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Multi-phase management is crucial for performance and durability of electrochemical cells such as batteries and fuel cells. In this paper we present a generic framework for describing the two-dimensional spatiotemporal evolution of gaseous, liquid and solid phases, as well as their interdependence with interfacial (electro-)chemistry and microstructure in a continuum description. The modeling domain consists of up to seven layers (current collectors, channels, electrodes, separator/membrane), each of which can consist of an arbitrary number of bulk phases (gas, liquid, solid) and connecting interfaces (two-phase or multi-phase boundaries). Bulk and interfacial chemistry is described using global or elementary kinetic reactions. Multi-phase management is coupled to chemistry and to mass and charge transport within bulk phases. The functionality and flexibility of this framework is demonstrated using four application areas in the context of post-lithium-ion batteries and fuel cells, that is, lithium-sulfur (Li-S) cells, lithium-oxygen (Li-O) cells, solid oxide fuel cells (SOFC) and polymer electrolyte membrane fuel cells (PEFC). The results are compared to models available in literature and properties of the generic framework are discussed.
Cell lifetime diagnostics and system be-havior of stationary LFP/graphite lithium-ion batteries
(2018)
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products (e.g., fuel cells, metal/air cells, electrolyzers) offer an additional observable, that is, the gas pressure. The dynamic coupling of current and/or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have introduced the term electrochemical pressure impedance spectroscopy (EPIS) [1,2]. EPIS shows a particular sensitivity towards transport processes of gas-phase or dissolved species, in particular, diffusion coefficients and transport pathway lengths. It is as such complementary to standard EIS, which is mainly sensitive towards electrochemical processes. This sensitivity can be exploited for model parameterization and validation. A general analysis of EPIS is presented, which shows the necessity of model-based interpretation of the complex EPIS shapes in the Nyquist plot (cf. Figure). We then present EPIS simulations for two different electrochemical cells: (1) a sodium/oxygen battery cell and (2) a hydrogen/air fuel cell. We use 1D or 2D electrochemical and transport models to simulate current excitation/pressure detection or pressure excitation/voltage detection. The results are compared to first EPIS experimental data available in literature [2,3].
Grey-box modelling combines physical and data-driven models to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling, as differential equations given by physical laws and neural networks can be combined in a single modelling framework. This simplifies the simulation and optimization and allows to consider irregularly-sampled data during training and evaluation of the model. We demonstrate this approach using two levels of model complexity; first, a simple parallel resistor-capacitor circuit; and second, an equivalent circuit model of a lithium-ion battery cell, where the change of the voltage drop over the resistor-capacitor circuit including its dependence on current and State-of-Charge is implemented as NODE. After training, both models show good agreement with analytical solutions respectively with experimental data.
Model-based analysis of Electrochemical Pressure Impedance Spectroscopy (EPIS) for PEM Fuel Cells
(2019)
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products, in particular fuel cells, offer an additional observable, that is, the gas pressure. The dynamic coupling of current or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have previously introduced the term electrochemical pressure impedance spectroscopy (EPIS) [1,2]. EPIS shows a particular sensitivity towards transport processes of gas-phase or dissolved species, in particular, diffusion coefficients and transport pathway lengths. It is as such complementary to standard EIS, which is mainly sensitive towards electrochemical processes. First EPIS experiments on PEM fuel cells have recently been shown [3].
We present a detailed modeling and simulation analysis of EPIS of a PEM fuel cell. We use a 1D+1D continuum model of a fuel/air channel pair with GDL and MEA. Backpressure is dynamically varied, and the resulting simulated oscillation in cell voltage is evaluated to yield the ▁Z_( V⁄p_ca ) EPIS signal. Results are obtained for different transport situations of the fuel cell, giving rise to very complex EPIS shapes in the Nyquist plot. This complexity shows the necessity of model-based interpretation of the complex EPIS shapes. Based on the simulation results, specific features in the EPIS spectra can be assigned to different transport domains (gas channel, GDL, membrane water transport).
Battery degradation is a complex physicochemical process that strongly depends on operating conditions and environment. We present a model-based analysis of lithium-ion battery degradation in smart microgrids, in particular, a single-family house and an office tract with photovoltaics generator. We use a multi-scale multi-physics model of a graphite/lithium iron phosphate (LiFePO4, LFP) cell including SEI formation as ageing mechanism. The cell-level model is dynamically coupled to a system-level model consisting of photovoltaics, inverter, power consumption profiles, grid interaction, and energy management system, fed with historic weather data. The behavior of the cell in terms of degradation propensity, performance, state of charge and other internal states is predicted over an annual operation cycle. As result, we have identified a peak in degradation rate during the battery charging process, caused by charging overpotentials. Ageing strongly depends on the load situation, where the predicted annual capacity fade is 1.9 % for the single-family house and only 1.3 % for the office tract.
Combined heat and power production (CHP) based on solid oxide fuel cells (SOFC) is a very promising technology to achieve high electrical efficiency to cover power demand by decentralized production. This paper presents a dynamic quasi 2D model of an SOFC system which consists of stack and balance of plant and includes thermal coupling between the single components. The model is implemented in Modelica® and validated with experimental data for the stack UI-characteristic and the thermal behavior. The good agreement between experimental and simulation results demonstrates the validity of the model. Different operating conditions and system configurations are tested, increasing the net electrical efficiency to 57% by implementing an anode offgas recycle rate of 65%. A sensitivity analysis of characteristic values of the system like fuel utilization, oxygen-to-carbon ratio and electrical efficiency for different natural gas compositions is carried out. The result shows that a control strategy adapted to variable natural gas composition and its energy content should be developed in order to optimize the operation of the system.
Modelling detailed chemistry in lithium-ion batteries: Insight into performance, ageing and safety
(2018)
Lithium-ion batteries show strongly nonlinear behaviour regarding the battery current and state of charge. Therefore, the modelling of lithium-ion batteries is complex. Combining physical and data-driven models in a grey-box model can simplify the modelling. Our focus is on using neural networks, especially neural ordinary differential equations, for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis for the grey-box model. Unknown parameters and dependencies are then replaced by learnable parameters and neural networks. We use experimental full-cycle data and data from pulse tests of a lithium iron phosphate cell to train the model. Finally, we test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.