Thermodynamic and Dynamic Analysis of a Wind-Powered Off-Grid Industrial Building Integrated With Solid Oxide Fuel Cell and Electrolyzer for Energy Management and Storage

In the wake of California’s outstanding target to achieve a 100% carbon-free energy system [1], more attention is being paid to naturally renewed energy sources like solar and wind. Penetration of these intermittent renewable energy sources (RES) in the electricity sector is faced with obstacles like grid congestion and integration cost that sometimes result in RES curtailment [2]. Short- and long-time mismatches between electricity generation and consumption as well as regional mismatch should also be addressed for full utilization of these RES. Deploying fluctuating RES in islanded microgrids with a proper energy storage system can solve the hassles of grid connection. A promising method for renewable electricity storage in large quantities for long timescales is to convert it into fuels like hydrogen or syngas (known as power-to-gas or PtG) using electrolyzers [3]. Currently, alkaline electrolyzers (AEL) are the most established and inexpensive technology utilized in industry. Recently, proton exchange membrane electrolyzer cell (PEMEC) technology has drawn more attention for PtG applications thanks to some advantages over AEL in terms of operating range and condition such as pressurized stacks. Moreover, PEMEC has a shorter startup time and faster dynamic response characteristics which makes it quite suitable for integration to highly variable power profiles like wind and solar photovoltaic (PV).

Another electrolysis technology that is beginning to be commercialized is the high-temperature solid oxide electrolysis cell (SOEC). SOEC has a higher operating temperature (700–850 °C), which enables higher efficiency compared to low-temperature electrolyzers like PEMEC (20–80 °C) and AEL (30–90 °C). As the temperature increases, while enthalpy change of water electrolysis reaction remains almost unchanged, the Gibbs free energy change of reaction (ΔG) decreases by as much as 30%. This means that with increased temperature, the minimum electrical energy required to drive the H₂O dissociation reaction decreases; Hence, in high-temperature electrolyzers, less electric demand is required for the hydrogen generation while a source of high-temperature heat is required for endothermic reactions.

So, unlike low-temperature electrolyzers where the majority of the energy demand for electrolysis is provided as electricity, in an SOEC, part of this energy could be provided as heat which is cheaper than electricity. In terms of electrochemistry, this translates into a drop in thermoneutral voltage of H₂O electrolysis from 1.481 V in the liquid phase to 1.285 V at 750 °C. Applying the thermoneutral voltage (V_TN) at the operating temperature of the electrolyzer provides the entire enthalpy demand of electrolysis without additional heat produced or required. If the applied voltage is higher (exothermic mode) or lower (endothermic mode) than V_TN additional cooling or heating is required to maintain a thermally desirable operation. The high operating temperature of SOEC also improves the kinetics, reducing activation polarization, and increases the ohmic conductivity of the solid electrolyte material [4].

While the high operating temperature of SOECs results in higher electricity-to-hydrogen conversion efficiency compared to low-temperature electrolyzers, such as AEL and PEMEC, it causes challenges for thermal management, cell stability, and lifetime. Thermal management of high-temperature fuel cell and electrolysis systems under dynamic operating conditions has significant importance. This is due to the thermal transients caused by repeated startup and shutdown processes and dynamic operation of SOEC, which can significantly accelerate cell degradation and mechanical failure. Thermal management of SOEC is of additional and critical importance when it is integrated with intermittent power sources such as wind. The operating temperature must be maintained within the permitted range of the stack which depends on the thermal expansion coefficient of its components, as well as the seals used [5–8]. The current work focuses upon thermal management as a result.

A variety of other important degradation mechanisms that affect SOEC systems have been studied. These include chemical/electrochemical and structural degradation that depends on several factors including the material used for electrodes and electrolyte, as well as the operating conditions such as current density, temperature, fuel utilization in solid oxide fuel cell (SOFC), and steam utilization in SOEC. One phenomenon contributing to chemical degradation is the diffusion of Ni into the electrolyte leading to ionic conductivity reduction. Also, the Ni in the fuel electrode cermet may undergo morphological evolution (sintering) that reduces Ni surface area and distribution in electrode, which has been studied extensively [9]. It has also been shown that stacks undergo degradation faster than single cells due to interactions with, and degradation of, the interconnects and piping [10,11]. General estimates, obtained experimentally, regarding acceptable levels of degradation are presented in Ref. [12].

Considering that SOECs have higher efficiency as a result of the high operation temperature, it is economically appealing if any heat demand comes from an excess or waste heat stream from other systems. This also improves the electricity-to-H₂ efficiency of electrolyzer [13]. In the following section, an overview of different systems that are combined with SOEC to provide the thermal demand is presented.

Some case studies have been accomplished for coupling SOEC with very high-temperature nuclear power plants with a coolant outlet temperature of 700–1000 °C or above. Both electric and thermal demand of H₂O electrolysis could be provided to SOEC by nuclear power. Techno-economic studies have shown that hydrogen production using SOEC is economically and technically feasible when coupled with very high-temperature nuclear reactors and can achieve an overall thermal-to-hydrogen efficiency of 50% or higher (higher heating value (HHV) based) [14]. Though cost-effective and efficient, this approach could not easily be applied for microgrids in all regions due to restrictions on nuclear power plants.

Solar-assisted hydrogen production with SOEC has also been a topic of interest for researchers. Similar to nuclear power, solar power can also supply electricity and heat demand to the electrolyzer. High operating temperature achieved in concentrating solar power (CSP) systems make them suitable for SOEC. Different system configurations are proposed for performance and cost improvement; in some cases, thermal energy storage (TES) is also added to CSP-assisted SOEC to prolong H₂ production time. In most systems, an electric heater was utilized just before the electrolyzer to meet the desired inlet condition as the temperature after all heat recovery (HR) units was still lower than the setpoint. For regions far from the sunbelt, providing high-temperature CSPs is challenging [15].

Another natural heat source that is studied for coupling with electrolyzers is geothermal energy. Investigations are mostly on the utilization of geothermal heat for low-temperature electrolyzers. However, recently, a few studies have been presented on feasibility, performance, and cost of employing geothermal sources for SOEC [16,17]. As the steam generated from geothermal energy is not at a sufficiently high temperature, SOEC was operated in the exothermic mode so that the heat from outlet streams could be recovered by inlet streams. While the need for an electric heater is thus eliminated, SOEC’s efficiency is harmed when operated in exothermic mode. While techno-economic analyses demonstrate low cost of geothermal-assisted SOEC compared to other methods, the obstacle for this application is that high-temperature geothermal sources are mostly specific to volcanic regions and are not easily accessible everywhere [18].

One of the novel approaches to provide the required heat for the endothermic reactions of SOEC is to exploit the generated heat from exothermic oxidation reactions in SOFC. Running SOEC and SOFC in one system can act as an energy storage unit where the SOEC converts electricity to H₂ (charge) and the SOFC oxidizes the generated H₂ (or a mixture of H₂ and methane) to generate electricity and heat (discharge). Such an approach was investigated in a study [19] for a reversible solid oxide cell (rSOC) system at steady-state conditions. In SOFC mode, the hot outlet streams were directed to a two-stage latent heat storage tank to melt the phase change material and store the heat within the TES medium; in SOEC mode, the inlet streams were first sent to the same TES to be heated to the SOEC inlet temperature. The work did not investigate the dynamics of mode switching and thermal behavior of the system in transient conditions.

Although using an rSOC may be more cost-effective than using two separate SOEC and SOFC stacks, the current design is investigated because (1) it may be more amenable to control for highly dynamic load following charge and discharge cycles, and (2) each stack (SOEC and SOFC) can be designed for optimal performance in one direction. One dispatch example includes SOEC operation that follows fluctuating renewable power (e.g., wind and solar) while the SOFC meets the building demand. This type of dispatch would be challenging with a single rSOC with mode switching leading to delays in demand response. By using two stacks, one can always be used for charging (SOEC) and the other for discharging (SOFC), while the stacks are thermally integrated. In order to study the feasibility of such a system, a dynamic simulation of heat integration is required to evaluate system performance to tackle the challenges before implementation.

The current work focuses on the dynamics and control of a thermally self-sustained energy storage system that integrates two solid oxide cells: one operating in electrolysis and the other in fuel cell mode. The main goal of the system is to achieve thermal management of the system without relying on external heat sources, i.e., preheating and controlling the inlet air and fuel streams to keep both SOEC and SOFC thermally stable and always available to either consume or produce power, respectively. This concept can avoid the thermal cycling effect caused by repeated startup and shutdown processes over long transient operation. Several control strategies were applied to guarantee the thermal balance of the system by actuating different components like control valves and air blower power.

The schematic presented in Fig. 1 summarizes the proposed energy storage system using thermally integrated modules of SOFC and SOEC power systems. The stand-alone hybrid system is sized for an 18-MW capacity wind farm and an industrial building with 5.4-MW peak electrical demand. The proposed microgrid system utilizes two individual but identical sets of solid oxide systems (each with approximately 100,000 cells arranged in a large number of stacks), one functioning as a power generator (fuel cell) with nominal power of 5.5 MW and the other operating in the reverse direction as an electrolyzer to convert wind power to H₂ gas. The SOEC-rated power is its thermoneutral point which occurs at 9.5 MW. While such large systems are rare today, there are examples in this size class [20]. The wind power is supplied to electrolyzer and its balance of plant for H₂ generation. Depending on the available wind power, the SOEC operates at endothermic, thermoneutral, and exothermic modes. The SOFC has two tasks: (1) meeting the electricity demand of the building when wind power is not available, and (2) providing the thermal management of the system including both SOFC and SOEC modules. The available heat from oxidation reactions in SOFC is transferred to the SOEC side using a network of heat exchangers with proper controllers. The heat is required for bringing the temperature of inlet streams of SOEC to the setpoint when it operates at endothermic and thermoneutral point.

The goals of this multipurpose energy system are as follows: (1) to build a dynamic physical model for an islanded microgrid with a wind farm and an SOFC as power sources, an industrial complex with variable power demand, a controllable SOEC for H₂ generation, and balance of plant (BoP) components; (2) store the wind power by electrochemical conversion of electricity to H₂ gas (PtG) using the SOEC; (3) provide reliable and clean power to the industrial complex with wind power and an H₂-fed SOFC; (4) exploit the heat from the exothermic reactions of the SOFC (and its oxidizer) for instantaneous thermal demand of the SOEC using a heat exchanger network and proper controllers; (5) achieve a thermally self-sustained energy system without an external heat source; and (6) evaluate the challenges of long-term operation for this stand-alone system by using real data for wind power generation and an industrial building load in the same region (Palm Springs). The data were obtained from Open Energy Information (OpenEI) online database [21] and a 2-week time window in January was used for the simulations.

The core of this stand-alone system is based on an SOFC for power generation and an SOEC for power storage along with the required balance of plant (BoP) and controllers. All components were physically modeled in Simulink/Matlab and integrated for a complete system design.

The model has been built based upon an in-house model of SOFC that was previously presented in Ref. [22]. Spatially and temporally resolved models were developed to capture their thermochemical and electrochemical behavior in steady-state (characterization) and transient (dynamic response) conditions.

The partial differential equations (PDE) resulted from solving the governing equations were converted to ordinary differential (ODE) equations by spatial discretization of the cell into five nodes along the flow direction in Simulink. The 10 cm × 10 cm cell is discretized in one dimension, i.e., it is divided into five sections with an area of 2 × 10 cm. As shown in Fig. 2, each node consists of four control volumes that are layered on top of each other resulting in a quasi-two-dimension model. The control volumes within each node include the following: (1) fuel channel (cathode in SOEC and anode in SOFC), (2) air channel (anode in SOEC and cathode in SOFC), (3) positive electrode–electrolyte–negative electrode (PEN) assembly, and (4) interconnect (which represents both fuel and air side plates as it is repeated in a stack of cells). Each control volume was modeled in Simulink to mimic all the thermal and electrochemical behavior of one node. Inlet streams with co-flow direction were introduced to node 1; assuming negligible spatial variation along the node, cell polarization model, as well as conservation laws for mass and energy, were resolved within the node. The outlet streams from node 1 were the inlet to the next node, and it was continued for all nodes. The outlet of the 5th node is the outlet of the cell. This was implemented in Simulink by copying the whole subsystem of a node 5 times in series. Hence, all the temporal and spatial behavior of variables are captured within the cell. The time-varying states are solved in Simulink using ODE 15 s with the following assumptions:

1. Each control volume output state including temperature, species concentration, and flowrate is representative of the conditions within that control volume (assuming a continuously stirred tank reactor (CSTR) method for chemical and electrochemical reactions) [23].

2. Performance of a single-cell SOFC and SOEC is assumed to represent the response of their respective stacks. Hence, the stacks are modeled by assuming 100,000 unit repeating cells with consideration of contact losses. As a result, the electric power and stream flows into and out of unit cell are scaled up by N_Cell.

3. Due to the very small channel cross-sectional area and slow gas flowrate in both air and fuel channels, the Reynolds number is within the laminar regime.

4. Only the dominant modes of heat transfer between different elements, i.e., conductive and convective modes, are considered and the radiation heat transfer is neglected for the sake of simplicity.

5. The stack is well insulated and therefore heat loss from the stack to the ambient is neglected.

6. Gas is assumed to be ideal and incompressible.

7. It is assumed that the current sign is negative for SOEC and positive for SOFC.

8. There is no anode gas recycle in the system and the fuel cell off-gas is directed to an afterburner (oxidizer) so that the unreacted H₂ from SOFC is completely oxidized.

The governing equations for modeling of a unit SOEC and SOEC are presented in the following sections.

Ohmic overpotential:

Activation overpotential:

Concentration overpotential:

The energy balance for each of the four control volumes within a node is provided in this section. Conduction heat transfer within solid phase, i.e., the PEN, interconnect plate, as well as the heat transfer between the PEN and interconnect, is modeled by Fourier law. Convective heat transfer between in solid–gas or gas–gas is modeled by Newton’s law of cooling using constant Nusselt number of 3.1 assuming a fully developed laminar flow of streams [28].

The time-dependent temperature in fuel electrode (FE), air electrode (AE), positive electrode–electrolyte–negative electrode (PEN), and interconnect (IC) is calculated from energy balance in these control volumes and expressed in Eqs (23)–(26). Where, ρ, V, and c_p are the denstity, volume, and specific heat transfer coefficient of each component. $Q˙hx$ is the heat exchanged within each control volume through conduction and convection. $Q˙el_rxn$ is the enthalpy change of reversible electrochemical reaction; hence, it is positive for exothermic H₂ oxidation and negative for endothermic H₂O reduction reaction. In Eq. (27), $Q˙SOC$ is the heat that is released to or required from the PEN for electrochemical reaction considering the electric power (P_SOC) generated or consumed by the reaction. Therefore, in Eq. (25), $Q˙SOC$ increases the PEN temperature for SOFC while in SOEC, depending on the input electric power (i.e., whether it runs in thermoneutral, exothermic, or endothermic mode) it maintains, increases, or decreases the PEN temperature.$E˙$ is the total enthalpy of the stream calculated via Eq. (28) where $N˙i$ is the molar flowrate of component i in the stream and h_i(T_i) is its corresponding enthalpy that is calculated from Eq. (29).

The total inlet flow stream to FE of SOFC is calculated from Eq. (30) based on the current I_SOFC (which is controlled by electric power), composition of H₂ at the inlet $(XH2_inlet)$⁠, and H₂ utilization $(UH2)$ in SOFC. Equation (31) represents the total inlet flowrate to FE of SOEC as a function of the inlet composition of steam $XH2O_inlet$⁠, steam utilization $UH2O$⁠, and the current I_SOEC. The species concentration at the outlet of each node (for SOEC and SOFC) is calculated from mass conservation and Faraday’s law in Eqs. (32)–(35) where the sign of current is positive for SOFC and negative for SOEC.

The air blower is used to provide enough pressure head and air flowrate for oxidation reactions in SOFC and sweeping gas in SOEC. The air is the cooling and heating medium for SOFC and SOEC, and its flowrate is controlled by blower power to maintain the cell temperature steady irrespective of dynamic conditions. The blower shaft speed varies until the inlet air to each stack can meet the requirements of that stack.

The system configuration is designed to take advantage of the exothermic nature of electrochemical oxidation reactions in SOFC and the oxidizer to provide the thermal demand for SOEC when it is in endothermic or standby mode. SOFC and SOEC are thermally integrated through an optimized network of heat exchangers and several control strategies to transfer the required amount of heat to the SOEC side in transient conditions. The process flow diagram (PFD) of the system is presented in Fig. 3.

In order to evaluate the system performance while operating dynamically, an instantaneous system efficiency (Θ_{SYS − instantaneous}) is defined in Eq. (47). The first fraction represents SOFC system efficiency, and the second fraction is the conversion efficiency of wind power to H₂. This is an extended version of round-trip efficiency which could be simplified to ratio of P_SOFC to P_Wind once the instantaneous H₂ production by SOEC $(n˙H2_prod)$ offsets the H₂ requirement by SOFC $(n˙H2_inlet)$ at that moment. In dynamic load and wind conditions, the instantaneous H₂ demand by SOFC is usually different from the generated H₂ by SOEC at that time; the higher value of $n˙H2_inlet$ than $n˙H2_prod$ results in lower Θ_{SYS − instantaneous}.

The total system efficiency $(ΘSYS_total)$ provided in Eq. (48) is defined for a specific time of operation and is therefore on an energy-based system output-to-input ratio. The inputs to the system boundary (in denominator) are wind energy (E_Wind) and energy content of net H₂ consumption by SOFC, and the only output of the system is the electricity generation by SOFC (E_SOFC) which supplies building demand. The energy consumption by BoP (air blower, steam generator, pump, and inverter) on the SOFC side is also supplied by SOFC, while on the SOEC side it is supplied by wind power; hence, the energy consumptions of individual BoP components are not shown in Eq. (48).

The goal of the system is to prevent or reduce the thermal stress-induced mechanical failure of the cells during long-term dynamic operation. To this end, it is attempted to maintain the local temperature gradient within an acceptable range of 10 K/cm. This can keep the spatial temperature gradient of the cell below the threshold for breaking. Also, to minimize the cell temporal temperature gradient, the average PEN temperature (arithmetic mean temperature of the nodes) is controlled to remain constant under all operating conditions [30].

Inlet air temperatures for both stacks are determined by proportional-integral (PI) controllers to keep the average PEN temperature constant under transient conditions. The SOFC inlet air temperature controller uses a feedback loop to maintain its PEN average temperature at 1073 K. A similar control strategy is employed for the SOEC to keep its PEN average temperature at 1023 K. The 50 K average temperature difference is selected to create the required temperature gradient between the heat source (SOFC) and heat sink (SOEC) for the heat transfer required by the current system design concept.

Inlet air flowrate is manipulated to minimize the spatial temperature gradient along the cells. The required amount of airflow is determined by blower power which is actuated in response to a feedback controller. To minimize the spatial temperature gradient, the maximum temperature difference between the inlet and outlet air is maintained under 100 K. This is set based on the 10 K/cm temperature gradient limit which results in 100 K for the 10 cm × 10 cm cells of the modeled SOFC and SOEC [30].

The air for SOFC provides the required oxidant and cooling effect for exothermic electrochemical oxidation reactions; however, for SOEC, it sweeps the generated oxygen from the air electrode and provides the required heating /cooling effect for endothermic/exothermic conditions to maintain thermal stability. At a thermoneutral point, air serves as the sweep gas to flush oxygen produced from electrochemical steam reduction reaction.

Thermal management of the overall system is implemented through multiple control valves actuated by feedback loops. The signal from the inlet air temperature controller of SOFC and SOEC actuates the control valves; the valves open such that the required amount of hot gas is directed to the hot side of each heat exchanger. The calculated amount of hot gas is enough to increase the temperature of the cold stream to the setpoint indicated by the cell temperature management controller. A process flow diagram (PFD) of the designed system is presented in Fig. 3. The top section depicts the power generation section (SOFC) and the bottom section illustrates the power storage/PtG part (SOEC).

Fuel utilization in SOFC is $Uf_SOFC=85%$ to prevent fuel starvation in the cell; the remaining 15% H₂ at the SOFC outlet is oxidized in oxidizer to raise the temperature of the hot source. The hot gas leaving the oxidizer is composed of steam, nitrogen, and oxygen. This hot gas is the carrier of high-grade thermal energy and is distributed among four HR units to provide the thermal demand of the system and eliminate the need for external electric heaters. HR1 and HR2 on SOFC side and HR3 and HR4 on the SOEC side use the oxidizer off-gas in their hot side. HR1 and HR2 are the only heat recovery units for inlet streams of SOFC. In the SOEC side, the inlet streams are first preheated by the outlet streams (products) of SOEC in HR5 and HR6, and if more heating is required, they are sent to HR3 and HR4.

In HR1 and HR2, heat is exchanged between the hot gas and inlet streams of air and fuel to the SOFC, respectively. A feedback controller with optimized proportional and integral gain values is implemented to actuate the valve (V1) position such that the flow of hot gas is directed to HR1 until the setpoint temperature of inlet air is reached. The error signal comes from the difference between the setpoint and measured temperature at the inlet. The SOFC inlet fuel temperature is always set at 973 K and is achieved by another PI controller that actuates valve positioner in V2. A significant amount of hot gas is used for process heating demands in the SOFC.

The remaining hot gas is sent to the SOEC side for its additional heating processes during the endothermic or hot-standby mode. The primary heating units for the SOEC are HR5 and HR6, where the inlet air and reactant stream (90% steam and 10% H₂) are preheated by the outlet air and product streams. The secondary heat recovery for air (HR3) and reactant (HR4) are used only when needed.

The red arrows in Fig. 3 show the path of the SOEC inlet streams in its exothermic mode. The exothermic mode happens when the SOEC runs with voltages above the thermoneutral voltage $(VSOEC>VTN_SOEC)$⁠. The thermoneutral voltage of the SOEC is $VTN_SOEC=1.285V$ at its average operating temperature which is 1023 K; it corresponds to the supplied electric power of $PSOEC=9.5MW$⁠. When the SOEC operates at electric powers higher than 9.5 MW, it enters the exothermic mode, and the temperature of outlet streams can go up to 100 K above the inlet streams. Hence, in exothermic mode, the inlet streams to SOEC only pass HR5 and HR6 to reach the setpoint inlet temperature. To avoid overheating of inlet streams by outlet streams in exothermic mode, PI controllers are used to only send enough amount of outlet streams of SOEC to the hot side of HR5 and HR6, respectively.

The control valves V4 and V6 block the passage of inlet streams to HR3 and HR4 when P_SOEC > 9.75 MW and open the path when P_SOEC < 9.75 MW. This power (P_SOEC = 9.75 MW) is selected as the threshold of the valves instead of P_SOEC = 9.5 MW to compensate the heat loss in heat exchanger and piping. Therefore, when P_SOEC > 9.75 MW, no heat was required from SOFC side for preheating the SOEC inlet streams. Orange arrows in Fig. 3 show the inlet streams paths in endothermic mode where they recover the heat from hot gas coming from the SOFC side too.

The system is designed such that the thermal demand of the SOEC is always provided, and it can follow the wind power in all part-load ranges to generate H₂. Steady-state simulations were performed to find the heat demand of the SOEC over its operating range and the most endothermic point of the SOEC. A controller was designed to adjust P_SOFC in response to thermal demand of the SOEC. This is explained in the following section.

Sometimes, the available hot gas from the oxidizer is not enough for SOEC thermal demand when the SOFC just follows the building load. This challenge is faced particularly during the time when the wind generation is poor and the SOEC is supplied with electric power lower than its thermoneutral point and requires heat for electrolysis reaction. During the off-peak hours of the building (nights or weekends for the industrial building under study), the SOFC runs at low electric power and the excess heat available is not sufficient for preheating the inlet streams of both SOFC and SOEC. Hence, a control strategy is developed to manipulate the SOFC by increasing P_SOFC to fulfill the desired inlet air temperature for the SOEC in endothermic mode. This ensures that the SOEC thermal input is always satisfied when working in endothermic conditions. The excess electricity is assumed to be either stored in a battery or dissipated. The algorithm for controlling the SOFC power was developed after the steady-state analyses to find the matching operating points of SOEC and SOFC.

Results from steady-state simulations are shown in this section. The purpose of these analyses was to evaluate the maximum heat demand of the SOEC and design a system with proper controllers for its thermal management. Figure 4 shows the thermal power required for heating the SOEC inlet air from ambient to the setpoint temperature at each operating electric power. The heat demand is very low when the SOEC is at minimum power or standby mode. This heat is required to keep the stack hot at $T¯PEN_SOEC=1023K$⁠, in the absence of considerable wind power. As P_SOEC increases, its heat demand or endothermicity increase and reach its maximum value at P_SOEC = 4 MW. Increasing the electric power beyond that level decreases the endothermicity until it approaches P_SOEC = 9.5 MW. From the voltage plot shown in Fig. 5, when P_SOEC = 9.5 MW, the voltage is 1.285 V which is the thermoneutral point as mentioned in Sec. 2.3.2. The heat from overpotential compensates part of the electrolysis heat demand. At the thermoneutral point, the heat loss offsets all the electrolysis heat demand, and no additional heating is required to be provided to the SOEC stack by inlet air. The SOEC inlet air only must be heated from ambient to the average PEN temperature of SOEC which is 1023 K; the outlet air temperature at thermoneutral point is also 1023 K.

Above P_SOEC = 9.5 MW, the heat from overpotential losses in SOEC exceeds the endothermic electrolysis heat demand and SOEC enters the exothermic mode. In this region, all the thermal demand for preheating the inlet streams to SOEC is provided by the corresponding outlet streams; so, no heat is required from the SOFC side. Hence, the inlet air must provide the required cooling for SOEC to maintain its average PEN temperature constant (1023 K) and keep the spatial temperature gradient within the tolerance (10 K/cm). As explained in Sec. 2.3.1, two feedback controllers are used for cell thermal management. One controller manipulates the inlet air temperature $(Tinlet_A_SOEC)$ to keep the average PEN temperature at 1023 K; the required $Tinlet_A_SOEC$ to satisfy this condition for each electric power of SOEC is presented in Fig. 6. The inlet temperature for electric powers above P_SOEC = 9.5 MW sharply dropped below 1023 K. The other controller manipulates the inlet air flowrate to maintain the maximum temperature gradient under 10 K/cm; the amount of air flowrate to meet this condition is provided in Fig. 7. The increase in air flowrate after the thermoneutral point is due to the increased cooling demand for the exothermic region.

The minimum amount of air flowrate to keep the stack in hot-standby mode is 1 kg/s (Fig. 7). The inlet air flowrate increases with the supplied electric power until the most endothermicity point is reached (P_SOEC = 4 MW). For electric powers between 8.5 MW and 10.5 MW, the air flowrate is kept at a minimum and only the inlet air temperature takes care of the thermal management; in this region, the air is mainly required to carry away the generated oxygen (as a sweep gas). After the thermoneutral point, the inlet air flowrate (with proper temperature $Tinlet_A_SOEC<1023K$⁠) increases again to provide the required cooling load for the SOEC. In Fig. 4, the thermal demand is minimum at P_SOEC = 10.5 MW because both inlet air temperature and flowrate were at their minimum value (⁠$Tinlet_A_SOEC=935K$⁠, $m˙inlet_A_SOEC=1kg/s$⁠).

After finding the most demanding point from the steady-state analysis, parametric analysis was performed on SOFC side to find the minimum P_SOFC that can provide the maximum heat demand of SOEC (P_SOEC = 4 MW) considering all the heat losses in the piping and heat exchangers. It was found that when P_SOFC = 4.2 MW, it could meet all the heat requirements for preheating of inlet streams to both SOFC and SOEC. To guarantee the thermal stability of both SOEC and SOFC in all conditions, a proportional controller is designed to increase P_SOFC proportional to the heat demand of SOEC if required. All the values of thermal power for P_SOEC < 9.5 MW in Fig. 4 are divided by the maximum thermal power required for P_SOEC = 4 MW (i.e., 3.5 MW); the normalized SOEC thermal demand is the proportional signal to the controller to calculate the required P_SOFC for SOEC thermal demand. The P_SOFC is found based on a linear relationship with normalized SOEC heat demand. At each moment, if the required P_SOFC for thermal management is more than P_SOFC required for the building load, then the controller increases this power to the higher value.

In this section, the system performance in transient conditions is investigated, across a range of endothermic, thermoneutral, and exothermic conditions. The dynamic response of both SOFC, SOEC, and the BoP components is evaluated to tackle the challenges of long-term operations with proper control systems. Load following capability of the SOFC and SOEC, their thermal behavior in response to controllers, efficiency, and H₂ production and consumption were analyzed.

The data for the wind power profile is adapted from the OpenEI database for an 18-MW wind farm in Palm Springs, California. To evaluate the system performance in critical conditions, a time window with a dynamic condition, albeit at low power generation levels, was selected (Day 1 on Sunday), as depicted in Fig. 8. For the majority of the time, the electric power of SOEC (shown in red dotted line) is less than thermoneutral level (P_SOEC < 9.5 MW). This is because of the low and poor wind conditions in that window. Due to the high fluctuation of wind power, it is not directly fed to the building to meet its electricity demand; it is directly supplied to the SOEC to generate H₂ to be used as a fuel for SOFC.

The SOFC follows the building load to provide reliable electricity and to cover its BoP power demand. In some periods, a gap is observed between the building demand and SOFC power. This increase of P_SOFC in addition to the building demand is in response to the thermal needs of the SOEC. The gap between magenta and blue lines in Fig. 8 occurs mainly at nights or the weekends when building load is low, while the SOEC is running to convert the wind power (even in the poor wind condition) to H₂.

When the heat from the SOFC following the building electricity demand was not sufficient for thermal demands of SOEC, P_SOFC was increased. The gaps between the SOFC and building powers are seen when P_SOEC is around 4 MW which corresponds to the most endothermic point of the SOEC (as observed in Fig. 4). The excess power of the SOFC that is not used by the building during these periods could be used in many ways; a more detailed discussion is provided in Sec. 3.2.3.

The dynamic response of the cell voltage in SOEC and SOFC is presented in Fig. 9. Comparison of the operating voltage in SOEC with its thermoneutral voltage shows that most often, $VSOEC<VTN_SOEC$ and SOEC operated in endothermic mode. This was also observed in Fig. 8 when P_SOEC < 9.5 MW during significant periods, leading to SOFC operation at high power levels to generate the required heat. The most endothermic point (P_SOEC = 4 MW) happens at V_SOEC = 1.14V. The operating voltage of SOFC (blue line) was at its lowest, V_SOFC = 0.68V, during the building’s peak demand. The voltage drop of SOFC due to the increase in P_SOFC in response to thermal demand of SOEC was found to be 0.1 V in the worst condition.

There are two goals in thermal management of the stacks which are achieved by two actuators. The first goal is to always keep the PEN average temperature $(T¯PEN)$ constant. $T¯PEN$ is controlled by air inlet temperature in both stacks. Performance of the cell temperature controllers could be seen in Fig. 10. The inlet temperature of streams to the fuel channel was fixed to be equal to the PEN average temperature $(T¯PEN)$ of each stack, i.e., 1073 K in SOFC and 1023 K in SOEC. The top plot in Fig. 10 shows that in SOEC, $T¯PEN_SOEC=1023K$ was maintained by providing hotter or colder inlet air for heating or cooling demand; this is due to the very dynamic operation of SOEC that causes endothermic, thermoneutral, and exothermic operation of SOEC. During endothermic periods, the inlet air temperature (blue dotted line) is higher than 1023 K; the heat is absorbed by the electrochemical reactions; hence, the outlet air temperature (blue dashed line) is less than 1023 K. In some hours, the inlet air temperature is much lower than 1023 K which corresponds to its exothermic mode. The bottom plot shows that the inlet air to the SOFC (red dotted line) was always lower than $T¯PEN_SOFC=1073K$ (about 70 K) to cool down the stack because the oxidation reactions in SOFC always result in its exothermic operation.

The other goal of thermal management is to maintain the PEN temperature gradient within the limit of 10 K/cm by manipulating the air flowrate and keeping the maximum air temperature variation along the cell under 100 K. The maximum temperature gradient along the PEN is controlled by air blower power which manipulates the air flowrate. As shown in the top plot of Fig. 11, the temperature difference between the inlet and outlet air streams was controlled to be lower than 100 K both in SOFC and in SOEC. The exothermicity and endothermicity of the stacks could be realized from the sign of $ΔTAir=TAir_Outlet−TAir_Intlet$ in this plot. For SOFC, it is always positive (ΔT_Air = 100 K); while for SOEC it varies between −100 K for the endothermic region and 100 K for exothermic operation (−100 < ΔT_Air < 100). The lower plot belongs to the absolute temperature gradient within the solid PEN that must be maintained under 100 K (10 K/cm * 10 cm). The absolute value of temperature change is chosen only for an easier comparison between SOEC and SOFC. In both SOFC and SOEC, the maximum temperature gradient along the PEN is within its tolerance. In SOFC, the maximum air temperature gradient was 75 K, while in SOEC, it was 60 K (for the most exothermic operation).

Performance of individual stack modules, as well as the overall system, is presented in Fig. 12. The red dashed line indicates the SOEC stack efficiency, defined in Eq. (46). SOEC efficiency above 100% $(ΘSOEC>100%)$ corresponds to the times when it runs in endothermic mode (when $VSOEC<VTN_SOEC$ in Fig. 9). This is based on the commonly used definition of electrolyzer performance, Eq. (46), which is the ratio of generated chemical power to supplied electric power. Since the input thermal power is the heat recovered from the hot gasses within the system (from the SOFC side), it is not considered in electric efficiency definition and the efficiency goes beyond 100% when SOEC runs endothermically; it reaches 100% at thermoneutral point when the applied electricity is enough for steam electrolysis. It drops under 100% in exothermic mode since the supplied electric power is more than the energy demand for electrolysis at that point and the excess electricity dissipates as heat.

The blue dotted line indicates the efficiency of SOFC module, Θ_SOFC, based on Eq. (45). The minimum efficiency of SOFC was 54.5% which occurred during the peak demand of building or during the time that SOEC was in extremely endothermic mode and the controller increased P_SOFC to provide the thermal demand. The maximum, 67.6%, was achieved at nights when the building load was minimum and wind generation was either high enough to cause exothermic operation of the SOEC or was so low that the SOEC was in standby and no extra high amount of heat was required from the SOFC side. The latter case (low wind power levels) also resulted in high instantaneous system efficiency, Θ_{SYS − instantaneous}, defined in Eq. (47).

This definition for Θ_{SYS − instantaneous} reflects the efficiency of both SOEC and SOFC in the system in terms of thermal management which is the purpose of this work. The definition can be simplified to a round-trip efficiency when H₂ consumption by SOFC is equal to the H₂ production by SOEC. It is observed that Θ_{SYS − instantaneous} follows Θ_SOFC trend when Θ_SOEC is above 100%; e.g., SOEC runs endothermically, while it is worsened in high wind conditions when SOEC runs exothermically. This means that the system is saving thermal energy by using SOFC for the endothermic operation of SOEC and it can capture even the small amount of wind generation using heat from SOFC. In opposite, during exothermic operation, the excess heat generation by SOEC is partly used for SOEC inlet stream preheating and the rest is wasted which harms Θ_{SYS − instantaneous}. It was 54% when the SOEC was endothermic with high efficiency and the SOFC was running at low power during the night. Θ_{SYS − instantaneous} reached its lowest (under 40%) when the SOEC was in exothermic mode and the SOFC load was at the peak level. When the conditions were a mixture of these two extremes, Θ_{SYS − instantaneous} was around 44% during this 2-week period.

Since Θ_{SYS − instantaneous} is a measure for thermal management of the system, it does not reflect clear information regarding the instant H₂ production and consumption in the system. To study the H₂ deficiency or excess for the 2-week period of simulation, an overall system performance index $ΘSYS_total$ was defined in Eq. (48). $ΘSYS_total$ is the ratio of output of the system, which is the total energy generation by SOFC in 2 weeks, to the total input to the system, total wind energy generation in 2 weeks and the difference in chemical energy of H₂ consumed by SOFC and H₂ produced by SOEC in 2 weeks. $ΘSYS_total$ was calculated to be 49.95% for the 2-week period of study. This number comes from the calculation of total input and output energies in 2 weeks: 1.18 GWh of SOFC energy generation as the system output, 2.02 GWh of wind generation as input, and 0.22 GWh of chemical energy of H₂ used from the storage tank as another input to the system. If the cumulative H₂ production and consumption in this period balance each other, then $ΘSYS_total$ becomes 55% (the ratio of SOFC to wind energy); generation of extra H₂ results in higher overall efficiency for this period.

The total H₂ production of this 18 MW wind farm by the 9.5 MW SOEC in 2 weeks was 49.5 tons, and the total consumption was 65.9 tons (56.0 tons oxidized in the SOFC and 9.90 tons converted in the oxidizer). This 16.4 tons of H₂ deficit was assumed to be available in the storage tank that was produced by the SOEC during previous windier time periods. It must be noted that the simulation was performed for a poor wind condition to evaluate the H₂ demand and thermal performance of the system for an undesirable weather condition in transient mode. In a day with ideal wind condition, like day 14 in Fig. 8, H₂ production from SOEC is calculated to be 9.22 tons while the H₂ consumption by SOFC is 2.66 tons and 6.56 tons could be stored. A full-year simulation of the wind farm and building demand is required to assess the total H₂ surplus or deficit in a year.

The focus of the paper is the system-level thermal balance, which is critical for the sustained operation of the SOEC. As a result, the many options that might exist for addressing excess electricity are not discussed. For example, the energy can be exported or stored in batteries. One option, consistent with the key thrust of this paper, is to send excess power of the SOFC to the SOEC, either directly or via a modest size buffer (i.e., battery).

Optimizing the battery size, its charge and discharge rates, the schedule for power discharge based on wind power, and the power electronics specifications would require significant space and would distract from the key issue of thermal management. As a sample illustration, however, a simple scenario is presented here: A battery with a capacity of 60 MWh and a nominal of 3.5 MW is used as the energy buffer. When the wind power results in the most endothermic conditions for SOEC and thus when SOFC is used to generate the needed heat (i.e., 3–5 MW of wind power delivered to SOEC), 3.5 MW is delivered from the battery to the SOEC as long as there is enough energy available. The results, from battery energy level in Fig. 13, show minimal curtailment (only a short period between days 10 and 11), which can be avoided if the excess power is sent directly to the SOEC. Similar results can be obtained with smaller batteries, though with longer periods of curtailment/direct injection of power to SOEC.

A key benefit of this approach is that it not only leads to higher levels of hydrogen generation, by increasing the power levels of SOEC during endothermic periods but also results in lower hydrogen consumption by the SOFC thanks to less thermal demand from the SOEC side. Note that during these periods, the fuel cell efficiency is increased. The end-result is excess electric energy of 12 MWh from SOFC (instead of 287 MWh) and a deficit of 6.2 tons of H2 (instead of 16.4 tons). It is important to note that this is a relatively simple demonstration of the options available and a full treatment to optimize this approach is beyond the scope of the current work. It is worth mentioning that this excess power generation by SOFC is a result of the control algorithm adopted for system thermal management. In this control method, the electric power of SOFC is manipulated in response to the thermal demand of the SOEC with a highly intermittent wind power input. In Ref. [31], with a predictable solar power input to the SOEC source, a different control structure was used.

A solid oxide-based system is designed and integrated with an 18-MW wind farm in Palm Spring, CA, to power an islanded industrial building with a maximum load of 5.4 MW. Dynamic and thermodynamic behavior of the system was evaluated for 2 weeks of poor wind conditions. The system is composed of two similar solid oxide modules, one as an SOFC with nominal power of 5.5 MW and the other as an SOEC with 9.5-MW thermoneutral power, and the balance of plant. The electricity from the wind farm is always converted to H₂ via SOEC; the H₂ is fed to SOFC to provide the building load. The SOFC is also thermally integrated into the SOEC to provide it with the required heat for endothermic electrolysis reactions and hot standby mode. The heat source of the system is the off-gas from anode tail gas oxidizer on the SOFC side. This hot stream is distributed among four heat recovery units: two for preheating the inlet streams to SOFC and two for SOEC side. Control system strategies are developed for power and thermal management of the cell and system in transient conditions. Several feedback controllers are designed to provide the proper amount of hot gas on the hot side of each heat exchanger to meet the setpoint temperature at the inlet of SOEC and SOFC.

The results from a dynamic simulation of the system for a 2-week profile of the wind farm and building, from OpenEI database, showed that the applied control strategies were effective in thermal management. The average cell temperature was maintained stable under highly dynamic operating conditions both for SOEC and for SOFC. Also, the temperature gradient of the cells was maintained within its tolerance of 10 K/cm. Due to poor wind condition during some hours, the SOEC ran endothermically and its heat demand exceeded the available heat in hot gas coming from the SOFC side. In response to this thermal demand, the SOFC power was manipulated by a controller such that the hot gas could satisfy this heat. The electricity of SOFC in addition to the building demand must be stored in a battery system for short-term storage. The dynamic simulations showed that it is feasible to achieve a thermally self-sustaining system for energy storage in a large scale using the power to the gas method. Annual simulation of the system is required to calculate the yearly wind generation, H₂ production, building load, and H₂ demand by SOFC to meet the building electric load and thermal demand of SOEC.

This work was supported by the National Science Foundation (Award No. 1461583).

i =

current (A)

j =

current density (Am⁻²)

F =

Faraday’s constant: 96485 (C mol⁻¹)

J =

moment of Inertia (kg m²)

P =

pressure (kPa)

Q =

thermal power (kW)

R =

universal gas constant (kJ/kmol.K)

T =

temperature (K)

D^eff =

effective diffusion coefficient (m²/s)

E⁰ =

reversible voltage (V)

h_i =

enthalpy of gas i (kJ/kmol)

j₀ =

exchange current density (Am⁻²)

j_L =

limiting current density (Am⁻²)

n_e =

number of electrons transferred

r_p =

pore radius (m)

Cp =

specific heat capacity (kJ/kmol K)

D_i,k =

Knudsen diffusion coefficient (m²/s)

E_act =

activation energy (kJ/kmol)

M_i =

molecular weight

N_cell =

number of cells in stack

$CR0$ =

reactant concentration in bulk flow

$N˙i$ =

molar flowrate of gas i (kmol s⁻¹)

Nu =

Nusselt number

ΔG =

Gibbs free energy change

β =

charge transfer coefficient in Butler Volmer

δ =

thickness (m)

γ =

pre-exponential in activation loss

ξ =

porosity

η =

overpotential loss

ρ =

density (kg/m³)

σ =

specific conductivity (m/Ω)

τ =

tortuosity

υ_p =

stoichiometric coefficient of product

υ_R =

stoichiometric coefficient of reactant

Θ =

efficiency

A_eld =

air electrode

Act =

activation

BP =

boiling point

Conc =

concentration

Ch_wall =

flow channel wall

Ely =

electrolyte

F_eld =

fuel electrode

IC =

interconnect (bipolar plates)

Ohm =

Ohmic

Sep_plate =

separator plate

TN =

thermoneutral