Power transition cycles of reversible solid oxide cells and its impacts on microgrids

Post-print version: Power transition cycles of reversible solid oxide cells and its impacts on microgrids H. del Pozo Gonzalez, L. Bernadet, M. Torrell, F.D. Bianchi, A. Taranc´on, O. Gomis-Bellmunt, J.L. Dominguez-Garcia This work has been published in Applied Energy: H. del Pozo Gonzalez, L. Bernadet, M. Torrell, F.D. Bianchi, A. Taranc´on, O. GomisBellmunt, J.L. Dominguez-Garcia, “Power transition cycles of reversible solid oxide cells and its impacts on microgrids”, Applied Energy, vol. 352, pp. 121887, 2023. Final version available at: URL: https://www.sciencedirect.com/science/article/abs/pii/S0306261923012515 DOI: 10.1016/j.apenergy.2023.121887 BibTex: @Article { gonzalez 2023 transitions , Title = {Power transition cycles of reversible solid oxide cells and its impacts on microgrids}, Author = {H. del Pozo Gonzalez, L. Bernadet, M. Torrell, F.D. Bianchi, A. Taranc´on, O. Gomis-Bellmunt, J.L. Dominguez-Garcia}, Journal = {Applied Energy}, Year = {2023}, Number = {}, Pages = {121887}, Volume = {352}, Doi = {10.1016/j.apenergy.2023.121887} } Power Transition Cycles of Reversible Solid Oxide Cells and its Impacts on Microgrids Hector del Pozo Gonzaleza,∗,Lucile Bernadeta,Marc Torrella,Fernando D. Bianchib, Albert Tarancóna,d,Oriol Gomis-Bellmuntc,d and Jose Luis Dominguez-Garciaa aCatalonia Institute for Energy Research (IREC), Jardins de les Dones de Negre 1, 2𝑎. - 08930 Sant Adrià de Besòs, Barcelona, Spain bInstituto Tecnológico Buenos Aires (ITBA) and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Iguazú 341, C1437, Ciudad Autónoma de Buenos Aires, Argentina. cCentre d’Innovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA), Departament d’Enginyeria Electrica, Universitat Politecnica de Catalunya (UPC), Barcelona 08028, Spain dInstitució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, 08010 Barcelona, Spain ARTICLE INFO Keywords: Reversible Solid Oxide Cells Transition Cycles Microgrids Hydrogen Solid Oxide Fuel cell Solid Oxide Electrolysis ABSTRACT Currently, reversible solid oxide cells (rSOC) are the only devices that allows a bidirectional conversion of H2O and H2, being able to operate as fuel cell and as electrolyzer. Thanks to the hightemperature operation, rSOC present a higher efficiency and additionally, provide a feasible solution for long-term energy storage in electrical systems. Experimental testing of rSOC have been mainly focused on cells characterization, thermal or degradation analysis, but the study of transition cycles has not been widely studied. The transitions between the operation as a solid oxide fuel cell (SOFC) and as a solid oxide electrolysis cell (SOEC) might have a significant impact on the rest of the electrical system in which the rSOC is integrated. This article analyzes experimentally the power responses of a rSOC stack, during each operating mode (SOEC-SOFC) and during transition between both modes. The results suggest that transition cycles can be achieved in less than 8 minutes and the total transition from SOEC rated power to SOFC rated power in less than 10 minutes, having a significant impact on microgrid operations, especially in islanded mode. The obtained results indicate that the most suitable role for rSOC in a microgrid is as grid-following. The grid-forming role is only possible if the rSOC operates along with a fast-response power source. 1. Introduction Electrical microgrids have emerged as an effective way to transform traditional networks. The concept divides large systems into multiple small-scale ones with the ability to operate connected to the conventional distribution and isolated grids [1,2]. In these systems, the role of electrical energy storage is fundamental to mitigate the renewable energy variability and thus make the operation of the entire microgrid more reliable. Reversible solid oxide cells (rSOC), due to their ability to operate as fuel cell and as electrolyzer are an interesting option to perform this role due to their high efficiency. In addition to high efficiency, these devices have fuel flexibility, since the cells have the ability to operate with several type of fuels (e.g. H2, CO, etc.), which allows their use in combined heat and power (CHP) plants. The global and CHP efficiency of Solid Oxide technology are higher than other technologies such as Proton-Exchange Membrane (PEM) commonly used in applications like transportation or backup power due to its fast start-up time, or alkaline technologies used in the military or aerospace sectors among others [3]. In addition, since rSOC can be used in larger exploitation systems, they result in a more cost-effective ∗Corresponding author: [email protected] (H. del Pozo Gonzalez) ORCID(s): 0000-0002-4270-1353 (H. del Pozo Gonzalez); 0000-0001-6637-0790 (L. Bernadet); 0000-0002-3946-1352 (M. Torrell); 0000-0001-7332-6501 (F.D. Bianchi); 0000-0002-1933-2406 (A. Tarancón); 0000-0002-9507-8278 (O. Gomis-Bellmunt); 0000-0002-0483-995X (J.L. Dominguez-Garcia) technology as long-term storage in electrical microgrids. A brief comparative of the main technologies is presented in Table 1. In the literature, it can be found several experimental rSOC studies focused on: degradation analysis [6], materials analysis [7], temperature effects [8] or pressure effects in stacks [9]. However, more in-depth experimental studies are needed to analyze the response times of this type of systems, especially during the transition between the two operation modes: solid oxide fuel cell (SOFC) and solid oxide electrolysis cell (SOEC). Among those, Aicart et al. [10] used a 25 cell stack with 1 kW-4 kW (SOFC-SOEC) rated power to investigate the transitions between electrolyzer mode and fuel cell mode with different fuel composition (H2and CH4). The analysis covers three power levels: minimum, medium power and proposed maximum power, seeking to achieve fast transitions between operating modes without damaging or impairing the performance of the system. The results obtained by the authors suggested that all transition cycles could be performed in an interval of 3 to 10 minutes without negatively affecting stack performance and lifetime. Srikanth et al. [11] presented a comprehensive investigation of a rSOC reactor behavior during mode switching and explored effective transition strategies. They employed a one-dimensional transient reversible solid oxide cell model validated through experiments using a commercially available reactor. One of their main findings revealed that implementing abrupt step changes from SOFC to SOEC or vice versa within a system context is not viable due to the HDP González et al.: Preprint submitted to Elsevier Page 1 of 10 Transition Cycles Reversible Solid Oxide Cells Table 1 Characteristics of different hydrogen cells for microgrid applications [3,4,5] Technology Temperature Fuel Cell Efficiency∗ Electrolyzer Efficiency* Maximum Power∗∗ Warm Start -up time Role Proton-exchange membrane <120◦C<60%<70%2.5MW Short: <1min Backup Alkaline <100◦C<50%<70%10 MW Short: <5min Backup Solid Oxide <1000◦C<60%<85%0.225 MW Long: >10min Long-Term *Nominal system efficiency (LHV) including auxiliaries and heat supply ** Industrial-scale stack maximum power capacity up to 2022: HyLYZER, Aqualizer and Sunfire, respectively. behavior of BoP components. Finally, a part of a long-term study of a 5/15kW-Class rSOC system, Peters et al. [12] investigated the rSOC dynamics when transitioning from fuel cell to electrolysis mode. Their findings revealed that, in most cases, the switching between these operating modes could be completed in less than three minutes. However, they also stated that when shifting from the fuel cell to the electrolysis mode, a waiting period of approximately 10 minutes was necessary to ensure stable evaporation in the steam generator. Microgrids including hydrogen energy systems have been analyzed by several authors. Garcia-Torres et al. [13] propose predictive control aimed to achieve an optimal load sharing in a microgrid composed of different types of batteries and two separate PEM-type fuel cell and electrolyzer systems. Quan et al. [14] analyze by simulation a gridforming control strategy in a microgrid with a PEM-type fuel cell and an electrolyzer. In [15], the authors study a solid oxide fuel cell power plant connected to an AC grid, in which the inverter controls regulate the stack current aiming to ensure a constant power factor of the plant at all possible power levels. Hutty et al. [3] present an economic and suitability study of a microgrid with solar energy, rSOC and battery storage for a residential microgrid, comparing the benefits of the technology against the estimated CAPEX for the microgrid. In [16,17,18], the authors analyze the feasibility of systems based on rSOC aimed to supply the electrical and thermal demands of a 20-unit residential flat building and electric and fuel cell vehicles. Motylinski et al [19] study the dynamic response of rSOC in lattice stability applications. The study seeks to identify the capability of these systems to stabilize an electrical network, and their behavior during the switching between SOFC and SOEC modes. The results were experimentally validated with approximated wind profiles. Baldinelli et al. [20] analyze the feasibility of using flywheels to complement the operation rSOC in grid-connected mode, but the rSOC are not modeled in detail. This article presents an experimental power analysis of rSOC focused on the dynamic behavior during the operation in SOFC and SOEC modes, and also transition cycles between these two modes. The obtained experimental results allow us to evaluate the operation of the rSOC in a microgrid and analyze their possible impact. The article also proposed a control strategy for the proper functioning of the microgrid with the rSOC inverter operating in grid-following and in grid-forming modes. A detailed description of the system layout, the modelling, and the experimental validation can be found in [21]. The article is structured as follows. Section 2presents a brief description of rSOC operation and their experimental power responses with different flows, with direct mode changes and respecting the transition cycles to achieve the desired fuel inlet composition. Section 3focuses on the integration of rSOC in a microgrid introducing the necessary controllers for the proper functioning of the network and the experimental evaluation under several scenarios according to the possible operating modes of the rSOC. Finally, in Section 4some conclusions are drawn. 2. Experimental Evaluation of Reversible Solid Oxide Cells 2.1. Experimental Set-up This section presents the working principles of rSOC and their experimental power response under several operating conditions. Figure 1shows the rSOC setup used in the experimental tests, which is a in-house reversible prototype. The figure also shows the balance of plant (BoP) elements, important for the efficient operation of the entire system. Its hot zone is composed by a furnace where the stack is placed and by two heat exchangers to pre-heat the inlet gases with the outlet ones. The cold zone gathers a steam generator, a condenser to separate the hydrogen and steam from the fuel outlet stream, the gas controllers and power electronics. The studied stack is a commercial stack from SOFCMAN company (China) made up of 30 anode-supported cells with an active surface area equal to 63 cm2. Its rated power is in the range of 0.7 − 1 kW (SOFC-SOEC). The parameter values and description of this rSOC can be found in Table 2. Before increasing the oven temperature and operating the stack, a weight of 120 kg is applied on top to maintain all the layers (cells, interconnects and meshes) sealed all together. Then the furnace temperature is increased by 1 ºC/min to avoid any thermal chock. Once the operating temperature is reached (750 ºC), H2is progressively introduced to reduce the fuel electrode. At the end of the reduction process, the stack is ready for operation. SOFC characterization is performed with pure H2at the fuel electrode and air at the oxygen electrode, while SOEC characterization needs a HDP González et al.: Preprint submitted to Elsevier Page 2 of 10 Transition Cycles Reversible Solid Oxide Cells Figure 1: Description of the main elements in the IREC Reversible Solid Oxide Testing Prototype [21] mixture of H2O with a small amount of H2(around 10%) to maintain the fuel electrode reduced and air at the oxygen side [22,23]. 2.2. Flow Impact in SOFC-SOEC Power Response The first experimental tests evaluate the impact of the gas flow on the stack power performance, when the stack remain in one operating mode (SOEC or SOFC) during the entire experiment. This allows us to obtain a baseline behavior to compare with the response during mode transitions. Performance characterization for different gas flow conditions was done by performing polarization curves, which consists in gradually increase the current while recording the voltage evolution. A sweeping rate of 40 A/min was used. Flow were changed on both electrodes at the time, always keeping a volumetric ratio of 2.5 between H2and air, in order to respect the stoichiometry of the reactions (water electrolysis or hydrogen reduction). The change in flow was performed, gradually increasing the hydrogen and air flows until reaching the desired values, to subsequently increase the current with steps of one ampere. The polarization curves in SOFC mode, presented in Figure 2correspond to flows of 5 NL/min of H2and 12.5 NL/min of air, 10 NL/min of H2 and 25 NL/min of air and 15 NL/min H2and 37.5 NL/min of air. On the other hand, in SOEC mode, the polarization curves from Figure 3correspond to flows of 5 NL/min, 10 NL/min, 15 NL/min of H2O. For all cases, the air flow was set to 26 NL/min. Figure 2shows the effect of different H2flows on the voltage and power responses. It is possible to observe that the lower flows of H2, (5 NL/min), means achieving low power levels reaching 65.8% percent of fuel utilization. The increase in the flows implies a greater amount of delivered power with flows of 10 NL/min or 15 NL/min, but decreasing the fuel utilization to 40% or less. This change is mainly related to two phenomena. One is the decrease of the Nernst potential by the gas flow increase. It corresponds to 20% of the voltage difference at 0.2 A/cm2(around 0.7 V when increasing the fuel flow from 5 NL/min to 15 NL/min and 2.5 times the air flow in comparison with measured values 3.44 V). The second is the reduction of the concentration overpotential, having higher flow helps bringing new reactants close to the reactive point and evacuating the products. The voltage and power responses in SOEC mode can be seen in Figure 3. Similarly, higher flow of H2O allows reaching power levels close to the rated values of the stack (with 15 NL/min of H2O), with low fuel utilization. These results suggest that the operation at rated powers of the reversible solid oxide system is reached with the highest flow in both modes. In the analyzed case, 90% of H2O–10% of H2 and 100% H2with a flow of 15 NL/min seem to be the most appropriate flows for the best exploitation of the rSOC in both operation modes. These experiments were carried out at 750◦C. 2.3. Transition Cycles This section analyzes the response times of the transition between the different operating conditions. These experiments consist in reaching the rated power at constant composition and flow in one mode (SOFC or SOEC), and switching from one mode to the other (SOFC to SOEC or SOEC to SOFC). In this last configuration, two scenarios are studied: without changing the gas conditions and adapting the gas conditions to the optimal ones before switching between the two modes. More precisely, the experiments were carried out imposing a maximum injection limited to 40 A/min followed by a series of safety protocols, in order to avoid rapid degradation of the electrolyte causing a decrease in the stack performance. Mainly, two safety protocols were imposed to ensure the safe operation of the system. The first protocol aims to restrict stack temperature variations to a maximum of 30◦C compared to the current value. The second protocol involves limiting the voltage values to 0.6 V per cell in SOFC mode (equivalent to 18 V for the full stack of 30 cells) and to 1.4 V per cell in SOEC mode (equivalent to 42 V for the full stack). Once the safety voltage threshold is reached, the current profile is automatically reset to 0 A, ensuring optimal safety conditions. HDP González et al.: Preprint submitted to Elsevier Page 3 of 10 Transition Cycles Reversible Solid Oxide Cells 0 0.1 0.2 0.3 0.4 0.5 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Figure 2: Effect of the gas flow on the polarization curves and power response in SOFC mode -0.4 -0.3 -0.2 -0.1 0 28 30 32 34 36 38 40 42 44 46 48 -0.4 -0.3 -0.2 -0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 Figure 3: Effect of the gas flow on the polarization curves and power response in SOEC mode Firstly, the transition cycles are analyzed keeping the inlet flows constant on both electrodes. Therefore, to be able to work in SOFC and SOEC mode, the fuel composition is fixed to 50% of H2and 50% of H2O at 750◦C. The experimental results are presented in Figure 4. The transition cycle corresponds to SOFC→SOEC→SOFC. It is possible to observe that the system is able to reach the rated power value only in SOEC mode and close to half the rated value in SOFC. Indeed, this non-symmetric behaviour can partially be explained by the difference of gas diffusion when the atmosphere is richer in H2or in H2O [24]. At high current densities, around 0.3 A/cm2for this stack, concentration over-potential at the fuel electrode becomes dominant. In SOEC mode, the produced H2is added to the initial H2, which is a small molecule in comparison with H2O. Its diffusion through the porosity of the fuel electrode is therefore easier than in the case of SOFC where there is an accumulation of H2O when consuming the H2. Figures 5and 6shows the experimental responses under changes in the power set-points when rSOC remains in one operating mode. Figure 5corresponds to a change in the power set-point from 0kW to 1kW and back to 0kW with the rSOC operating in SOEC mode. Figure 6presents the 𝑡1𝑡2𝑡3𝑡4𝑡5 Time [s] 28.0 53.6 113.4 173.2 199.0 Power [kW] 0.00 0.379 -1.00 0.38 0.00 Figure 4: Experimental power results corresponding to SOFCSOEC-SOFC direct transitions at 750◦C with 50%H2and 50%H2O (10,4 NL/min) and 26 NL/min of air. results corresponding to a similar scenario but when the rSOC remains in SOFC mode and the maximum power setpoint is 0.3kW. It is possible to observe that the duration of transitions are lower than a minute in each mode of operation. The final test analyzes a transition cycle from SOEC to SOFC with a change in fuel composition. The most HDP González et al.: Preprint submitted to Elsevier Page 4 of 10 Transition Cycles Reversible Solid Oxide Cells 𝑡1𝑡2𝑡3 Time [s] 32.4 68.8 105.2 Power [kW] 0.00 1.02 0.00 Figure 5: Experimental response corresponding to a change in the power set-point from 0kW to 1kW and back to 0kW in SOEC mode, with 10 NL/min of H2O, 1.1 NL/min of H2and 26 NL/min of air 𝑡1𝑡2𝑡3 Time [s] 31.4 53.8 76.6 Power [kW] 0.00 0.304 0.00 Figure 6: Experimental response corresponding to a change in the power set-point from 0kW to 0.3kW and back to 0kW in SOFC mode, with 10 NL/min of H2and 26 NL/min of air. demanding case consists in a transition from a rich H2O concentration (i.e. 90% H2O and 10% H2O) in SOEC mode to a rich hydrogen concentration (100% H2) in SOFC mode. The result of this test is presented in Figure 7. Initially, the cell operates in SOEC mode with a concentration of 90% H2O 10% H2. At 𝑡1= 119.5minutes, the power becomes zero (zero current) and the concentration changes until reaching 100% H2. In Figure 7, the change in open circuit voltage or Nernst potential until the partial pressure of H2and H2O are being stables can be appreciated, specifically between the instants 𝑡1and 𝑡2, a period of about 8minutes. As the voltage must remain constants for a suitable stack performance, this indicates that it is necessary to wait approximately 8 minutes to switch from one mode to the other. This transition time is important when the rSOC operates within a microgrid since this imposes a time interval in which the stack cannot supply power and must be compensated by other generators. 3. Transition Impacts on Microgrid Operation In this section, the impact of the response times of the rSOC on a microgrid is analyzed by simulations. For this purpose, the rSOC is integrated into a microgrid including other renewable energy sources under different operating scenarios. 𝑡1𝑡2 Time [min] 119.5 127.7 Stack Voltage [V] 26.94 35.10 Figure 7: Experimental results corresponding to a transition cycle from SOEC to SOFC with concentration change from 90%H2O-10%H2(SOEC) to 100% H2(SOFC) 3.1. Model for Microgrid Analysis In order to include the experimental dynamics shown in the previous section in a desired microgrid, the dynamic model developed in our previous work [21] is used. The basis of dynamic model relies on electrochemistry and thermodynamics principles, which able us to obtain the voltage and power values of the rSOC each time instant, being the commands entering to the microgrid. The electrochemical behavior determine the operating voltage of the cell (𝑉𝑐) in each mode. In SOFC mode, 𝑉𝑐is given by: 𝑉𝑆𝑂𝐹 𝐶 =𝐸𝑁−𝜂𝑜ℎ𝑚 −𝜂𝑎𝑐𝑡 −𝜂𝑐𝑜𝑛,(1) and in SOEC mode, as the injected current is negative, by: 𝑉𝑆𝑂𝐸𝐶 =𝐸𝑁+𝜂𝑜ℎ𝑚 +𝜂𝑎𝑐𝑡 +𝜂𝑐𝑜𝑛,(2) being 𝐸𝑁the Nernst voltage, 𝜂𝑜ℎ𝑚 ohmic losses, 𝜂𝑎𝑐𝑡 the activation losses and 𝜂𝑐𝑜𝑛 the concentration losses. The ohmic losses are dominated by the current density (in A∕cm2) and the specific area resistance (ASR) per cm2as 𝜂𝑜ℎ𝑚 =⋅𝐴𝑆𝑅. (3) Activation losses are related to the kinetics of the chemical reactions that take part in the process, and are defined by: 𝜂𝑎𝑐𝑡 =𝑅𝑇 4𝛼𝑎𝐹sinh−1 (𝑖 2𝑖𝑜,𝑎 )+𝑅𝑇 4𝛼𝑐𝐹sinh−1 (𝑖 2𝑖𝑜,𝑐 ).(4) Finally, concentration losses are dominated by changes in the concentration of the reactants at the Triple-Phase Boundary (TPB), as: 𝜂𝑐𝑜𝑛 =𝑅𝑇 2𝐹ln (𝑝𝑇 𝑃 𝐵 𝐻2𝑂𝑝𝐻2 𝑝𝐻2𝑂𝑝𝑇 𝑃 𝐵 𝐻2) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ Anode +𝑅𝑇 4𝐹ln (𝑝𝑂2 𝑝𝑇 𝑃 𝐵 𝑂2) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟ Cathode .(5) Finally, to ensure a safe thermodynamic behavior of the system, the thermal balance of the rSOC system is defined by: Δ 𝑄= 𝑄𝑠𝑡𝑎𝑐𝑘 + 𝑄𝑜𝑣 − 𝑄𝑐𝑜𝑛 − 𝑄𝑒𝑛𝑣,(6) HDP González et al.: Preprint submitted to Elsevier Page 5 of 10 Transition Cycles Reversible Solid Oxide Cells 0 50 100 -1 -0.5 0 0 20 40 60 80 -0.1 0 0.1 0.2 0.3 0.4 0 50 100 150 200 -1 -0.5 0 0.5 110 120 130 140 150 15 20 25 30 35 40 Figure 8: Comparison between experimental transitions (Figures 4to 7) and model response: a) SOEC Mode, b) SOFC Mode, c) SOFC-SOEC-SOFC 50%-50% and d) Transition with change of composition where  𝑄𝑠𝑡𝑎𝑐𝑘 is the stack heat,  𝑄𝑜𝑣 the oven heat losses,  𝑄𝑐𝑜𝑛 the convection losses and  𝑄𝑒𝑛𝑣 the environmental losses. Once the voltage is obtained, the power of the cells can be calculated according to the ohms law as: 𝑃=𝑛𝑐𝑉𝑐.(7) The description of the mentioned variables and their values can be found in Table 2. Figure 8presents a comparison of responses in relation to the experiments presented in Figures 4to 7. The model dynamics are similar to the experimental response of the system, as presented in the previous validation of the model [21] and respect the transition times of the experiments, which is important for a reliable integration in the microgrid. A thorough validation and more details of the rSOC operation can be found in our previous work [21]. 3.2. Microgrid Analysis: An Islanded Approach In order to evaluate the rSOC capabilities within a electrical network, the microgrid illustrated in Figure 9is used. This microgrid consists of three inverters: two interfacing generators and another connecting the rSOC. The generators in Figure 9correspond to renewable power sources (wind, solar, etc.) and also to energy storage devices (BESS, compressed air storage, etc.), being able to replicate for example house-level applications (e.g. PV+Storage), higher power applications (e.g. Wind+Storage) or industrial grids (e.g. Diesel or Gas Generators). The rSOC dynamics are introduced as modeled in Section 3.1. The green areas indicate the units of the microgrid delivering power whereas the red ones denote the units absorbing power. The components of the microgrid have been sized according to the reversible solid oxide prototype characteristics. The grid-forming operation of the microgrid is controlled through the droop control, a strategy widely known in the literature [25]. The Table 2 Reversible Solid Oxide Stack Parameters [21] 𝐒𝐭𝐚𝐜𝐤 𝐏𝐚𝐫𝐚𝐦𝐞𝐭𝐞𝐫 𝐒𝐲𝐦𝐛𝐨𝐥 𝐕𝐚𝐥𝐮𝐞 𝐔𝐧𝐢𝐭𝐬 Stack Area 𝐴𝑠63 cm2 Stack Mass 𝑀𝑠5.5 kg Faraday Constant 𝐹96485 C/mol Number of Cells 𝑛𝑐30 - Oven Power 𝑃𝑜𝑣 2.75 kW Oven Losses Constant 𝑘𝑙,𝑜𝑣 0.7 W∕(m2⋅K) Universal Gas Constant 𝑅8.314472 J∕(mol ⋅K) Air Gas Constant 𝑅𝑎𝑖𝑟 286.9 J∕(kg ⋅K) Inlet Manifold Valve Constant 𝑖𝑚 5⋅10−8 kg∕(Pa ⋅s) Outlet Manifold Valve Constant 𝑜𝑚 3.3⋅10−8 kg∕(Pa ⋅s) Anode Valve Constant 𝑎𝑛 1.5⋅10−8 kg∕(Pa ⋅s) Cathode Valve Constant 𝑐𝑎 0.94 ⋅10−8 kg∕(Pa ⋅s) Electrolyte Thickness (8YSZ) 𝐿𝑒10 𝜇m O2Effective Diffusion Coefficient 𝐷𝑂20.0228 cm2∕s H2O Effective Diffusion Coefficient 𝐷𝐻2𝑂0.0436 cm2∕s H2Effective Diffusion Coefficient 𝐷𝐻20.0927 cm2∕s Hydrogen Lowest Heating Value 𝐻𝐿𝐻𝑉 2241.8 kJ∕mol Ionic Conductivity Pre-exponential Factor 𝜎0,𝑒𝑙 466 𝑠−1 Electrolyte Activation Energy 𝐸𝑒𝑙 8.26 ⋅104J/mol Cathode Phenomenological Coefficient 𝛾𝑐𝑎 5.23 ⋅106A∕cm2 Anode Phenomenological Coefficient 𝛾𝑎𝑛 6.64 ⋅106A∕cm2 Cathode Activation Energy 𝐸𝑎𝑐𝑡,𝑐𝑎 105J/mol Anode Activation Energy 𝐸𝑎𝑐𝑡,𝑎𝑛 7.96 ⋅104J/mol Contact Resistance 𝑅𝑐𝑡 0.3 Ω Degradation Rate [7]𝜅1.2 𝑚Ω𝑐𝑚2∕𝑘ℎ Figure 9: Islanded microgrid with two generators, a rSOC and a load. Green areas denote the units delivering power whereas the red ones denote the units absorbing power. fundamental aspects of this type of control are introduced next. The primary control is implemented with a droop scheme that adjusts the power supplied by each converter by regulating the frequency and voltage amplitude. The droop control HDP González et al.: Preprint submitted to Elsevier Page 6 of 10 Transition Cycles Reversible Solid Oxide Cells allows the system inverters to work in parallel sharing the network load by changing the angular frequency 𝜔𝑘of the inverter according to: 𝜔𝑘=𝜔−𝑚𝑘𝑃𝑘,(8) where 𝜔𝑛is the nominal grid frequency and 𝑚𝑘the droop coefficient with respect to the active power 𝑃𝑘. On the other hand, the voltage control law is as follows: 𝑉𝑘=𝑉−𝑛𝑘𝑄𝑘,(9) where 𝑉𝑘is the output voltage of the inverter, 𝑉is the nominal voltage of the network and 𝑛𝑘is the droop coefficient with respect to the reactive power 𝑄𝑘. Finally, the secondary control adds two terms to the droop expressions (8) and (9) resulting: 𝜔𝑘=𝜔−𝑚𝑘𝑃𝑘+𝛿𝜔 𝑘(10) 𝑉𝑘=𝑉−𝑛𝑘𝑄𝑘+𝛿𝑉 𝑘,(11) where 𝛿𝜔 𝑘and 𝛿𝑉 𝑘are the frequency and voltage corrections computed according to the averaging technique as: 𝛿𝜔 𝑘=𝑘𝜔 𝑝(𝜔∗−𝜔)+𝑘𝜔 𝑖∫(𝜔∗−𝜔)𝑑𝑡 (12) and 𝛿𝑉 𝑘=𝑘𝜔 𝑝(𝑉∗−𝑉)+𝑘𝑉 𝑖∫(𝑉∗−𝑉)𝑑𝑡 𝛿𝑄 𝑖=𝑘𝑄 𝑝(𝑄−𝑄𝑘)+𝑘𝑄 𝑖∫(𝑄−𝑄𝑘)𝑑𝑡 (13) where 𝛿𝑉 𝑖=𝛿𝑉 𝑖+𝛿𝑄 𝑖,𝑉and 𝑄denotes the average voltage amplitude and reactive power, respectively, and 𝑘𝜔 𝑝,𝑘𝜔 𝑖, 𝑘𝑉 𝑝,𝑘𝑉 𝑖,𝑘𝑄 𝑝and 𝑘𝑄 𝑖are proportional and integral control parameters. More details about the design of this microgrid control scheme can be find in e.g. [1,2,25] 3.3. Modes of Operation The capability of rSOC to operate in islanded microgrid is analyzed here with two scenarios, which include the operation of the rSOC inverter in grid-following and grid-forming. The results indicate that the grid-following operation seems to be the most suitable scheme for the rSOC. 3.3.1. Grid-following Mode In the grid-following operation, the rSOC absorbs and supplies power to the microgrid. Due to grid-following is the most probable mode of operation, the response of the microgrid considering direct mode change, with a 50%-50% composition (H2-H2O), and considering the transition cycle, will be analyzed. •Transition cycle with a 50%H2-50%H2O composition: The results of a direct change mode are presented in Figure 10. It can be seen that the increase in the Figure 10: Active power and frequency responses of the microgrid with the rSOC acting in grid-following mode and with a direct-mode change with 50%-50% H2-H2O at 750◦C. power of generator 1 to satisfy the load and the energy necessary to carry out the electrolysis at t1= 5 s. At t2= 19.5s, when the generator 1 reaches its power limits (3 kW), the generator 2 must be activated in order to supply the additional power demanded by the load and the rSOC. It can be observed the proper operation of the power sharing algorithm and the secondary control as they are able to balance the power and restore the frequency to their nominal values. At t3= 41.4s the SOEC mode reach 1 kW, and performs the electrolysis up to t4= 55s, when the direct transition of SOEC mode to SOFC mode starts. When this direct transition from electrolyzer mode to fuel cell mode occurs, it can be seen how the power of generators 1 and 2 is reduced, according to the amount of power injected by the rSOC. At t5= 114.6s, the power delivered by the rSOC reaches a value around 0.4kW in SOFC mode. Notice that during the entire transition cycle, the secondary control maintains the frequency close to 50 Hz with the contributions of generators 1 and 2, demonstrating its robustness under power changes. As expected, the slow dynamics of the rSOC governs the entire system response. •Transition cycle with change of composition: Figure 11 shows the active powers of rSOC and the generators and the frequencies of inverters 1 and 2 during a transition cycle from 90% H2O and 10% H2in SOEC HDP González et al.: Preprint submitted to Elsevier Page 7 of 10 Transition Cycles Reversible Solid Oxide Cells Figure 11: Active power and frequency responses of the microgrid with the rSOC acting in grid-following mode and with a transition cycle from 90%-10% H2-H2O to 100% H2at 750◦C. mode to 100% H2in SOFC mode. As shown in Figure 7, the transition cycle increases the operation times since the rSOC needs at least 8minutes to completely change the operating mode. Nevertheless, it can be seen that the power and frequency responses are similar to the previous case. The droop and secondary controls are able to maintain the frequency close to the nominal value by properly commanding the two generators to compensate the power supplied or absorbed by the rSOC. Therefore, in terms of dynamic performance, the transition cycle does not alter the microgrid behavior, increases the rSOC performance compared to the direct mode change due to higher power in each mode when higher fuel concentration is achieved and thus improves the efficiency of the overall system. 3.3.2. Grid-Forming mode: What is needed? The second scenario presents the behavior of the system with the rSOC inverter working in grid-forming. This mode of operation can only be carried out in SOFC mode. This operating mode can be useful in case the other generators are not able to provide their maximum power and the levels of H2stored are high. In this way, the rSOC inverter is able to contribute in the power sharing algorithm. However, this need the help of a fast-response energy storage system, as Figure 12: Active power and frequency responses of the system in grid-forming operation. In grey, the necessary power from a battery for operating in grid-forming. for example, lithium batteries, due to the response times of the rSOC technology. Also, note that for operating in the power sharing algorithm, rSOCs must maintain certain thermal effects to ensure a safe constant power delivery. Figure 12 compares the behavior of the microgrid operating in grid-forming mode with and without a battery energy storage to provide the necessary fast power compensation. The purple line corresponds to the power delivered by the rSOC working alone and the yellow line to the power contributed when the rSOC operates along with a battery. Clearly, it can be seen that in the first case the power sharing algorithm is not able to ensure the necessary fast response contrary to the second case. The grey area indicates the total amount of power that must be supplied by the battery for the correct operation of the islanded microgrid, in which the dynamics is not directly dominated by the hydrogen power response. Without this amount of power the microgrid operation will become unstable. Therefore, only a proper operation could be achieved with the use of a battery and a rSOC, as shown in the frequency response plot. 4. Conclusions Reversible solid oxide cells have the potential for being a key technology in the transition to hydrogen-based societies, thanks to the higher efficiency and fuel flexibility. This work HDP González et al.: Preprint submitted to Elsevier Page 8 of 10