Solid oxide electrolysis cell system and method of operating solid oxide electrolysis cell system

Abstract

To provide a method of operating a solid oxide electrolysis cell (SOEC) system at partial load.SOLUTION: A method is provided wherein the SOEC system includes a plurality of branches electrically connected in parallel, and each branch includes at least one SOEC stack. The method includes determining a thermally neutral target voltage below which operation is endothermic and above which operation is exothermic; and executing pulse width modulation current control by cycling an ON phase and an OFF phase for each branch such that the SOEC system operates at an average operating power equal to a chosen percentage of the operating power at the thermally neutral target voltage. In the ON phase, all of the SOEC stacks in a branch operate at the thermally neutral target voltage, and in the OFF phase, all of the SOEC stacks in the branch operate at 0% power. Each branch is configured to be operated independently of the other branches.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to and the benefit of U.S. Provisional Patent Application No. 63 / 060,854, filed August 4, 2020, the entire disclosure of which is incorporated herein by reference. [Background technology]

[0002] The present disclosure relates to electrolysis cell systems for producing fuel, primarily hydrogen, from electricity. In particular, the present disclosure relates to solid oxide electrolysis cell systems and methods of operating solid oxide electrolysis cell systems for part load and rapid response capabilities.

[0003] An electrolysis cell is a device capable of converting electrical input energy into chemical energy stored in a fuel, such as a hydrocarbon fuel, through an electrochemical reaction. Generally, an electrolysis cell comprises an anode, an electrolyte layer, and a cathode. The electrolyte layer facilitates the transfer of ions between the anode and the cathode and drives the reactions within the anode and cathode that produce the chemical fuel.

[0004] Electrolysis cells are often characterized by a type of electrolyte layer used for the transport of specific ions. For example, one type of electrolysis cell is the solid oxide electrolysis cell (SOEC), which incorporates a solid ceramic electrolyte to transport negatively charged oxygen ions from the cathode to the anode.

[0005] At the cathode, the oxygen-containing reactant (often CO vapor) dissociates due to the applied electric current to form hydrogen or CO, along with oxygen ions that transport charge through the electrolyte to the anode. H2O+2e→H2+O 2- (1) CO2+2e→CO+O 2- (2)

[0006] The oxygen ions combine at the anode to form gaseous oxygen according to a reaction. O2 - →1 / 2O2+2e (1)

[0007] The solid ceramic electrolyte of an SOEC is a solid, non-porous metal oxide. For example, the solid ceramic electrolyte of an SOEC can include Y2O3-stabilized ZrO2 (YSZ). The cathode of an SOEC can include, for example, a metal / YSZ cermet. In some examples, the cathode of an SOEC can include a porous dual-phase nickel and yttria-stabilized zirconia (Ni / YSZ) cermet. The anode of an SOEC can be, for example, Sr-doped LaMnO3.

[0008] SOEC operating temperatures typically range from about 650°C to about 1000°C, at which point ionic conduction by oxygen ions occurs. Referring to FIG. 1, a non-limiting example of the relationship between SOEC operating current (horizontal axis) and electrochemical heat generation (vertical axis) is shown, e.g., for temperatures of 650°C, 700°C, and 750°C. It is desirable for SOECs to operate at a target operating point where they operate in a thermally neutral state (i.e., a voltage below which the SOEC stack operates endothermic and above which the SOEC stack operates exothermic). The thermally neutral state is temperature dependent. For example, if the SOEC operating temperature is 750°C, the target operating point is approximately 1.285 V / cell. Most electrolytic stack technologies operate only in their respective exothermic regions based on their reaction kinetics. High-performance SOEC stacks offer the potential for either exothermic or endothermic operation, depending on the conditions.

[0009] In the example of FIG. 1, point d is the target operating point, although it is understood that the target operating point may vary between systems and applications. The shaded zone identifies an example of a preferred operating range. This preferred operating range reflects the need to supply heat to or remove heat from the stack as it deviates from thermal neutrality. The higher the heat load (exothermic or endothermic), the more complex and expensive the resulting thermal management strategy and the higher the stress applied to the SOEC stack. Depending on the design, the SOEC stack can be configured to operate at temperatures up to 0.2 W / cm.2 However, the preferred operating range is 0.1 W / cm 2 A more preferred operating range is less than 0.05 W / cm 2 At point d, the stack is at 750°C, -1 A / cm 2 The SOEC stack is operating at 700°C and is operating in a thermally neutral state. When operating at point d, the SOEC system only needs to preheat the inlet gas, which can be done using the heat of the process exhaust. If the operating power is reduced, for example, to point b, the SOEC stack is operating outside the preferred operating range (shaded zone) and the SOEC stack operation is endothermic. The SOEC stack will either cool toward 700°C (due to poor overall performance at low temperatures) and then reach thermally neutral again, or the SOEC stack will need to connect an auxiliary heater to maintain the stack at operating temperature. If the SOEC stack is allowed to cool, the SOEC system will need to accommodate a different operating temperature.

[0010] For example, if the operating power is increased again to point a, the increase quickly propels the SOEC stack into a severely exothermic state. This tends to bring the stack back up to the target operating temperature, but it is a relatively slow process. Considering a typical SOEC stack, a transition upwards of 50°C requires a time span of minutes. Meanwhile, local overheating and increased exhaust temperature can begin to adversely affect SOEC stack and system operation, potentially adversely affecting its useful life. The curve is not symmetrical. The overheating for a given increase in operating power is much greater than the cooling associated with a decrease in operating power of the same magnitude. Additionally, the thermal state affects cell voltage, and a change from an endothermic to an exothermic operating state can result in a large change in stack voltage, potentially exceeding 30%. Therefore, the associated power electronics must be capable of handling a wider voltage range, which tends both to increase the cost of the power electronics and to decrease their efficiency.

[0011] If the SOEC load is reduced to 50% load and the SOEC stack is cooled to 650°C (point c), it is difficult to increase the operating power beyond about 60% without waiting for the stack and process to heat up again, which is a relatively slow process. In a typical SOEC stack, a 100°C increase in temperature can take tens of minutes.

[0012] The system turndown ratio is defined as the ratio of the system peak power to its lowest sustainable operating point. The operational turndown of a solid oxide electrolysis cell system is typically adapted by changing process conditions, not stack conditions, particularly by changing reactant flows or concentrations and / or by shifting the operating temperature. Conventional solutions for operating in or passing through the endothermic operating range present in high-performance SOEC systems involve rapidly passing through the endothermic region to avoid subcooling, which essentially precludes sustained part-load operation. Another conventional solution involves adding auxiliary heat to the process. Because some heating is required for initial heating to operating temperature, these heaters, if properly designed, can also help maintain temperature during endothermic operation. Yet another conventional solution involves allowing the stack to cool, stopping the endothermic heat, and reducing their efficiency to a point where a new equilibrium is established at a lower operating temperature.

[0013] A need exists for a method of operating a solid oxide electrolysis cell system at high turndown without significantly driving balance of plant requirements in terms of additional heaters, the ability to operate over a wide temperature range, etc. In particular, a need exists for a method of operating a solid oxide electrolysis cell system for part load and rapid response capabilities. Summary of the Invention

[0014] In a particular embodiment, a solid oxide electrolysis cell system includes multiple branches electrically connected in parallel, each branch including at least one solid oxide electrolysis cell stack, each solid oxide electrolysis cell stack including multiple solid oxide electrolysis cells. A method for operating a solid oxide electrolysis cell system at part load includes determining, for a given operating temperature, a thermally neutral target voltage at which operation of the solid oxide electrolysis cell system is endothermic below the thermally neutral target voltage and at which operation of the solid oxide electrolysis cell system is exothermic above the thermally neutral target voltage, and performing pulse-width modulated current control by cycling an on phase and an off phase for each of the branches during an operating cycle of the solid oxide electrolysis cell system, such that the solid oxide electrolysis cell system operates at an average operating power equal to a selected percentage of the operating power at the thermally neutral target voltage for the operating cycle of the solid oxide electrolysis cell system. During the on phase, all of the solid oxide electrolysis cell stacks in a given branch operate at the thermally neutral target voltage. In the off-phase, all of the solid oxide electrolysis cell stacks in a given branch are unloaded to their open circuit voltages and operate at 0% of their rated power. Each branch is configured to operate in either the on-phase or the off-phase independently of the other branches.

[0015] In some aspects of the method or system, all of the branches are in the off phase during at least one period of the actuation cycle.

[0016] In some aspects of the method or system, all of the branches are in the on phase during at least one period of the actuation cycle.

[0017] In some aspects of the method or system, at least one branch is in the on-phase while at least one branch is in the off-phase during at least one period of the operating cycle. This minimizes pulsations in the total output power at any one time. The more stacks electrically connected in parallel and individually switched, the less pulsations are imposed due to on-phase and off-phase transitions.

[0018] In some aspects of the method or system, the switching between the on and off phases occurs during successive periods within the operating cycle, as opposed to during a fixed period.

[0019] In some aspects of the method or system, in an operating cycle, the first branch is in an on phase for the duration of the first period, while the second branch is in an off phase for the duration of the first period, the second branch is switched to the on phase at the start of the second period and remains in the on phase for the duration of the second period, and the first branch remains in the on phase for the duration of the second period, or is switched to the off phase at the start of the second period and remains in the off phase for the duration of the second period.

[0020] In some aspects of the method or system, performing pulse width modulation current control includes selecting a pulse width modulation frequency and duty cycle such that the prevailing thermal conditions are thermal, such that a transition period between an on phase and an off phase or between an off phase and an on phase occupies less than 10 percent of the duration of the operating cycle.

[0021] In some aspects of the method or system, the pulse width modulation frequency and duty cycle are selected such that each branch switches from an on phase to an off phase before cell starvation due to reactant depletion occurs.

[0022] In some aspects of the method or system, the pulse width modulation frequency and duty cycle are selected by a programmed controller to target a prevailing thermal state that is thermally neutral or a slightly net endothermic or slightly net exothermic state, so that the temperature of the solid oxide electrolysis cell stack is constant or ramped in a controlled manner between target operating temperatures that reflect system demand.

[0023] In some aspects of the method or system, the pulse width modulation time constant is τ e (the electrical time constant associated with the voltage response to a change in current, typically on the order of a few milliseconds) and τ c (the chemical time constants associated with reactant supply and reactant depletion at the electrochemical locations within the SOEC stack, typically on the order of seconds).

[0024] In some aspects of the method or system, the prevailing thermal conditions avoid severe endothermic and severe heat generating regions of the overall stack operating window. In some aspects of the method or system, the operating current density of each branch is 50 mW / cm at a thermally neutral target voltage during the ON phase. 2 The current density may be within the range

[0025] In some aspects of the method or system, the pulse width modulation time constant is selected such that heat generation during an entire pulse width modulation cycle is dominated by the on-time and off-time states, and not by the states during the transition between on and off or the transition between off and on.

[0026] In some aspects of the method or system, the on-phase is selected to be at or near thermal neutral. A near thermal neutral state may be selected if the system control desires to shift the operating temperature toward a new operating point (e.g., in preparation for a sustained idle period where cooling may be desired, or in preparation for recovery from a sustained idle period where heating may be desired).

[0027] In some aspects of the method or system, the on-phase is selected to be at or near thermal neutral. If the off-time state is not completely thermally neutral due to excessive heat loss or heat generation from the process balance, a near thermally neutral state may be selected, in which case the on-phase would be selected to provide the heat absorption or generation necessary to balance the overall thermal state to control the SOEC stack temperature.

[0028] In some aspects of the method or system, the pulse width modulation time constant is selected so that the product and reactant concentrations near the electrochemically active region are dominated by the average state during the entire pulse width modulation cycle, rather than the state during the on and off times of the actuation cycle.

[0029] In some aspects of the method or system, the pulse width modulation time constant is selected so that the thermal conditions and resulting temperatures during a complete pulse width modulation cycle are dominated by average conditions rather than by conditions during the on and off times of an actuation cycle.

[0030] In some aspects of the method or system, the pulse width modulation frequency and duty cycle are determined by a pulse width modulation time constant τ pwm is chosen to define a temperature constant (T / T) that simultaneously allows partial power operation of the overall system while maintaining a near-constant capacity factor and a substantially constant temperature due to the different magnitudes of the respective process time constants while operating at substantially thermal neutrality (or a small but controlled deviation from thermal neutrality).

[0031] In some embodiments of the method or system, the resulting actuation strategy is τ as in a conventional controlled SOEC system. t Rather than being limited by the thermal time constant associated with the thermal mass of the SOEC stack and the temperature response to heat flow (typically on the order of minutes), τ e This allows the SOEC stack to operate at a thermal state (temperature) that retains the ability to ramp to full power in times on the order of milliseconds (eg, milliseconds).

[0032] In some embodiments of the method or system, the resulting actuation strategy is τ as in a conventional controlled SOEC system. t Rather than being limited by the thermal time constant associated with the thermal mass of the SOEC stack and the temperature response to heat flow (typically on the order of minutes), τ flowThis allows the SOEC stack to operate in thermal conditions that maintain operation at full power while retaining the ability to ramp to full power in times on the order of 100 sq ft (e.g., seconds).

[0033] In some embodiments of the method or system, the resulting operating strategy allows the SOEC stack to operate under part-load conditions in a manner that allows for power turndown in increments of 10:1 while maintaining full operating temperature and operating in a thermally neutral manner without the need for substantial external heating.

[0034] In some embodiments of the method or system, the resulting actuation strategy is that two or more electrically parallel branches of the stack are switched according to a pulse width modulation sequence in a manner such that at least one branch is in the on-phase while at least one other branch is in the off-phase. For example, a 50% power demand will have only half the stacks in the on-phase at any particular time, but all stacks will experience a 50% duty cycle over the pulse width modulation repeat period.

[0035] In some embodiments of the method or system, the resulting actuation strategy is that two or more electrically parallel branches are switched according to a pulse width modulation sequence in such a way that the weaker branch may be less loaded than the more powerful branch for the overall benefit of system life and efficiency.

[0036] In some aspects of the method or system, the total power cycle is a first predetermined percentage of rated power, each of the branches operates at 100% for a predetermined percentage of the time, and the first predetermined percentage of rated power is equal to the predetermined percentage of time during which each of the branches operates at 100%.

[0037] In some aspects of the method or system, the maximum instantaneous power step is a second predetermined percentage of the rated power, where the second predetermined percentage of the rated power is calculated by dividing 100% by the number of branches of the solid oxide electrolysis cell system.

[0038] In some aspects of the method or system, at least one of the branches operates at 100% of rated power in a first on-phase and at 0% of rated power in the next on-phase immediately following the first on-phase.

[0039] In some aspects of the method or system, at least one of the branches is unloaded and operated at 0% of rated power at regular intervals in the operating cycle of the solid oxide electrolysis cell system.

[0040] In some aspects of the method or system, at least one of the branches is unloaded at irregular intervals in the operating cycle of the solid oxide electrolysis cell system.

[0041] In some aspects of the method or system, the branches in the first subset are the same for two consecutive cycles in an operating cycle of the solid oxide electrolysis cell system.

[0042] In some aspects of the method or system, the branches within the first subset are different for two consecutive cycles in an operating cycle of the solid oxide electrolysis cell system.

[0043] In some aspects of the method or system, each of the plurality of solid oxide electrolysis cells comprises an anode, a cathode, and a solid ceramic electrolyte.

[0044] In some aspects of the method or system, the solid ceramic electrolyte comprises a non-porous metal oxide.

[0045] Those skilled in the art will appreciate that the above aspects are not mutually exclusive and can be combined.

[0046] These and other advantageous features will become apparent to one who considers the disclosure and drawings. [Brief explanation of the drawings]

[0047] [Figure 1] For example, Figure 1 shows the relationship between operating current (horizontal axis) and electrochemical heat production (vertical axis) for each of 650°C, 700°C, and 750°C. [Figure 2] An example of independent on / off switching of the SOEC stacks is shown in an SOEC system operating at 95% net power. [Figure 3] An example of independent on / off switching of the SOEC stacks is shown for an SOEC system operating at 53% net power. [Figure 4] An example of independent on / off switching of the SOEC stacks is shown for an SOEC system operating at 12% net power. [Figure 5] 1 illustrates experimental test results of a sub-scale solid oxide electrolysis stack operating in a furnace according to an exemplary embodiment. [Figure 6] Experimental voltage and temperature response results of a sub-scale solid oxide electrolysis stack gradually stepped through part load conditions from 10% to 70% load according to an exemplary embodiment are compared. DETAILED DESCRIPTION OF THE INVENTION

[0048] Referring generally to the drawings, disclosed herein is a method of operating an SOEC system for part-load and rapid response capabilities. As discussed above, the SOEC system includes at least one solid oxide electrolysis cell. Preferably, multiple solid oxide electrolysis cells can be stacked and interleaved with interconnecting plates that distribute gas to the electrode / electrolyte interfaces and function as flow current collectors to form a solid oxide electrolysis cell stack. The SOEC system can include multiple SOEC stacks forming at least some electrically parallel branches; for example, 40 SOEC stacks can be connected to 20 electrically parallel branches. According to the operation method, each SOEC branch can be loaded from open circuit to full load while operating in a thermally neutral or near-thermally neutral state, independent of the other SOEC branches. Each SOEC branch includes one or more SOEC stacks. The operation method also provides the ability for the SOEC system to operate at part-load but under thermal conditions that allow for a rapid (approximately instantaneous) transition to full load.

[0049] A typical partial duty cycle for an SOEC stack is described as follows: Phase 1—The SOEC stack is operating at zero current, i.e., thermally neutral, at the nominal operating temperature. The reactant flow through the stack is set according to the nominal power demand. Phase 2 - The SOEC stack switches to full current in a thermally neutral state. The SOEC stack voltage response is nearly instantaneous, with the time spent at partial load (endothermic) condition being, for example, a few milliseconds. The heat absorbed during this transition time is negligible compared to the thermal mass of the SOEC stack. Negligible temperature change occurs. Phase 3—The SOEC stack is now thermally neutral and full current, and the flow may be too low to support this current indefinitely. However, there is enough gas adjacent to the active area of the solid oxide electrolysis cell to support some operating time. Depending on the design, this may be on the order of tenths of a second, for example. Phase 4 - The SOEC stack is switched to open circuit before cell starvation due to reactant depletion occurs. Phase 5—The stack is now held at open circuit voltage (OCV) for a period proportional to the desired load target and proportional to the time the SOEC stack has been at full load. For example, a target of 40% of the full load operating point with an on-time of 1 / 10 seconds would have an off-time of 1.5 / 10 seconds. During this time, gas flow continues uninterrupted, clearing products from the active area of the SOEC / SOEC stack and providing new reactants for the next cycle. The SOEC stack is in a thermally neutral state. The cycle then repeats from Phase 1.

[0050] Referring to Figure 1, a non-limiting example of the relationship between SOEC operating current (horizontal axis) and electrochemical heat production (vertical axis) is shown, e.g., for 650°C, 700°C, and 750°C. In the example of Figure 1, point d is the target operating point, although it is understood that the target operating point may vary between systems and applications. At point d, the stack is at 750°C, -1 A / cm 2 The SOEC stack is operating at point d, which is thermally neutral. When operating at point d, the SOEC system only needs to preheat the inlet gas, which can be done using the heat of the process exhaust. If the operating power is reduced, for example, to point b, the SOEC stack is operating outside the preferred operating range (shaded zone) and the SOEC stack operation is endothermic. For example, the target operating point may be the thermally neutral 50 mW / cm, depending on the stack and system design. 2The temperature may be within, above, or below the preferred operating range. A stack operating outside the preferred operating range may be described as heavily exothermic or heavily endothermic. A stack operating within the preferred operating point, but not at the thermally neutral target voltage, may be described as slightly exothermic or slightly endothermic. Upon power unloading from point d, the SOEC stack will either cool toward 700°C (due to poor overall performance at low temperatures) and then reach thermally neutral again, or the SOEC stack will need to connect an auxiliary heater to maintain the stack at operating temperature. If the SOEC stack is allowed to cool, the SOEC system will need to accommodate a different operating temperature.

[0051] For example, if the operating power is increased again to point a, the increase quickly propels the SOEC stack into a severely exothermic state. This tends to return the stack to the target operating temperature, a relatively slow process associated with the thermal time constant of the SOEC stack. Before thermal equilibrium is reestablished, local overheating and increased exhaust temperature begin to adversely affect the SOEC stack and system operation, potentially adversely affecting its useful life. The curve is not symmetrical. The overheating for a given increase in operating power is much greater than the cooling associated with the same magnitude decrease in operating power. Additionally, the thermal state affects cell voltage, and a change from an endothermic to an exothermic operating state can produce a large change in the stack that can exceed 30%. Therefore, the associated power electronics must be capable of handling a wider range of voltages, which tends both to increase the cost of the power electronics and to decrease their efficiency.

[0052] If the SOEC load is reduced to 50% load and the SOEC stack is cooled to 650°C (point c), it is difficult to increase the operating power beyond about 60% without waiting for the stack and process to heat up again, which is due to the thermal time constant τ t This is a relatively slow process indicated by

[0053] A method for operating an SOEC system at part load (hereinafter, "operation method") is described herein. The SOEC system includes multiple solid oxide electrolysis cell stacks connected in parallel. Each SOEC stack includes multiple solid oxide electrolysis cells. The operation method includes determining, for a given operating temperature, a thermally neutral target voltage below which operation of the SOEC system is endothermic and above which operation of the SOEC system is exothermic, and performing pulse-width modulated current control by cycling the on and off phases of each SOEC stack such that during an operating cycle of the SOEC system, the SOEC system operates at an average operating power equal to a selected percentage of the operating power at the thermally neutral target voltage. As used herein, "operation cycle" refers to a period during which the electrolysis cell stacks are operating in accordance with embodiments of the present invention, as opposed to operating at a steady voltage or being powered off for an extended period of time. An electrolysis cell stack is considered to be operating at "100% power" or "full power" when it operates at a thermally neutral target voltage at a given operating temperature. This may also be referred to as "rated power" at a given operating temperature. During the on-phase, the electrolysis cell stack operates at the thermally neutral target voltage. During the off-phase, the electrolysis cell stack is unloaded and operates at 0% power. The solid oxide electrolysis cell stack may be divided into multiple electrically parallel branches. In any electrical branch during the on-phase, the solid oxide electrolysis cell stack in the branch operates at 100% power. In the off-phase, the solid oxide electrolysis cell stack in the branch is unloaded to an open circuit voltage. Each solid oxide electrolysis cell stack electrical branch is configured to operate at 100% power or be unloaded independently from the other solid oxide electrolysis cell stack electrical branches. The SOEC system may include a controller programmed to perform the steps of an operating method.

[0054] According to the operation method, the pulse width and load of the SOEC stack are controlled so that during the on-pulse (Mode 1), the SOEC system operates in a near-thermal-neutral state. During the off-pulse (Mode 2), the stack is unloaded, which is essentially a thermal-neutral state. By switching between Modes 1 and 2, the stack is kept in a near-thermal-neutral state while operating at partial load, which would otherwise be heavily endothermic. The operation method takes advantage of different time constants associated with: 1) the voltage response (cell voltage vs. current), which has a response time in the millisecond range; 2) the electrochemical reaction response as a function of capacity factor (flow vs. current), which has a response time in the subsecond range; and 3) the thermal response (temperature vs. current), which has a response time in the multiple seconds range. These time constants are physical characteristics of the materials and design of the SOEC stack and system.

[0055] At least three characteristic time constants can be identified within SOEC stacks and systems. τ e : the electrical time constant related to the voltage response to a change in current, typically in milliseconds; τ c : the chemical time constants associated with reactant supply and reactant depletion at the electrochemical locations within the SOEC stack, typically on the order of seconds, and τ t : Thermal time constant related to the thermal mass of the SOEC stack and its temperature response to heat flow, typically on the order of minutes.

[0056] The two dynamic time constants of interest can also be considered as follows: τ pwm : A controlled time constant associated with the pulse width modulated current modulation strategy described above. τ flow : A controlled time constant related to the overall system's ability to ramp flow rate in response to a required step change in operating power, for example.

[0057] As long as the operating frequency is sufficiently slow and operation is dominated by on-times and off-times (not transition times), the stack will be nominally thermally neutral. As used herein, the term "prevailing thermal state" refers to the thermal state of the cell for more than 90 percent of the duration of the operating cycle. Thus, if the prevailing thermal state of an electrolysis cell stack is thermally neutral, the stack will operate in a thermally neutral state for more than 90% of the duration of the operating cycle. In particular, as long as the operating frequency is fast enough so that the inlet gas does not pass all the way through the SOEC stack and passes through the cell active area without reacting, the effective capacity factor will be set by the nominal flow rate. These impose constraints on both the maximum and minimum operating frequencies. Given the several orders of magnitude difference in the time constants of these two processes, there is significant room to find an operable frequency that meets both requirements. Neither process imposes significant thermal transients on the stack or system because they are significantly faster than thermal heating.

[0058] For example, Figure 5 shows experimental test results of a sub-scale solid oxide electrolysis stack operating in a furnace according to an exemplary embodiment. This is an ideal environment for fast transient response, with furnace heat supporting endothermic stack operation. Figure 5 shows the same operating conditions, first operated in pulse-width modulation mode (the subject of this disclosure) and then repeated with a typical steady-load strategy. In each case, the operating conditions start at no load, step to 30% load, dwell for 30 minutes, then step to full load, dwell for 30 minutes, followed by unloading.

[0059] Keeping in mind that lower voltage reflects higher efficiency, it should be observed that, first, at 30% load, the pulse-width modulation test operates at a higher efficiency. This is because the operating temperature is maintained and, therefore, it can operate at peak efficiency. In contrast, steady-state operation at 30% load operates at approximately 5% less efficiency because the stack cools by operating endothermically. This is only possible if the test is performed in a furnace that acts to maintain the temperature around the endothermic stack. In a real system, maintaining the operating temperature of the endothermic stack would be more difficult, and the resulting cooling and efficiency losses would likely be greater.

[0060] Further, with reference to Figure 5, it should be noted that a step change to full load has a small voltage recovery in the pulse width modulated case, while the recovery is much larger in the conventional case. This reflects the lower operating temperatures reached during part-load operation and the associated inefficiencies when stepping up to full load. In a real generation system, not only will the part-load temperature be likely to be low, but the available drive voltage may not be high enough to drive the cold stack to peak current, resulting in endothermic operation continuing to increase the transition time, potentially significantly.

[0061] Figure 6 compares experimental voltage and temperature response results of a sub-scale solid oxide electrolysis stack gradually stepped through part load conditions from 10% to 70% load according to an exemplary embodiment. The black data points are the average in-stack temperature (squares) and average cell voltage (circles) when operating in pulse width modulation mode, while the white data points are the same results when operating in conventional steady state mode.

[0062] It is noteworthy that in pulse-width modulation mode, the stack temperature is constant regardless of the set point, whereas in conventional operation, the stack gradually cools with a minimum temperature occurring at approximately 40% load. This subscale test was performed in an electric furnace with a constant temperature set point; in a real system, the stack temperature would be expected to decrease more significantly. Also noteworthy is the higher stack efficiency at all part-power operating points, with a nearly perfect linear response. Higher efficiency is beneficial for obvious reasons, e.g., reducing the energy cost per volume of electrolysis gas. Linearity is beneficial for improving the predictability and controllability of the resulting overall system.

[0063] Furthermore, by avoiding endothermic operation, the stack (and system) is able to respond better to transient conditions compared to conventional operation, and therefore has better load-following capabilities. However, the added benefit of easier temperature and electrical control also improves the system when the stack is controlled with a pulse-width modulation control strategy. Furthermore, it is known that thermal transients are a degradation mechanism for solid oxide electrolysis stacks, and by operating with pulse-width modulation control, the majority of thermal transients that would otherwise be induced can be avoided.

[0064] By allowing operation at part load while maintaining thermal neutrality in the stack, the system does not need to be designed to support severe endothermic operation or large fluctuations in operating temperature. This provides a significant simplification in system design. Additionally, by maintaining the SOEC stack near thermal neutrality, the system can respond much more responsively to changes in power, even under part load conditions.

[0065] Referring to Figures 2-4, the operation of a relatively small SOEC system including five branches electrically connected in parallel is described in further detail. Each branch includes one SOEC stack and is identified as Stack 1, Stack 2, Stack 3, Stack 4, or Stack 5. However, it is understood that each branch may include any number of SOEC stacks; for example, each branch may include 20 to 40 SOEC stacks. Examples of switching operation methods are shown at 95% net power (Figure 2), 53% net power (Figure 3), and 12% net power (Figure 4). The net power percentages represent the average operating power divided by the rated power of the system (i.e., operating power at thermally neutral voltage). The operating cycles for the first 100 cycles are shown, with each number on the x-axis identifying the cycle number. Each shade of the bar represents a specific SOEC stack operating at full current (Mode 1). Therefore, for cycle numbers where a particular SOEC stack is not shaded, it is understood that that particular SOEC stack is unloaded (Mode 2). The dashed line shows the total instantaneous power, while the dotted line shows the time-averaged power. With five SOEC stacks, the maximum instantaneous power step (calculated by dividing 100% of the SOEC system by the number of SOEC stacks) is set to 20% of rated power, which sets the requirements for all electrical systems (e.g., capacitor banks) that may be needed. As the number of stacks increases, the amount of smoothing required decreases.

[0066] Referring to Figure 2, in the first cycle at 95% net power, the first SOEC stack is off (no shading on stack 1) and the other four SOEC stacks are operating at 100% power (shading on stacks 2-5), resulting in a total power of less than 95% of rated power. In the second cycle, all of the SOEC stacks are operating at 100% power (shading on stacks 1-5), resulting in a total power of greater than 95% of rated power, a condition that persists through the fourth cycle. In the fifth cycle, the third SOEC stack is off (no shading on stack 3) and the other four SOEC stacks are operating at 100% power (shading on stacks 1, 2, 4, and 5), resulting in a total power of less than 95% of rated power again. As seen in Figure 2, each SOEC stack operates in thermal neutrality or near thermal neutrality, independent of the other SOEC stacks, and can be loaded from open circuit to full load while maintaining 95% net power. In some embodiments, the total power cycle is a first predetermined percentage of rated power, each of the solid oxide electrolysis cell stacks operates in the on phase for a predetermined percentage of the time, and the first predetermined rated power percentage is equal to the predetermined percentage of time during which each of the solid oxide electrolysis cell stacks operates at 100% power. In Figure 2, each of the five stacks is on 95% of the time (i.e., a predetermined percentage of time) of the cycle, and the total cycle power is also 95% of rated power (i.e., the first predetermined percentage of rated power).

[0067] As shown in Figure 2, each individual stack (or electrical branch) has an on-time that, when averaged over an entire operating cycle, is equal to the desired output power level (when expressed as a percentage of rated power). As shown in Figure 2, the timing of each stack (or electrical branch) is offset relative to each other branch so that the total stacks in their on-cycles are not varied by more than one stack (or electrical branch) at a time. For example, over the course of the 100 step cycles shown, there is no time step in which fewer than four stacks are on simultaneously, even though each of the stacks is off exactly five times.

[0068] In some examples, at least one of the SOEC stacks is unloaded at regular, repeating intervals in the operating cycle of the solid oxide electrolysis cell system (e.g., a regular pattern such as on for five on phases, off for one off phase, on for five on phases, off for one off phase, etc.). In some examples, at least one of the solid oxide electrolysis cell stacks is unloaded at irregular, non-repeating intervals in the operating cycle of the solid oxide electrolysis cell system (e.g., an irregular pattern such as on for five on phases, off for two off phases, on for three on phases, off for four off phases, etc.).

[0069] Referring to FIG. 3, an example of a switching operation method for maintaining 53% net output power is shown. In the first cycle, the fourth and fifth SOEC stacks are 100% on (stacks 4 and 5 are shaded), while the first three SOEC stacks are off (stacks 1 through 3 are not shaded). The SOEC system is operating at 53% output power; there is no cycle in which all five SOEC stacks are on. Instead, in any given cycle, two or three SOEC stacks are 100% on. In any particular cycle, no more than four stacks and no fewer than two stacks are on. Each stack (or electrical branch) operates at the same 53% overall duty when evaluated over a sufficiently long period of time (shown and achieved here over 100-cycle steps). The target power level need not be a discrete value related to the number of stacks. As the desired resolution increases, the overall length of the switching cycle may also increase, but any part-load condition of the SOEC system is achievable with a suitable cycle. In 100 steps (as shown in Figure 3), the output power can be modulated to nearly 1%, where each SOEC stack is on for 53% of the overall cycle. There are relatively few positions where any particular stack is on for two consecutive cycles, and 53% is only slightly above 50%, reflecting that all stacks are on exactly 50% of the time.

[0070] Referring to Figure 4, an example of a switching operation method to maintain 12% output power is shown. Each SOEC stack is turned on approximately once every eight cycles. The SOEC stacks each switch between open circuit ("off"), which is essentially thermally neutral, and full power ("on"), which is configured to be thermally neutral, resulting in an operating point that results in no SOEC stack cooling other than waste heat loss from the process. This waste heat loss can be balanced by selecting a slightly exothermic on-phase, assuming heat loss is small, which should be typical for an efficient electrolysis system.

[0071] One constraint on turndown is the minimum switching frequency, which is tied to the period it takes for reactant molecules to flow from the inlet to the outlet of the electrochemically active region. In the example of Figure 4, if the off-period is 8 cycles, the switching frequency must be selected so that the 8 cycles do not result in excessive reactant bypass flow through the unpowered SOEC stack. This may not be as significant a constraint, since the system flow rate is adjusted for a lower power condition (12% net power). If the flow rate is 8 times lower, the flow rate period will also be 8 times longer, and therefore no change in switching frequency is required. If the flow rate is not 8 times lower, the switching period will not affect the overall capacity factor, since there will be excess reactant flow even during the on-period.

[0072] 2-4, or any other net power maintained in accordance with the method of operation, reactant flow does not need to be interrupted or redirected to selected SOEC stacks. The reactant flow is distributed evenly to all SOEC stacks and does not affect the capacity factor of the SOEC stacks or the system, as long as the switching frequency is appropriately selected.

[0073] In the example shown, two underlying assumptions are made: 1) In any particular cycle, power is distributed to the stack (electrical branch) that has not requested power for the longest period of time. This ensures a rotating power demand that minimizes the continuous on- and off-time of any particular stack. 2) Each stack (or electrical branch) supplies power in precise proportion to the system-level power demand. Neither assumption is necessary for the overall control strategy. For example, random or semi-random determination of which stack to turn on in a particular cycle can be used. Individual power branches do not need to operate in precise proportion to overall system demand, but instead can operate in response to both system demand and individual branch capacity (or health), so that weaker branches can be loaded less than more powerful branches, or certain branches can be preferentially heated (or cooled) in preparation for or in response to slower power transients.

[0074] Referring to Figure 1, the above operating method allows the SOEC stack to always operate at point d or point e from a thermal and power standpoint. Both points d and e are thermally neutral. At 50% power, the SOEC stack spends half the time at point d and half the time at point e. The SOEC stack can be maintained at full operating temperature and ramped to full power as fast as reactants become available, without any fluctuations in operating voltage or temperature.

[0075] Furthermore, consider the range of 20% to 30% of rated power. In this region, even allowing the SOEC stack to cool down to 650°C is insufficient to move it out of a severe endothermic state. Process heaters or very low stack temperatures are required, which present control challenges and severe limitations in dynamic response capabilities. As a result, a further advantage of this operating method is the extended turndown capability compared to conventional control strategies.

[0076] By avoiding severely endothermic part-load conditions, system balance can be simplified because there is no need to support severely endothermic or severely exothermic conditions. Instead, the SOEC system and SOEC stack operate at a specific design offset toward near-thermal neutrality, or toward endothermic or exothermic operation as desired. Similarly, the SOEC system can compensate for stack degradation over time while maintaining a narrow operating window under conditions most favorable to stack life and performance. Additionally, the SOEC system can operate at part-load conditions while holding the SOEC stack in a state that facilitates near-instantaneous load up to full load, enabling much faster transient response than would otherwise be possible.

[0077] Depending on the operating method, the SOEC stack will be maintained at operating temperature even when operating under partial load conditions. This means that power absorption from the SOEC stack can be increased to full power on the sub-second scale for short-term transients and on the second scale for long-term transients requiring flow rate changes. This significantly increases the potential for grid voltage and frequency stabilization, as the available modulation is much greater than in conventional controlled SOEC systems.

[0078] The above-described operating method allows for sustained operation of the SOEC system under partial load (i.e., not full load) conditions. The operating method does not rely on auxiliary heating. Instead, the operating method relies on self-heating of the SOEC stack. This allows for separation of heating requirements, thereby simplifying balance of plant in SOEC systems where balance of plant is an auxiliary device necessary to ensure the SOEC system operates as a reliable power source. In accordance with the operating method, heat is generated where it is needed (within the SOEC stack), eliminating the need to optimize heat transfer from a separate heater to the SOEC stack and providing simplification to the overall hot module. Therefore, the operating method also reduces the thermal load on the SOEC stack for a potential increase in stack efficiency and lifespan.

[0079] As shown in FIG. 1, the performance / temperature curve is not symmetrical. If the SOEC stack is allowed to cool with a part-load operation strategy, the SOEC stack will be limited in its ability to ramp power upward. For example, if operating at 50% power, the SOEC stack may only be able to quickly increase to 60% power, and may take several minutes to ramp to 100% power while maintaining reasonable temperatures within the SOEC stack. In contrast, the above-described operation method allows for fast ramping from any power level to any other power level, as fast as the process gas can be ramped.

[0080] The operating method may be particularly suitable for highly modular stack arrays, where the impact of electrical switching on the power bus can be mitigated by sequentially phasing stacks. For example, at 50% load, half of the stacks are on at any particular time, and there is no time when all stacks are active. In a single stack, current switching can impose noise on the resulting DC bus, which can have adverse consequences for the efficiency of the system power electronics. In highly modular systems (i.e., systems in which many stacks share the same DC bus), the transition time of each stack can be offset relative to the other stacks to minimize bus noise. The more stacks operating electrically in parallel, the less the operating method affects bus voltage and noise. In some aspects, the switching is systematic. In particular, the order and timing of SOEC stacks being on or off at any given part-load condition is the same. In other aspects, the switching is pseudo-random. In particular, the order and timing of SOEC stacks being on or off at any given part-load condition is not the same. For example, if one SOEC stack is weaker than another, a pseudo-random approach may smooth out the resulting electrical noise. A pseudo-random approach may provide advantages in terms of eliminating forced noise and unplanned bias in the system.

[0081] In some embodiments, the application of pulse-width modulated power can be used to control the net thermal operating state of the SOEC stack in a manner independent of the net electrical state. This concept is described herein in terms of maintaining a net thermally neutral state under partial electrical load conditions that would otherwise be endothermic. This concept can equally be applied to targeting a specific thermal state, for example, to apply a net heat generating state as a way to help heat the stack. The application of pulse-width modulated power under partial load conditions allows for independent control of the stack thermal state and, as a result, can be used to move the stack temperature up or down in response to other system demands.

[0082] In some embodiments, the operating frequency of an SOEC stack can vary between a lower boundary indicated by the stack geometry and the net flow period for any fluid particle to move from the cell active area inlet to the cell active area outlet, and a higher boundary indicated by the point of diminishing efficiency recovery due to switching losses, and ultimately, the point at which cell electrical performance begins to equalize with part-load conditions and thermal benefits begin to disappear.

[0083] As used herein, the terms "approximately," "about," "substantially," and similar terms are intended to have a broad meaning consistent with commonly accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. It should be understood by those of ordinary skill in the art who review this disclosure that these terms are intended to enable description of the particular features described and claimed without limiting the scope of those features to the precise numerical ranges provided. Accordingly, these terms should be interpreted to indicate that insubstantial or insignificant modifications or variations of the subject matter described and claimed are considered to be within the scope of the invention as recited in the appended claims.

[0084] As used herein, the terms "coupled," "connected," and the like mean that two members are joined directly or indirectly to one another. Such joining can be fixed (e.g., permanent) or movable (e.g., removable or releasable). Such joining can be achieved by the two members or the two members and an additional intermediate member being integrally formed with one another as a single, unitary body, or by the two members or the two members and an additional intermediate member being attached to one another.

[0085] References herein to the location of elements (e.g., "top," "bottom," "upper," "lower," etc.) are used merely to describe the orientation of the various elements in the figures. It should be noted that the orientation of the various elements may differ according to other exemplary embodiments, and such variations are intended to be encompassed by the present disclosure.

[0086] It is important to note that the construction and arrangement of the various exemplary embodiments are illustrative only. While only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications (e.g., changes in the size, dimensions, structure, shape, and proportions of various elements, parameter values, mounting arrangements, material use, color, orientation, etc.) are possible without substantially departing from the novel teachings and advantages of the subject matter described herein. For example, elements shown as integrally formed may be composed of multiple parts or elements, the position of elements may be reversed or otherwise changed, and the nature or number of individual elements or positions may be altered or changed. The order or sequence of any process or method steps may be changed or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the various exemplary embodiments without departing from the scope of the invention. For example, the heat recovery heat exchanger may be further optimized.

[0087] The operations described above may be performed by a computer programmed to execute the steps of an algorithm. Embodiments of the subject matter and operations described herein may be implemented in digital electronic circuitry, or in computer software embodied in tangible media, firmware, or hardware, including the structures disclosed herein and their structural equivalents, or in a combination of one or more of these. Embodiments of the subject matter described herein may be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on one or more computer storage media for execution by or to control the operation of a data processing apparatus. Alternatively, or in addition, the program instructions may be encoded in an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal generated to encode information for transmission to a suitable receiving device for execution by a data processing apparatus. A computer storage medium may be, or may be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of these. Furthermore, while a computer storage medium is not a propagated signal, a computer storage medium may be a source or destination of computer program instructions encoded in an artificially generated propagated signal. A computer storage medium may also be, or may be contained in, one or more separate components or media (e.g., multiple CDs, disks, or other storage devices). Thus, a computer storage medium may be tangible and non-transitory.

[0088] The operations described herein may be implemented as operations performed by a data processing device or processing circuitry on data stored in one or more computer-readable storage devices or data received from other sources.

[0089] An apparatus may include special purpose logic circuitry, such as an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). In addition to hardware, an apparatus may also include code that creates an execution environment for the computer program in question, such as code comprising processor firmware, a protocol stack, a database management system, an operating system, a cross-platform runtime environment, a virtual machine, or a combination of one or more of these. The apparatus and execution environment may implement a variety of different computing model infrastructures, such as web services, distributed computing, and grid computing infrastructures.

[0090] A computer program (also known as a program, software, software application, script, or code) can be written in any type of programming language, including compiled or interpreted, declarative or procedural, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, object, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files storing one or more modules, subprograms, or portions of code). A computer program located at one site or distributed across multiple sites and interconnected by a communications network can be deployed to run on one computer or on multiple computers.

[0091] The processes and logic flows described herein may be performed by one or more programmable processors or processing circuits executing one or more computer programs to perform actions by operating on input data and generating output. The processes and logic flows may also be performed by, and apparatus may also be implemented as, special purpose logic circuitry, such as an FPGA or ASIC.

[0092] Processors or processing circuits suitable for executing a computer program include, by way of example, both general-purpose and special-purpose microprocessors, as well as any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random-access memory, or both. The essential elements of a computer are a processor for performing actions in accordance with the instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include one or more mass storage devices, e.g., magnetic, magneto-optical, or optical disks, for storing data, or be operatively attached to receive data from or transfer data to them, or both. However, a computer need not have such devices. Furthermore, a computer can be embedded in another device, e.g., a mobile phone, personal digital assistant (PDA), mobile audio or video player, game console, global positioning system (GPS) receiver, or portable storage device (e.g., a universal serial bus (USB) flash drive), to name a few. Suitable devices for storing computer program instructions and data include, by way of example, all forms of non-volatile memory, media, and memory devices, including semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks, such as internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0093] To provide for interaction with a user, embodiments of the subject matter described herein may be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display), OLED (organic light-emitting diode), TFT (thin film transistor), plasma, other flexible configurations, or any other monitor for displaying information to a user, and a keyboard, a pointing device, e.g., a mouse, trackball, or the like, or a touchscreen, touchpad, or the like, through which a user can provide input to the computer. Other types of devices may also be used to provide interaction with a user; for example, feedback provided to the user may be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback, and input from the user may be received in any form, including acoustic input, voice input, or tactile input. Additionally, a computer may interact with a user by sending documents to and receiving documents from a device used by the user, e.g., by sending a web page to a web browser on the user's client device in response to a request received from the web browser.

Claims

1. 1. A method for operating a solid oxide electrolysis cell system at part load, the solid oxide electrolysis cell system including a plurality of branches electrically connected in parallel, each branch including at least one solid oxide electrolysis cell stack, each solid oxide electrolysis cell stack including a plurality of solid oxide electrolysis cells, the method comprising: determining a thermal-neutrality target voltage for a given operating temperature, where operation of the solid oxide electrolysis cell system is endothermic below the thermal-neutrality target voltage and operation of the solid oxide electrolysis cell system is exothermic above the thermal-neutrality target voltage; performing pulse width modulated current control by cycling on and off phases for each of the branches such that during an operating cycle of the solid oxide electrolysis cell system, the solid oxide electrolysis cell system operates at an average operating power equal to a selected percentage of an operating power at the thermally neutral target voltage for an operating cycle of the solid oxide electrolysis cell system; In the on-phase, all of the solid oxide electrolysis cell stacks in a given branch operate at the thermally neutral target voltage, and in the off-phase, all of the solid oxide electrolysis cell stacks in the given branch are unloaded to an open circuit voltage and operate at 0% of rated power; each of the branches is configured to operate in the on phase or the off phase independently of the other branches.

2. The method of claim 1 , wherein all of the branches are in the off phase during at least one period of the operating cycle.

3. 3. The method of claim 1, wherein all of the branches are in the on phase during at least one period of the operating cycle.

4. 4. The method according to claim 1, wherein during at least one period of the operating cycle, at least one branch is in the on-phase while at least one other branch is in the off-phase.

5. 5. The method of claim 1, wherein the switching between the on-phase and the off-phase occurs during consecutive periods within the operating cycle, as opposed to during a fixed period.

6. In the operating cycle, a first branch is in the on phase for the duration of a first period, while a second branch is in the off phase for the duration of the first period; the second branch is switched to the on phase at the start of a second period and remains in the on phase for the duration of the second period; 6. The method of claim 1, wherein the first branch remains in the on phase for the duration of the second period, or is switched to the off phase at the start of the second period and remains in the off phase for the duration of the second period.

7. 7. The method of claim 1, wherein each branch comprises a plurality of solid oxide electrolysis cell stacks.

8. Implementing pulse width modulated current control 8. The method of claim 1, comprising selecting a pulse width modulation frequency and a duty cycle such that a transition period between an on phase and an off phase or between an off phase and an on phase occupies less than 10 percent of the duration of the operating cycle and such that the prevailing thermal state is thermal neutral.

9. 9. The method of claim 8, wherein the pulse width modulation frequency and the duty cycle are selected such that each branch switches from the on phase to the off phase before cell starvation due to reactant depletion occurs.

10. 9. The method of claim 8, wherein the pulse width modulation frequency and the duty cycle are selected by a programmed controller to select the prevailing thermal state to be thermally neutral or to target a slightly net endothermic or slightly net exothermic state, such that the temperature of the solid oxide electrolysis cell stack is constant or ramped in a controlled manner between target operating temperatures that reflect system demand.

11. The operating current density of each branch is 50 mW / cm at the thermal neutral target voltage during the ON phase. ２ The method according to any one of claims 1 to 10, wherein the current density is within the range of

12. the total power cycles is a first predetermined percentage of the rated power; each of said branches is operated in said on phase for a predetermined percentage of time; 12. The method of claim 1, wherein the first predetermined percentage of rated power is equal to a predetermined percentage of the time during which each of the branches operates in the on-phase.

13. 13. The method of any one of claims 1 to 12, wherein the maximum instantaneous power step is a second predetermined percentage of rated power, and the second predetermined percentage of rated power is calculated by dividing 100% by the number of branches of the solid oxide electrolysis cell system.

14. The method of claim 13 , wherein magnitude electrical smoothing is determined based on the maximum instantaneous power step.

15. 15. The method according to any one of claims 1 to 14, wherein at least one of the branches operates at 100% of rated power in a first ON phase and at 0% of rated power in a subsequent OFF phase immediately following the first ON phase.

16. 16. The method of any one of claims 1 to 15, wherein at least one of the branches is unloaded and operated at 0% of rated power at regular intervals in the operating cycle of the solid oxide electrolysis cell system.

17. The method of claim 1 , wherein at least one of the branches is unloaded at irregular intervals during an operating cycle of the solid oxide electrolysis cell system.

18. 18. A solid oxide electrolysis cell system operated according to the method of any one of claims 1 to 17.

19. 1. A solid oxide electrolysis cell system comprising: a plurality of branches electrically connected in parallel, each branch including at least one solid oxide electrolysis cell stack, each solid oxide electrolysis cell stack including a plurality of solid oxide electrolysis cells; determining a thermal-neutrality target voltage at which operation of the solid oxide electrolysis cell system is endothermic below the thermal-neutrality target voltage and at which operation of the solid oxide electrolysis cell system is exothermic above the thermal-neutrality target voltage; a controller programmed to perform pulse width modulated current control by cycling on and off phases for each of the branches so that the solid oxide electrolysis cell system operates at the thermally neutral target voltage during an operating cycle of the solid oxide electrolysis cell system; In the on-phase, the branch operates at the thermal neutral target voltage; In the off phase, the branch is unloaded to its open circuit voltage and operates at 0% of its rated power; A solid oxide electrolysis cell system, wherein each of the branches is configured to operate in the on phase or the off phase independently of the other branches.

20. 20. The solid oxide electrolysis cell system of claim 19, wherein each of the plurality of solid oxide electrolysis cells comprises an anode, a cathode, and a solid ceramic electrolyte between the anode and the cathode.

21. 21. The solid oxide electrolysis cell system of claim 20, wherein the solid ceramic electrolyte comprises a non-porous metal oxide.

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