, and the electrolyzer cell 230 is implemented as the phenomenon-in-the-loop hardware 104 comprising of resistors 110a, 110b, ... 11 On in environment chamber 112.

[0044] Method of Setting up Phenomenon-in-the-loop hardware

[0045] Fig. 3 shows an example method to set up a phenomenon-in-the-loop hardware (e.g., 104). In the example shown in Fig. 3, the method includes fabricating samples of thesolid oxide cells and conducting material characterization. The material characterization is analyzed in a continuum-level electrochemistry code. Specifically, a hybrid computational- experimental simulation is employed that couples the nature of SOFC electrochemical and thermal transport phenomena to be replicated and thus characterized, but in a surrogate manner that circumvents the previously stated difficulties. SOFC polarization (i.e., voltagecurrent) data may be obtained over a domain of conditions to validate and / or calibrate computational electrochemical models.

[0046] In Fig. 3, the models and streamlined variants thereof are then used in the realtime PiLS platform (e.g., 104) that also includes a physical replica with embedded resistor heaters for mimicking the thermal response of SOFCs to variable operating conditions. The validated electrochemical code is used to predict and prescribe distributed byproduct heat generation throughout the physical replica, and temperature fields thus physically evolve. The temperature profiles may be measured and reported back to the code via the simulation platform that will include the data acquisition as well as the Object Linking and Embedding for Process Control (OPC) data transmission. The heat generation field prediction is then updated accordingly. The larger thermal time-constants (e.g., on the order of seconds to tens of seconds) as provided by the hybrid computational-experimental simulation can facilitate viable real-time computational-experimental simulation, and coupled thermalelectrochemical transport is thus characterized in a more physically verified manner. The explicit advancement beyond the present HyPer attempt is that the fuel cells’ thermal simulation would be physically based as opposed to being computationally resolved, yet remains synchronized with the electrochemical computational modeling.

[0047] Fuel-cell Design Validation

[0048] To validate the “interconnect (partial) hollows” approach as well as characterize altemative / baseline interconnect designs with high fidelity simulation of components, a phenomenon-in-the-loop simulation (PiLS) may be implemented to provide higher fidelity, yet viable, solid oxide cell dynamic simulation. Hardware-in-the-loop simulation traditionally involves an entire component or set of components being computationally simulated within a system context. PiLS instead considers that certain energy system components that need to be dynamically characterized may be too constrained (e.g., delicate, expensive) to be rigorously experimentally tested, but too multi-faceted or arduous to be completely computationally characterized. Therefore, this blended approach endeavors to develop component replicas that have certain physical similarities to the “real world” technology, and computationally represent other relevant phenomena as necessary.

[0049] The general technical approach framework is as follows. The design and development include the SOEC thermal replica with MOSFET-driven embedded heater power control, heater resistance temperature detection (RTD), and reactant flow rate control that is initially manually controlled and interpreted by a user. In parallel, an electrochemical computational program that models SOC electrochemical and thermal transport behavior was developed to ultimately couple with the physical SOEC thermal replica. The program primarily controls the actuation of "‘by-product,’7local cell heat generation via the embedded resistive heaters, and it receives the resultant spatial cell temperature field data. This realtime, empirical temperature data informs the electrochemical model in a closed-feedback loop arrangement. Once the manually-controlled SOEC thermal replica and electrochemical computational model are established and validated independently, they were to be integrated and linked together in the aforementioned closed feedback loop arrangement.

[0050] Experimental Results and Additional Examples

[0051] A study was conducted that developed and employed hy brid computational- experimental simulator to validate a new solid oxide fuel cell design having “interconnect (partial) hollows” features. Initial results included temperature field evolution measurement and initial indication of high temperature component material appears to be stable. The hybrid system allows further development and characterization of cell component designs and facilitates further research in the domain of passive thermal management techniques for high efficiency SOCs.

[0052] As a preceding step in validating and characterizing the “interconnect (partial) hollows” design concept (402, Fig. 4), a traditional interconnect “baseline” design was targeted for initial fabrication and validation stages. The interconnects and heater frames are integral components in the physical cell (stack) assembly, along with the ceramic heaters that provide the simulated SOEC heat generation. The components (Fig. 4) were fabricated / machined (prior to this project’s period of performance) out of SS 316 to encompass / complete one cell replica. The heater frame had an additional, minimal thickness that served the purpose of encapsulating the heater array, representing the positive (electrode)-electrolyte-negative (electrode) (PEN) structure, and providing a smooth, continuous surface for the fuel and air reactant flows.

[0053] There are two distinct interconnect parts that vary in the flow channel geometry. As detailed in Fig. 4. there is the ‘Blocked Flow Interconnect’ and the ‘Flow Through Interconnect’.

[0054] Image 404 shows PLA (White Color) and SS316 (Gray Color) versions of the i3dMFG fabricated ‘Flow Through Interconnect' and ‘Blocked Flow Interconnect’ components. Image 406 shows X-Ray Scan of Internal Channels / Geometry of 'Flow Through Interconnect'; (Right) X-Ray Scan of Internal Channels / Geometry of ‘Blocked Flow Interconnect'.

[0055] Both interconnect geometries incorporate nineteen 2x2 mm square cross-section channels. The ‘Flow Through Interconnect’ part, however, has the channels pass through the total length of the main body of the interconnect part, whereas the ’Blocked Flow Interconnect’ has an identical, interior channel arrangement with the channel openings closed off at both ends of the main body. This is done to simulate both cell sides’ channels geometry (i.e., the hydrogen / steam and air / oxidant passageways) and hence physically simulate axial conduction through the interconnect halves. The experimental setup, however, is presently capable of physically allowing only one side’s simulated flows (i.e., air / oxidant stream flows). The hydrogen / steam flow side is thus represented by the channels region in the ‘Blocked Flow Interconnect’.

[0056] Ceramic pad heaters (e.g., 110) were arranged in a dual column array arrangement to represent the PEN structure in an actual SOEC assembly and simulate the heat of the electrochemical reaction along the cell. The full cell assembly and arrangement of the heaters can be seen in Fig. 5.

[0057] Image 502 of Fig. 5 shows a SOEC assembly with high temperature electrical connections and ancillary assembly components; (Right) View of exposed ceramic heater array on bottom interconnect half. Image 504 shows (Left) a view of SOEC assembly with high temperature electrical connections made with heater array, and (Right) side view of heater electrical connections made through ceramic wire blocks. Image 506 shows views of electrically-insulative TIM paste used to separate the heater platinum wires from the stainless-steel interconnect material during operation.

[0058] Because of the high temperature operation of the cell and the cell environment, there were limited options to proceed with the ceramic heater electrical power and RTD (resistance temperature detection) connections. The study employed, as shown in Fig. 5, high temperature, stable, electrically-insulative ceramic wire blocks that were custom fabricated to safely house contact-to-contact electrical connections between the ceramic heaters and the power delivery and temperature measurement components.

[0059] Thermal interface material (TIM) paste with electrically-insulative properties was used and applied within the narrow gap (as seen in Fig. 5) where the ceramic heater wirescome out of the interconnect “sandwich'’ structure to connect with the externally-fed electrical wiring. This was an important precaution to take to ensure the heater wires did not contact either of the interconnect plates and cause an electrical short. An insulative chamber cover was incorporated as well to ensure minimal heat loss to the ambient environment during continued high temperature operation as can be seen in the full experimental apparatus view in Fig. 6.

[0060] Heater Power Delivery / Control Framework. The study used high temperature heating (HTH) elements provided by Rauschert (Germany). The imprinted circuit design on the ceramic substrate (shown as 602 in Fig. 6) allows for applications exceeding 750 °C (where conventional cartridge heaters fail) and up to 1000 °C of continuous stable operation, which makes these well-suited for the high temperature SOEC operation between 600°C - 700°C.

[0061] Image 604 shows (Left) a view of full experimental apparatus in operation, and (Right) a view of insulative box chamber containing the SOEC assembly.

[0062] Regarding the heater power delivery control, the general, operational framework utilizes a metal-oxide-semiconductor field-effect transistor (MOSFET)- based supply voltage control approach from a constant main voltage (24 V) fed from the main power supply (as seen in Fig. 7). Specifically, Fig. 7 shows a view of one “quadrant” of heater power delivery' scheme.

[0063] The MOSFET gate served a role as a relay switch module that is triggered by a pulse width modulation (PWM) signal sent from NI DAQ instrumentation, and based upon the signal duty factor and amplitude managed via a developed LabView program. With the variable control of the PWM signal duty factor, an equivalent scaled voltage effect can be administered to the heater of interest. The shunt resistor allows for current draw to be measured as well to determine the effective heater power delivered. In the initial implementation, the power delivery scheme is arranged in quadrants with four main power supplies branching to eight MOSFET circuits, each controlling the modulated power to two (paired) heaters (i.e., sixteen total ceramic heaters). This framework of operation and dynamic control of the heaters allows for coupled operation with the developed electrochemical model informing the heater power levels.

[0064] RTD Measurement Framework. With regards to heater temperature measurement, the platinum circuit path follows a R-T characteristic curve. If one measures the voltage (V) and current (I), the circuit resistance can be measured at the operating temperature with Rt=VI. The corresponding temperature to that determined resistance value can be calculated as follows:(Eq. 1)

[0065] In Equation 1, Rt is the resistance at operating temperature, Rois the resistance at room temperature (~ 20 °C), and a correlation factor for this particular heater type is -0.00315 K-l (or -0.00315 °C'1). As suggested by the heater manufacturer, Rauschert, the temperature calculation via this suggested R-T characteristic formula was deemed the most practical measurement method. The explicit temperature measurement itself is quite difficult as relayed by Rauschert. The area is too small for a pyrometer, and, with a thermocouple, the measured temperature is lower than the actual temperature due to the larger area heat emission. As a closing point regarding the Rauschert ceramic heater overview, it is key to note that, due to different room temperature resistances by way of manufacturing tolerances, each heater was considered individually as the Ro (circuit resistance at room temperature) can and did vary amongst the 16 heaters.

[0066] In order to determine an individual heater's Rt during the full experimental SOC replica operation, a step-down buck converter component is used in conjunction with the main 24V power supply to step dow n to a 2.5V ’‘excitation” signal that is passed through to a series arrangement of a 20 shunt resistor (as seen in Fig. 8 A) and the approximately -2 internal RTD circuit resistance of the heater. Then, using voltage divider law calculations in real-time, the change in measured voltage drop across the 20 shunt resistor can be appropriately correlated and used to determine the real-time value of the heater’s Rt value. The resultant, real-time heater temperature can thus be calculated. This measurement framew ork serves as the basis for the real-time temperature measurement of all 16 heaters in the cell assembly. Specifically, Fig. 8A shows one series arrangement of the RTD heater temperature measurement circuit. Fig. 8B show s a view of SOEC thermal replica with positioning of K-type thermocouples for measuring cell temperature field.

[0067] Coupled EC Model-Lab View Hardware Control-Measurement Framework. As mentioned in the general introduction to the technical approach, an electrochemical (EC) computational program developed via MATLAB-Simulink was under development in parallel with the SOEC thermal replica hardware and LabView hardw are control. It is to be ported into, and integrated with, the developed LabView replica hardware control softw are block tobe able to send inputs and receive outputs from each other. The electrochemical computational program determines the heat rate profile for each heater element in the array of 16 heaters and would relay this output as an input into the aforementioned LabView hardware control program that was developed. The desired heater power setpoints will be compared to the real-time, measured heater power values, and the PWM signal duty factor for each MOSFET will be adjusted accordingly in this implemented PID loop arrangement.

[0068] As a result of the heater array heat generation profile established across the cell replica, a temperature field will evolve and be measured by the replica hardware LabView program by way of the RTD measurement circuit arrangements mentioned prior. The resultant spatial cell temperature data will be relayed back to the electrochemical model in this control loop arrangement to inform an updated heat generation profile for the cell replica.

[0069] This hybrid experimental-computational system will operate through several scenarios of relevant SOC operational conditions, and data will be collected on the thermal response and spatio-temporal evolution of the thermal replica with the baseline, conventional interconnect design and compared to computationally-derived expected results. Ultimately, an additional aspiration is that of interconnect designs with varied, optimal arrangements of the “partial hollows” design being manufactured and incorporated within the thermal replica (in lieu of the baseline interconnect design). The hybrid simulation platform will be operated as similarly done with the baseline interconnect design to characterize differences (e.g., improvements) in cell thermal response and apparent thermal gradients.

[0070] Technical Results. Critical progress during this project effort was achieved on developing and establishing the technical approach framework and the baseline system of operation for gathering results in future efforts. Along the developmental path, there were critical testing efforts to validate the operation and material stability' of the cell replica setup. Fig. 6 displays operation of a key test conducted to ensure the high temperature operational stability of the cell replica materials and critical ancillary subcomponents such as the high temperature heater wire electrical connections and electrically -insulative thermal interface paste material at the high end of the SOC operation temperatures (-800-900 °C). A series of three thermal cycling tests (wherein the array of 16 ceramic heaters were gradually powered to -75 W each) were conducted successfully to achieve elevated cell temperatures, and the critical materials and connections were stable through extended operation of -12 hours. This was critical to achieve in order to gain confidence for further thermal tests and full-scale testing efforts involving the coupled, hybrid computational-experimental approach tocharacterize the baseline interconnect design’s performance and characterization of thermal performance metrics of the novel "‘interconnect (partial) hollows” design approach.

[0071] At these reported stages of cell thermal testing, the RTD temperature measurement circuits of the heaters were not fully implemented, and therefore, high-temperature K-type thermocouples were positioned as seen in Fig. 12 to capture the temperature field of the cell replica.

[0072] During the thermal cycling tests, the array of 16 heaters were fully powered with 75 W applied to each, and the resultant temperature field was measured at the aforementioned locations in Fig. 5 (see 504). As mentioned prior, the primary objective of the thermal cycling tests was to evaluate the material stability and reliability of the cell components with the targeted cell local temperature set at 900 °C. This was achieved successfully as confirmed by instrumentation. After this testing milestone was achieved, initial efforts to characterize and identify temperature gradients were pursued.

[0073] Fig. 9 shows results for SOC replica locational temperatures with variable heater array heat generation. As can be seen in Fig. 9, locational temperature data was plotted against elapsed time from a point where the right half (8 heaters) of the array of 16 heaters were incrementally powered down to zero input power to induce a thermal gradient in the cell. The goal was to detect and study the implications of such action from the start of the ramp down period (t = 0:00). As can be seen from the graph, it is clear that initially the temperature difference between the cell left and right ends was 12.6 °C, but it gradually reached up to a difference of 45.3 °C. Further testing and analysis will have to be conducted in the future regarding the significance and implications of these results, and the basis for this characterization will be important in future testing.

[0074] Conclusion

[0075] As used in the specification and the appended claims, the singular forms ‘‘a,” ‘‘an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0076] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0077] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense but for explanatory purposes.

[0078] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application, including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that can be performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods.

[0079] The following patents, applications, and publications, as listed below and throughout this document, are hereby incorporated by reference in their entirety herein.

Claims

What is claimed1. A method to determine physical phenomenon (e.g., temperature field evolution) in solid oxide fuel cells and electrolyzer cells using a computational-experimental simulator, the method comprising: obtaining validation and / or calibration of know n computational electrochemical models for components of a plant over a temperature range for a phenomenon-in-the-loop simulation; applying an authenticated model in the form of validated code in a closed-control- loop computation simulation platform in combination with a real-time physical simulation platform, the real-time physical simulation platform comprising a thermal replica solid oxide cell (SOC). the real-time physical simulation platform having embedded resistor heaters that emulate distributed heat generation throughout the SOC during variable operating conditions (e.g., to replicate by-product heat), wherein the real-time physical simulation platform is synchronized with the closed-control-loop computation simulation platform; in a closed loop operation in the closed control loop computation simulation platform: generating distributed heat generation throughout the SOC during variable operating conditions; measuring and recording the generation of distributed heat and resulting temperature fields; adjusting the distributed heat generation using updated temperature fields in the real-time simulation platform in a feedback loop, wherein the recorded generation of distributed heat and resulting temperature fields are employ for measurable temperature field evaluation in the replica, to be used for the design or evaluation of a solid oxide fuel cell and / or solid oxide electrolyzer cell.

2. The method of claim 1, wherein temperature profile are measured and employed in the closed-control-loop computation simulation platform through a data acquisition board that couples to the closed-control-loop computation simulation platform through an Object Linking and Embedding for Process Control (OPC) data transmission.

3. The method of claim 1, wherein the embedded resistor heaters comprise SOEC thermal replica with MOSFET-driven embedded heater pow er control.

4. The method of claim 1, wherein the real-time physical simulation platform interfaces to the closed-control-loop computation simulation platform through a data-acquisition board having DAC channels and ADC channels, wherein the DAC channels are connected to a power supply to energize each of the embedded resistor heaters, and wherein the ADC channels are connected to temperature sensors placed in the embedded resistor heaters.

5. The method of claim 1, wherein the real-time physical simulation platform comprises repeating unit cells of embedded resistor heaters within a co-flow SOFC.

6. A system comprising: a closed-control-loop computation simulation platform; and a real-time physical simulation platform, the real-time physical simulation platform comprising a thermal replica solid oxide cell (SOC), the real-time physical simulation platform having embedded resistor heaters that emulate distributed heat generation throughout the SOC during variable operating conditions (e.g., to replicate by-product heat), wherein the real-time physical simulation platform is synchronized with the closed-control- loop computation simulation platform; wherein, in a closed loop operation in the closed control loop computation simulation platform, the real-time physical simulation platform is configured to (i) generate distributed heat generation throughout the SOC during variable operating conditions, (ii) measure and record the generation of distributed heat and resulting temperature fields, and (iii) adjust the distributed heat generation using updated temperature fields in the real-time simulation platform in a feedback loop, wherein the recorded generation of distributed heat and resulting temperature fields are employ for measurable temperature field evaluation in the replica, to be used for the design or evaluation of a solid oxide fuel cell and / or solid oxide electrolyzer cell.

7. The system of claim 6, wherein temperature profile are measured and employed in the closed-control-loop computation simulation platform through a data acquisition board that couples to the closed-control -loop computation simulation platform through an Object Linking and Embedding for Process Control (OPC) data transmission.

8. The system of claim 6. wherein the embedded resistor heaters comprise SOEC thermal replica with MOSFET-driven embedded heater power control.

9. The system of claim 6. wherein the real-time physical simulation platform interfaces to the closed-control-loop computation simulation platform through a data-acquisition board having DAC channels and ADC channels, wherein the DAC channels are connected to a power supply to energize each of the embedded resistor heaters, and wherein the ADC channels are connected to temperature sensors placed in the embedded resistor heaters.

10. The system of claim 6, wherein the real-time physical simulation platform comprises repeating unit cells of embedded resistor heaters within a co-flow SOFC.